diff --git a/.github/workflows/test.yml b/.github/workflows/test.yml index e49e955..2689e3e 100644 --- a/.github/workflows/test.yml +++ b/.github/workflows/test.yml @@ -4,23 +4,28 @@ on: [push, pull_request, workflow_dispatch] jobs: test: - runs-on: ${{ matrix.os }} - strategy: - matrix: - os: [windows-latest, macOS-13, ubuntu-latest] - python-version: ['3.8', '3.9', '3.10'] - fail-fast: false + runs-on: ubuntu-latest + defaults: + run: + shell: bash -el {0} + steps: - - uses: actions/checkout@v2 - - name: Set up Python ${{ matrix.python-version }} - uses: actions/setup-python@v4 - with: - python-version: ${{ matrix.python-version }} - - name: Install pynumad - run: | - python -m pip install --upgrade pip - pip install -e . - - name: Test with pytest - run: | - pip install --upgrade pytest coverage - coverage run --source=pynumad --omit="*/tests/*" -m pytest + # Step 1: Checkout your code + - name: Checkout Code + uses: actions/checkout@v3 + + - name: Set up environment + uses: conda-incubator/setup-miniconda@v3 + with: + environment-file: environment.yml + # python-version: "3.9" # setup-miniconda seems to ignore this setting. + auto-activate-base: false + - name: Check environmnet + run: | + conda info + conda list + - name: Run tests + run: | + python -c "import opensg" + pip install pytest + pytest opensg/tests/ diff --git a/environment.yml b/environment.yml index 1aab482..2daffd0 100644 --- a/environment.yml +++ b/environment.yml @@ -2,20 +2,24 @@ name: opensg_env channels: - conda-forge dependencies: - - python=3.10 + - python=3.12 - numpy - scipy - mpi4py - meshio - - petsc4py + - petsc4py=3.21.5 - yaml - contextlib2 # For compatibility - pathlib - typing-extensions - - fenics-dolfinx - - fenics-basix - - fenics-ufl + - fenics-dolfinx=0.8.0 + - fenics-basix=0.8.0 + - fenics-ufl=2024.1.0 + - fenics-ffcx=0.8.0 - mpich - pyvista - pyyaml - # - gmsh # I have to install this through pip for it to work. + - pip + - pip: + - -e . + - gmsh diff --git a/examples/compute_eb_blade.py b/examples/compute_eb_blade.py index a43b6b8..77236b3 100644 --- a/examples/compute_eb_blade.py +++ b/examples/compute_eb_blade.py @@ -3,6 +3,7 @@ # import pynumad import opensg import numpy as np +import time # load blade.yml into pynumad # blade_path = join("data", "blade.yaml") @@ -24,53 +25,68 @@ mesh_data = opensg.load_yaml(mesh_yaml) blade_mesh = opensg.BladeMesh(mesh_data) -section_mesh = blade_mesh.generate_segment_mesh(segment_index=1, filename="section.msh") - -section_layups = section_mesh._generate_layup_data() - -frame = section_mesh.generate_local_orientations() - -section_mesh.extract_boundaries() - -section_mesh.generate_boundary_ABD() - - - -pause - - -## Extract the mesh for the section -nodes = mesh_data['nodes'] -numNds = len(nodes) -elements = mesh_data['elements'] -numEls = len(elements) - -ndNewLabs = -1*np.ones(numNds,dtype=int) -elNewLabs = -1*np.ones(numEls,dtype=int) -elLayID = -1*np.ones(numEls,dtype=int) - -# iterate through blade - -segment_matrices = [] - -for i in range(len(blade.ispan)): - # select ith blade segment - blade_segment_mesh = opensg.blade.select_segment(blade_mesh_info) - # analysis options - # solid vs shell - # whole segment vs boundary - # analyses: - # stresses/stiffness/buckling - # stresses after beamdyn - data = opensg.compute_eb_segment(blade_segment_mesh) - # data = opensg.compute_eb_boundaries(blade_segment_mesh) - # data = opensg.compute_timo_segment(blade_segment_mesh) # ***** high priority - # data = opensg.compute_eb_buckling(blade_segment_mesh) - # data = opensg.compute_timo_buckling(blade_segment_mesh) # **** top priority - # data = opensg.compute_timo_boundaries(blade_segment_mesh) +stiffness_matrices = [] +compute_times = [] +for i in range(1, 2): + start_time = time.time() + print(time.time()-start_time) + + segment_mesh = blade_mesh.generate_segment_mesh(segment_index=i, filename="section.msh") + print(time.time()-start_time) + + ABD = segment_mesh.compute_ABD() + print(time.time()-start_time) + + stiffness_matrix = segment_mesh.compute_stiffness_EB(ABD) + print(time.time()-start_time) + + stiffness_matrices.append(stiffness_matrix) + end_time = time.time() + compute_times.append(end_time - start_time) + +print("Average compute time for a single segment: ", sum(compute_times)/len(compute_times)) +print("Maximum compute time for a single segment: ", max(compute_times)) + +# combine matrices into a global +combined_stiffness_matrices = np.concat(stiffness_matrices) + +np.savetxt('stiffness_m.txt', combined_stiffness_matrices, fmt='%d') + +# pause + + +# ## Extract the mesh for the section +# nodes = mesh_data['nodes'] +# numNds = len(nodes) +# elements = mesh_data['elements'] +# numEls = len(elements) + +# ndNewLabs = -1*np.ones(numNds,dtype=int) +# elNewLabs = -1*np.ones(numEls,dtype=int) +# elLayID = -1*np.ones(numEls,dtype=int) + +# # iterate through blade + +# segment_matrices = [] + +# for i in range(len(blade.ispan)): +# # select ith blade segment +# blade_segment_mesh = opensg.blade.select_segment(blade_mesh_info) +# # analysis options +# # solid vs shell +# # whole segment vs boundary +# # analyses: +# # stresses/stiffness/buckling +# # stresses after beamdyn +# data = opensg.compute_eb_segment(blade_segment_mesh) +# # data = opensg.compute_eb_boundaries(blade_segment_mesh) +# # data = opensg.compute_timo_segment(blade_segment_mesh) # ***** high priority +# # data = opensg.compute_eb_buckling(blade_segment_mesh) +# # data = opensg.compute_timo_buckling(blade_segment_mesh) # **** top priority +# # data = opensg.compute_timo_boundaries(blade_segment_mesh) - segment_matrices.append(data) +# segment_matrices.append(data) -# ideally, we could also have a step to run beamdyn -opensg.beamdyn.run_analysis(blade_mesh_info, segment_matrices) \ No newline at end of file +# # ideally, we could also have a step to run beamdyn +# opensg.beamdyn.run_analysis(blade_mesh_info, segment_matrices) \ No newline at end of file diff --git a/opensg/__init__.py b/opensg/__init__.py index 59bef2d..2f61d90 100644 --- a/opensg/__init__.py +++ b/opensg/__init__.py @@ -1,7 +1,10 @@ -from opensg.solve import ksp_solve, ABD_mat, nullspace -from opensg.timo import local_frame_1D, directional_derivative, local_grad, ddot +from opensg.solve import compute_ABD_matrix, compute_timo_boun, compute_stiffness_EB_blade_segment +# from kirklocal.timo import local_frame_1D, directional_derivative, local_grad, ddot from opensg.io import load_yaml, write_yaml from opensg.mesh import BladeMesh -from opensg import util +from opensg.compute_utils import solve_ksp, solve_boun, compute_nullspace, \ + create_gamma_e, R_sig, Dee, sigma, eps, local_boun, local_frame_1D, \ + local_frame, local_frame_1D_manual, local_grad, deri, ddot, gamma_d, \ + construct_gamma_e, gamma_h, gamma_l, A_mat, initialize_array, dof_mapping_quad, generate_boundary_markers __version__ = "0.0.1" \ No newline at end of file diff --git a/opensg/blade_utils.py b/opensg/blade_utils.py deleted file mode 100644 index e69de29..0000000 diff --git a/opensg/compute_utils.py b/opensg/compute_utils.py new file mode 100644 index 0000000..19bc54d --- /dev/null +++ b/opensg/compute_utils.py @@ -0,0 +1,478 @@ +from mpi4py import MPI +import numpy as np +import dolfinx +import basix +from dolfinx.fem import form, petsc, Function, locate_dofs_topological +from ufl import TrialFunction, TestFunction, rhs, as_tensor, dot, SpatialCoordinate, Measure +import petsc4py.PETSc +from dolfinx.fem.petsc import assemble_matrix + +from mpi4py import MPI +import ufl +from contextlib import ExitStack + + +def generate_boundary_markers(xmin, xmax): + def is_left_boundary(x): + return np.isclose(x[0], xmin) + def is_right_boundary(x): + return np.isclose(x[0], xmax) + return is_left_boundary, is_right_boundary + + +def solve_ksp(A, F, V): + """Krylov Subspace Solver for Aw = F + + Parameters + ---------- + A : array + stiffness matrix + F : array + Load or force vector + V : function space + _description_ + + Returns + ------- + array + solution vector (displacement field) + """ + w = Function(V) + ksp = petsc4py.PETSc.KSP() + ksp.create(comm = MPI.COMM_WORLD) + ksp.setOperators(A) + ksp.setType("preonly") + ksp.getPC().setType("lu") + ksp.getPC().setFactorSolverType("mumps") + ksp.getPC().setFactorSetUpSolverType() + ksp.getPC().getFactorMatrix().setMumpsIcntl(icntl = 24, ival = 1) # detect null pivots + ksp.getPC().getFactorMatrix().setMumpsIcntl(icntl = 25, ival = 0) # do not compute null space again + ksp.setFromOptions() + ksp.solve(F, w.vector) + w.vector.ghostUpdate( + addv = petsc4py.PETSc.InsertMode.INSERT, mode = petsc4py.PETSc.ScatterMode.FORWARD + ) + ksp.destroy() + return w + +def compute_nullspace(V): + """Compute nullspace to restrict Rigid body motions + + Constructs a translational null space for the vector-valued function space V + and ensures that it is properly orthonormalized. + + Parameters + ---------- + V : functionspace + _description_ + + Returns + ------- + NullSpace + Nullspace of V + """ + # extract the Index Map from the Function Space + index_map = V.dofmap.index_map + + # initialize nullspace basis with petsc vectors + nullspace_basis = [ + dolfinx.la.create_petsc_vector(index_map, V.dofmap.index_map_bs) + for _ in range(4) + ] + + with ExitStack() as stack: + vec_local = [stack.enter_context(xx.localForm()) for xx in nullspace_basis] + basis = [np.asarray(xx) for xx in vec_local] + + # identify the degrees of freedom indices for each subspace (x, y, z) + dofs = [V.sub(i).dofmap.list for i in range(3)] + + # Build translational null space basis + for i in range(3): + basis[i][dofs[i]] = 1.0 + + # Create vector space basis and orthogonalize + dolfinx.la.orthonormalize(nullspace_basis) + + ret_val = petsc4py.PETSc.NullSpace().create(nullspace_basis, comm = MPI.COMM_WORLD) + + return ret_val + +def create_gamma_e(x): + """_summary_ + + Parameters + ---------- + x : _type_ + _description_ + + Returns + ------- + _type_ + _description_ + """ + gamma_e = as_tensor([ + (1, 0, 0, x[0], 0, 0), + (0, 1, 0, 0, x[0], 0), + (0, 0, 0, 0, 0, 0), + (0, 0, 0, 0, 0, 0), + (0, 0, 0, 0, 0, 0), + (0, 0, 1, 0, 0, x[0]), + ]) + + return gamma_e + +def R_sig(C, t): + """Compute rotation matrix + + Parameters + ---------- + C : _type_ + _description_ + t : _type_ + _description_ + + Returns + ------- + _type_ + _description_ + """ + th = np.deg2rad(t) + c, s, cs = np.cos(th), np.sin(th), np.cos(th) * np.sin(th) + R_Sig = np.array([ + (c**2, s**2, 0, 0, 0, -2 * cs), + (s**2, c**2, 0, 0, 0, 2 * cs), + (0, 0, 1, 0, 0, 0), + (0, 0, 0, c, s, 0), + (0, 0, 0, -s, c, 0), + (cs, -cs, 0, 0, 0, c**2 - s**2), + ]) + ret_val = np.matmul(np.matmul(R_Sig, C), R_Sig.transpose()) + return ret_val + +def Dee(x, u, material_props, theta, Eps): + """ Simplifying gamma_e.T*C*gamma_e + + Parameters + ---------- + i : _type_ + _description_ + + Returns + ------- + _type_ + _description_ + """ + C = sigma(u, material_props, theta, Eps)[1] + x0 = x[0] + dee = as_tensor([ + (C[0, 0], C[0, 1], C[0, 5], x0 * C[0, 0], x0 * C[0, 1], x0 * C[0, 5]), + (C[1, 0], C[1, 1], C[1, 5], x0 * C[1, 0], x0 * C[1, 1], x0 * C[1, 5]), + (C[5, 0], C[5, 1], C[5, 5], x0 * C[5, 0], x0 * C[5, 1], x0 * C[5, 5]), + (x0 * C[0, 0], x0 * C[0, 1], x0 * C[0, 5], x0 * x0 * C[0, 0], x0 * x0 * C[0, 1], x0 * x0 * C[0, 5]), + (x0 * C[1, 0], x0 * C[1, 1], x0 * C[1, 5], x0 * x0 * C[1, 0], x0 * x0 * C[1, 1], x0 * x0 * C[1, 5]), + (x0 * C[5, 0], x0 * C[5, 1], x0 * C[5, 5], x0 * x0 * C[5, 0], x0 * x0 * C[5, 1], x0 * x0 * C[5, 5]), + ]) + return dee + +def sigma(vector, material_parameters, theta, Eps): + E1, E2, E3 = material_parameters["E"] + G12, G13, G23 = material_parameters["G"] + v12, v13, v23 = material_parameters["nu"] + S = np.zeros((6, 6)) + S[0, 0], S[1, 1], S[2, 2] = 1 / E1, 1 / E2, 1 / E3 + S[0, 1], S[0, 2] = -v12 / E1, -v13 / E1 + S[1, 0], S[1, 2] = -v12 / E1, -v23 / E2 + S[2, 0], S[2, 1] = -v13 / E1, -v23 / E2 + S[3, 3], S[4, 4], S[5, 5] = 1 / G23, 1 / G13, 1 / G12 + C = np.linalg.inv(S) + C = R_sig(C, theta) + s1 = ufl.dot(as_tensor(C), eps(vector)[1] + Eps) + return as_tensor([(s1[0], s1[5], s1[4]), (s1[5], s1[1], s1[3]), (s1[4], s1[3], s1[2])]), C + +def eps(vector): # (Gamma_h * w) + E1 = ufl.as_vector([0, 0, vector[2].dx(0), (vector[1].dx(0)), (vector[0].dx(0)), 0]) + ans = as_tensor([ + (E1[0], 0.5 * E1[5], 0.5 * E1[4]), + (0.5 * E1[5], E1[1], 0.5 * E1[3]), + (0.5 * E1[4], 0.5 * E1[3], E1[2]), + ]) + return ans, E1 + +####################################Finite Element Implementation ########################################## +# Local Frame for Boundary (should be same as quad mesh local frame) +# Local frame from OpenSG (wind blade quad mesh) + +### local reference frames +def local_frame(mesh): + t = ufl.Jacobian(mesh) + t1 = ufl.as_vector([t[0, 0], t[1, 0], t[2, 0]]) # tangential curvilinear direction -1 + t2 = ufl.as_vector([t[0, 1], t[1, 1], t[2, 1]]) # tangential curvilinear direction -2 + e3 = ufl.cross(t1, t2) # normal direction + e3 /= ufl.sqrt(ufl.dot(e3, e3)) + e1= t2/ ufl.sqrt(ufl.dot(t2, t2)) # 1- direction + e2 = ufl.cross(e3, e1) + e2 /= ufl.sqrt(ufl.dot(e2, e2)) # 2- direction + return e1, e2, e3 + # Note: we don't require local_frame when we are using input orientation stored in EE1, EE2,N. +# On comparison of local_frame(mesh) and given dc matrix (EE1,EE2,N), the difference is former is clockwise about beam axis, while later is ccw about beam axis +# for circumferential tangent direction. local_frame(mesh)-[e1,e2,e3] can be interpolated to DG (deg 0) with shape 3 to compare both data. +# manually generated local frame of 1D curved mesh +def local_frame_1D_manual(mesh_l, num_cells_l): + coord = mesh_l.geometry.x + V_l = dolfinx.fem.functionspace(mesh_l, basix.ufl.element( + "DG", mesh_l.topology.cell_name(), 0, shape = (3, ))) + c_to_v = mesh_l.topology.connectivity(mesh_l.topology.dim, 0) # cell_to_vertex connectivity + E2 = Function(V_l) + for cell in range(num_cells_l): + vertices = c_to_v.links(cell) + dofs = V_l.dofmap.cell_dofs(cell) + n = coord[vertices[1]]-coord[vertices[0]] # [x2-x1,y2-y1,z2-z1] + E2.vector[3*cell:3*cell+3] = n/np.linalg.norm(n) + e1= ufl.as_vector([1,0,0]) # Global x-axis + e3 = ufl.cross(e1,E2) + return e1,E2,e3 + +def local_frame_1D(mesh): + t = ufl.Jacobian(mesh) + t1 = ufl.as_vector([t[0, 0], t[1, 0], t[2, 0]]) # tangent vector of 1D curved mesh + e2 = t1/ ufl.sqrt(ufl.dot(t1, t1)) + e1 = ufl.as_vector([1,0,0]) # Right Lay up + e3 = ufl.cross(e1,e2) + e3 = e3/ ufl.sqrt(ufl.dot(e3, e3)) + return e1, e2, e3 + +# Note grad(e2) will give derivatives of e2 in (x,yz,) global mesh frame. But, to obtain derivatives along local curvoilinear coordinates, +# we use directional derivatives. +def deri(e): + # derivatives of local frame (Refer: Prof: Yu thesis) + #a3,1 + e1,e2,e3 = e[0],e[1],e[2] + a1_1 = ufl.dot(e1,ufl.grad(e1)) + a1_2 = ufl.dot(e2,ufl.grad(e1)) # directional derivative of e2 along e1 direction. + a2_1 = ufl.dot(e1,ufl.grad(e2)) + a2_2 = ufl.dot(e2,ufl.grad(e2)) + a3_1 = ufl.dot(e1,ufl.grad(e3)) + a3_2 = ufl.dot(e2,ufl.grad(e3)) + + # Initial Curvatures (Shell Element) + k11= ufl.dot(a3_1,e1) + k12= ufl.dot(a3_1,e2) + k21= ufl.dot(a3_2,e1) + k22= ufl.dot(a3_2,e2) + k13= ufl.dot(a1_1,e2) + k23= ufl.dot(a1_2,e2) + return k11, k12, k21, k22, k13, k23 + +def local_grad(ee,q): + return ufl.dot(ee, ufl.grad(q)) + +def ddot(w,d1): + return (d1[0] * w[0] + d1[1] * w[1] + d1[2] * w[2]) + +############################################################################ +# We need four matrices for our energy form/weak form +# EB requires only (Gamma_h and Gamma_e) matrix +# Timo needs (Gamma_l and Gamma_d) matrix. Note in paper, Gamma_l mentioend, but that does not contribute to Timoshenko like model. +# For input, local frame (e), spatial coordinate x and dx is required as Gamma_h for left boun/right boun/main qaud mesh would be different. +# Gamma_h*w column matrix +def gamma_h(e,x,w): + k11,k12,k21,k22,k13,k23= deri(e) # extracting initial curvatures + x11,x21,x31= local_grad(e[0],x[0]), local_grad(e[0],x[1]), local_grad(e[0],x[2]) + x12,x22,x32= local_grad(e[1],x[0]), local_grad(e[1],x[1]), local_grad(e[1],x[2]) + y1,y2,y3= local_grad(e[2],x[0]), local_grad(e[2],x[1]), local_grad(e[2],x[2]) + d1 = [x11,x21,x31] + d2 = [x12,x22,x32] + d3 = [y1,y2,y3] + + d11 = ufl.as_vector([-k11*d3[ii]+k13*d2[ii] for ii in range(3)]) + d22 = ufl.as_vector([-k22*d3[ii]-k23*d1[ii] for ii in range(3)]) + d12 = ufl.as_vector([-k21*d3[ii]+k23*d2[ii] for ii in range(3)]) + d21 = ufl.as_vector([-k12*d3[ii]-k13*d1[ii] for ii in range(3)]) + + w_d1 = [local_grad(e[0],w[i]) for i in range(3)] + w_d2 = [local_grad(e[1],w[i]) for i in range(3)] + w_d11 = [local_grad(e[0],w_d1[i]) for i in range(3)] + w_d22 = [local_grad(e[1],w_d2[i]) for i in range(3)] + + w_d12 = [local_grad(e[1],w_d1[ii]) for ii in range(3)] + w_d21 = [local_grad(e[0],w_d2[ii]) for ii in range(3)] + w_11 = [local_grad(d11,w[ii]) for ii in range(3)] + w_22 = [local_grad(d22,w[ii]) for ii in range(3)] + w_12 = [local_grad(d12,w[ii]) for ii in range(3)] + w_21 = [local_grad(d21,w[ii]) for ii in range(3)] + + G1 = ddot(w_d1,d1) + G2 = ddot(w_d2,d2) + G3 = ddot(w_d1,d2)+ddot(w_d2,d1) + G4 = -k11*G1-k12*0.5*G3-ddot(w_d11,d3)+k13*ddot(w_d2,d3)-ddot(w_11,d3) + G5 = -k22*G2-k21*0.5*G3-ddot(w_d22,d3)-k23*ddot(w_d1,d3)-ddot(w_22,d3) + G6 = -(k11+k22)*0.5*G3-k12*G2-k21*G1+k23*ddot(w_d2,d3)-k13*ddot(w_d1,d3) \ + -ddot(w_d12,d3)-ddot(w_d21,d3)-ddot(w_12,d3)-ddot(w_21,d3) + + ret_val = as_tensor([G1,G2,G3,G4,G5,G6]) + return ret_val + +def gamma_l(e,x,w): + # e,x required as element can be of left/right boundary or quad mesh + y1,y2,y3 = x[2],x[0],x[1] # In MSG-Shell formulations, y1 should be the beam axis & (y2,y3) as cross-sectional coordinates) + + # In mesh data, z coordinates are + k11,k12,k21,k22,k13,k23= deri(e) + x11,x21,x31= local_grad(e[0],x[0]), local_grad(e[0],x[1]), local_grad(e[0],x[2]) + x12,x22,x32= local_grad(e[1],x[0]), local_grad(e[1],x[1]), local_grad(e[1],x[2]) + y1,y2,y3= local_grad(e[2],x[0]), local_grad(e[2],x[1]), local_grad(e[2],x[2]) + d1 = [x11,x21,x31] + d2 = [x12,x22,x32] + d3 = [y1,y2,y3] + dd1,dd2,dd3 = ufl.as_vector(d1), ufl.as_vector(d2), ufl.as_vector(d3) + # wd = [w[i].dx(0) for i in range(3)] # dx(0) is for w' + + # Gamma_l*w' column matrix (w' defined by same function space as test/trail function + # are basis functions which are same for both w and w') + w_d1 = ufl.as_vector([local_grad(dd1,w[ii]) for ii in range(3)]) + w_d2= ufl.as_vector([local_grad(dd2,w[ii]) for ii in range(3)]) + + L1,L2 = x11*(ddot(d1,w)),x12*(ddot(d2,w)) + L3 = ddot(x11*dd2+x12*dd1,w) + L4 = -2*x11*ddot(w_d1,d3)+ddot(k11*(y1*dd3-x11*dd1)-0.5*k12*(x12*dd1+x11*dd2),w) + L5 = -2*x12*ddot(w_d2,d3)+ddot(k22*(y1*dd3-x12*dd2)-0.5*k21*(x12*dd1+x11*dd2),w) + L6 = -2*ddot(x11*w_d2+x12*w_d1,d3)+ddot(k12*(y1*dd3-x12*dd2)+k21*(y1*dd3-x11*dd1)-0.5*(k11+k22)*(x12*dd1+x11*dd2),w) + ret_val = as_tensor([L1,L2,L3,L4,L5,L6]) + return ret_val + +# Gamma_e matrix +def construct_gamma_e(e,x): + k11,k12,k21,k22,k13,k23= deri(e) + x11,x21,x31= local_grad(e[0],x[0]), local_grad(e[0],x[1]), local_grad(e[0],x[2]) + x12,x22,x32= local_grad(e[1],x[0]), local_grad(e[1],x[1]), local_grad(e[1],x[2]) + y1,y2,y3= local_grad(e[2],x[0]), local_grad(e[2],x[1]), local_grad(e[2],x[2]) + + d1 = [x11,x21,x31] + d2 = [x12,x22,x32] + d3 = [y1,y2,y3] + Rn = x[1]*(x11*x32+x12*x31)-x[2]*(x11*x22+x12*x21) + + E41 = -k11*(x11**2-y1**2)-k12*x11*x12 + E51 = -k21*x11*x12-k22*(x12**2-y1**2) + E61 = -k11*x11*x12-k12*(x12**2-y1**2)-k22*x11*x12-k21*(x11**2-y1**2) + + E42 = k11*(y1*(x[1]*y3-x[2]*y2)+x11*(x[2]*x21-x[1]*x31))+k12*0.5*(-Rn)+2*x11*(y2*x31-y3*x21) + E52 = k22*(y1*(x[1]*y3-x[2]*y2)+x12*(x[2]*x22-x[1]*x32))+k21*0.5*(-Rn)+2*x12*(y2*x32-y3*x22) + + E62 = (k11+k22)*0.5*(-Rn)+(k12+k21)*(y1*(x[1]*y3-x[2]*y2))+k12*x12*(x[2]*x22-x[1]*x32)\ + +2*(y2*(x12*x31+x11*x32)-y3*(x12*x21+x11*x22))+k21*x11*(x[2]*x21-x[1]*x31) + + E43= k11*x[2]*(y1**2-x11**2)-k12*x11*x12*x[2]+x11*(y3*x11-2*y1*x31) + E53= k22*x[2]*(y1**2-x12**2)-k21*x11*x12*x[2]+x12*(y3*x12-2*y1*x32) + E63= -(k11+k22)*x[2]*x11*x12+x[2]*(k12*(y1**2-x12**2)+k21*(y1**2-x11**2))-2*y1*(x12*x31+x11*x32)+2*y3*x11*x12 + + E44= k11*x[1]*(-y1**2+x11**2)+k12*x11*x12*x[1]+x11*(-y2*x11+2*y1*x21) + E54= k22*x[1]*(-y1**2+x12**2)+k21*x11*x12*x[1]+x12*(-y2*x12+2*y1*x22) + E64= (k11+k22)*x11*x12*x[1]+x[1]*(k12(-y1**2+x12**2)+k21*(-y1**2+x11**2))+2*y1*(x12*x21+x11*x22)-2*y2*x11*x12 + + ret_val = as_tensor([ + (x11**2, x11*(x[1]*x31-x[2]*x21), x[2]*x11**2, -x[1]*x11**2), + (x12**2, x12*(x[1]*x32-x[2]*x22), x[2]*x12**2, -x[1]*x12**2), + (2*x11*x12,Rn, 2*x11*x12*x[2], -2*x11*x12*x[1]), + (E41,E42,E43,E44), + (E51,E52,E53,E54), + (E61,E62,E63,E64)]) + return ret_val + +def gamma_d(e,x): + x11, x21, x31 = local_grad(e[0],x[0]), local_grad(e[0],x[1]), local_grad(e[0],x[2]) + x12, x22, x32 = local_grad(e[1],x[0]), local_grad(e[1],x[1]), local_grad(e[1],x[2]) + y1, y2, y3= local_grad(e[2],x[0]), local_grad(e[2],x[1]), local_grad(e[2],x[2]) + O = ufl.as_vector((0,0,0,0)) + R = ufl.as_vector((-y1,-y3*x[1]+y2*x[2],-x[2]*y1,x[1]*y1)) + ret_val = as_tensor([O,O,O,x11*x11*R,x12*x12*R,2*x11*x12*R]) + return ret_val + + +def local_boun(mesh, frame, subdomains): + # Obtaining preprocessing mesh terms for boundary as well as main wb (quad mesh). + # not to confuse with l here, it applies for right boundary as well by giving appropriate arguments + V = dolfinx.fem.functionspace(mesh, basix.ufl.element( + "S", mesh.topology.cell_name(), 2, shape = (3, ))) + le1, le2, le3 = frame + e1l, e2l, e3l = Function(V), Function(V), Function(V) + + fexpr1 = dolfinx.fem.Expression(le1,V.element.interpolation_points(), comm = MPI.COMM_WORLD) + e1l.interpolate(fexpr1) + + fexpr2 = dolfinx.fem.Expression(le2,V.element.interpolation_points(), comm = MPI.COMM_WORLD) + e2l.interpolate(fexpr2) + + fexpr3 = dolfinx.fem.Expression(le3,V.element.interpolation_points(), comm = MPI.COMM_WORLD) + e3l.interpolate(fexpr3) + + frame = [e1l,e2l,e3l] + dv = TrialFunction(V) + v = TestFunction(V) + x = SpatialCoordinate(mesh) + dx = Measure('dx')(domain=mesh, subdomain_data=subdomains) + + return frame, V, dv, v, x, dx + + + +def A_mat(ABD, e_l, x_l, dx_l, nullspace_l, v_l, dvl, nphases): + F2 = sum([dot(dot(as_tensor(ABD[i]),gamma_h(e_l,x_l,dvl)), gamma_h(e_l,x_l,v_l))*dx_l(i) for i in range(nphases)]) + A_l = assemble_matrix(form(F2)) + A_l.assemble() + A_l.setNullSpace(nullspace_l) + return A_l + +def solve_boun(ABD, meshdata, nphases): + mesh = meshdata["mesh"] + # frame = meshdata["frame"] + frame = local_frame_1D(mesh) + subdomains = meshdata["subdomains"] + nullspace = meshdata["nullspace"] + # For applying bc, we only require solved fluctuating functions (V0) as input to bc. + e, V, dv, v_, x, dx = local_boun(mesh,frame,subdomains) + mesh.topology.create_connectivity(1, 1) + V0 = initialize_array(V)[0] + A = A_mat(ABD, e,x,dx,compute_nullspace(V),v_,dv, nphases) + for p in range(4): + Eps = construct_gamma_e(e,x)[:,p] + F2 = sum([dot(dot(as_tensor(ABD[i]),Eps), gamma_h(e,x,v_))*dx(i) for i in range(nphases)]) + r_he = form(rhs(F2)) + F = petsc.assemble_vector(r_he) + F.ghostUpdate(addv = petsc4py.PETSc.InsertMode.ADD, mode = petsc4py.PETSc.ScatterMode.REVERSE) + nullspace.remove(F) + w = solve_ksp(A,F,V) + V0[:,p]= w.vector[:] + return V0 + +def initialize_array(V_l): + xxx = 3*len(np.arange(*V_l.dofmap.index_map.local_range)) # total dofs + V0 = np.zeros((xxx,4)) + Dle = np.zeros((xxx,4)) + Dhe = np.zeros((xxx,4)) + Dhd = np.zeros((xxx,4)) + Dld = np.zeros((xxx,4)) + D_ed = np.zeros((4,4)) + D_dd = np.zeros((4,4)) + D_ee = np.zeros((4,4)) + V1s = np.zeros((xxx,4)) + return V0,Dle,Dhe,Dhd,Dld,D_ed,D_dd,D_ee,V1s + +# dof mapping makes solved unknown value w_l(Function(V_l)) assigned to v2a (Function(V)). +# The boundary of wind blade mesh is a 1D curve. The facet/edge number is obtained from cell to edge connectivity (conn3) showed in subdomain subroutine. +# The same facet/edge number of extracted mesh_l (submesh) is obtaine din entity_mapl (gloabl mesh number). refer how submesh was generated. +#Therefore, once identifying the edge number being same for global(mesh)&boundary mesh(mesh_l), we equate the dofs and store w_l to v2a. +# The dofs can be verified by comparing the coordinates of local and global dofs if required. +def dof_mapping_quad(V, v2a, V_l, w_ll, boundary_facets_left, entity_mapl): + dof_S2L = [] + deg = 2 + for i,xx in enumerate(entity_mapl): + dofs = locate_dofs_topological(V, 1, np.array([xx])) + dofs_left= locate_dofs_topological(V_l, 1, np.array([boundary_facets_left[i]])) + for k in range(deg+1): + if dofs[k] not in dof_S2L: + dof_S2L.append(dofs[k]) + for j in range(3): + v2a.vector[3*dofs[k]+j] = w_ll[3*dofs_left[k]+j] # store boundary solution of fluctuating functions + return v2a diff --git a/opensg/mesh.py b/opensg/mesh.py index f71fa2f..9e25163 100644 --- a/opensg/mesh.py +++ b/opensg/mesh.py @@ -3,9 +3,14 @@ import basix from dolfinx.io import gmshio from mpi4py import MPI - +from ufl import dot, as_tensor, rhs +from dolfinx.fem.petsc import assemble_matrix +from dolfinx.fem import form, petsc, Function, locate_dofs_topological, apply_lifting, set_bc +from scipy.sparse import csr_matrix +import scipy import opensg + class BladeMesh: """This class processes and stores information about a wind turbine blade's mesh """ @@ -131,8 +136,8 @@ def generate_segment_mesh(self, segment_index, filename): parent_blade_mesh=self, msh_file=filename) return segment_mesh - - + + class SegmentMesh(): def __init__( self, @@ -175,12 +180,16 @@ def __init__( lnn = self.subdomains.values[:]-1 self.num_cells = self.mesh.topology.index_map(self.mesh.topology.dim).size_local cells = np.arange(self.num_cells, dtype=np.int32) - # NOTE: Unsure what this next line does. + self.subdomains = dolfinx.mesh.meshtags(self.mesh, self.mesh.topology.dim, cells, np.array(lnn,dtype=np.int32)) self.tdim = self.mesh.topology.dim self.fdim = self.tdim - 1 + self._generate_layup_data() + self._build_local_orientations() + self._build_boundary_submeshes() + return def _generate_layup_data(self): @@ -213,7 +222,7 @@ def _generate_layup_data(self): return layup_database - def generate_local_orientations(self): + def _build_local_orientations(self): # Local Orientation (DG0 function) of quad mesh element (from yaml data) VV = dolfinx.fem.functionspace( self.mesh, basix.ufl.element( @@ -240,32 +249,26 @@ def generate_local_orientations(self): self.N = N self.EE2 = EE2 frame = [EE1,EE2,N] + self.frame = frame return frame - - - def extract_boundaries(self): + + + def _build_boundary_submeshes(self): # extract geometry pp = self.mesh.geometry.x - is_left_boundary, is_right_boundary = opensg.util.generate_boundary_markers( + is_left_boundary, is_right_boundary = opensg.generate_boundary_markers( min(pp[:,0]), max(pp[:,0])) - facets_left = dolfinx.mesh.locate_entities_boundary( self.mesh, dim=self.fdim, marker=is_left_boundary) facets_right = dolfinx.mesh.locate_entities_boundary( self.mesh, dim=self.fdim, marker=is_right_boundary) - right_mesh, right_entity_map, right_vertex_map, right_geom_map = dolfinx.mesh.create_submesh( - self.mesh, self.fdim, facets_right) left_mesh, left_entity_map, left_vertex_map, left_geom_map = dolfinx.mesh.create_submesh( self.mesh, self.fdim, facets_left) - - self.right_submesh = { - "mesh": right_mesh, - "entity_map": right_entity_map, - "vertex_map": right_vertex_map, - "geom_map": right_geom_map} + right_mesh, right_entity_map, right_vertex_map, right_geom_map = dolfinx.mesh.create_submesh( + self.mesh, self.fdim, facets_right) self.left_submesh = { "mesh": left_mesh, @@ -273,10 +276,17 @@ def extract_boundaries(self): "vertex_map": left_vertex_map, "geom_map": left_geom_map} + self.right_submesh = { + "mesh": right_mesh, + "entity_map": right_entity_map, + "vertex_map": right_vertex_map, + "geom_map": right_geom_map} + # generate subdomains self.mesh.topology.create_connectivity(2,1) # (quad mesh topology, boundary(1D) mesh topology) cell_of_facet_mesh = self.mesh.topology.connectivity(2,1) + # NOTE: found a different way to determine connectivity that didn't need this block -klb # Cell to Edge connectivity # cell_edge_map = [] # for i in range(self.num_cells): @@ -287,7 +297,11 @@ def extract_boundaries(self): # cell_edge_map = np.ndarray.flatten(np.array(cell_edge_map)) # - def subdomains_boundary(boundary_mesh, boundary_marker, boundary_entity_map): + def subdomains_boundary( + boundary_mesh, + boundary_marker, + boundary_entity_map + ): boundary_VV = dolfinx.fem.functionspace( boundary_mesh, basix.ufl.element("DG", boundary_mesh.topology.cell_name(), 0, shape=(3, ))) @@ -295,14 +309,15 @@ def subdomains_boundary(boundary_mesh, boundary_marker, boundary_entity_map): boundary_e2 = dolfinx.fem.Function(boundary_VV) boundary_n = dolfinx.fem.Function(boundary_VV) - boundary_subdomains = [] - - boundary_facets_left = dolfinx.mesh.locate_entities(boundary_mesh, self.fdim, boundary_marker) - + boundary_facets = dolfinx.mesh.locate_entities(boundary_mesh, self.fdim, boundary_marker) # TODO: review the subdomain assingments with akshat + boundary_subdomains = [] for i, xx in enumerate(boundary_entity_map): # assign subdomain - idx = int(np.where(cell_of_facet_mesh.array==xx)[0]/4) # 4 is for number of nodes in quad element + # 4 is for number of nodes in quad element + # NOTE: we should find a different way to do this that doesn't assume quad elements if + # we plan to expand to other elements. + idx = int(np.where(cell_of_facet_mesh.array==xx)[0]/4) boundary_subdomains.append(self.subdomains.values[idx]) # assign orientation for j in range(3): @@ -310,25 +325,28 @@ def subdomains_boundary(boundary_mesh, boundary_marker, boundary_entity_map): boundary_e2.x.array[3*i+j] = self.EE2.x.array[3*idx+j] boundary_n.x.array[3*i+j] = self.N.x.array[3*idx+j] - frame = [boundary_e1, boundary_e2, boundary_n] + boundary_frame = [boundary_e1, boundary_e2, boundary_n] boundary_subdomains = np.array(boundary_subdomains, dtype=np.int32) boundary_num_cells = boundary_mesh.topology.index_map(boundary_mesh.topology.dim).size_local boundary_cells = np.arange(boundary_num_cells, dtype=np.int32) boundary_subdomains = dolfinx.mesh.meshtags(boundary_mesh, boundary_mesh.topology.dim, boundary_cells, boundary_subdomains) - return boundary_subdomains, frame, boundary_facets_left - # Mapping the orinetation data from quad mesh to boundary. The alternative is to use local_frame_1D(mesh_l). + + return boundary_subdomains, boundary_frame, boundary_facets + # Mapping the orinetation data from quad mesh to boundary. The alternative is to use local_frame_1D(self.left_submesh["mesh"]). # Either of both can be used in local_boun subroutine - self.left_submesh["subdomains"], self.left_submesh["subdomains"], self.left_submesh["subdomains"] = subdomains_boundary( + self.left_submesh["subdomains"], self.left_submesh["frame"], self.left_submesh["facets"] = subdomains_boundary( self.left_submesh["mesh"], is_left_boundary, self.left_submesh["entity_map"]) - self.right_submesh["subdomains"], self.right_submesh["subdomains"], self.right_submesh["subdomains"] = subdomains_boundary( + self.right_submesh["subdomains"], self.right_submesh["frame"], self.right_submesh["facets"] = subdomains_boundary( self.right_submesh["mesh"], is_right_boundary, self.right_submesh["entity_map"]) + + return - def generate_boundary_ABD(self): + def compute_ABD(self): nphases = max(self.subdomains.values[:]) + 1 ABD_ = [] for i in range(nphases): - ABD_.append(opensg.ABD_mat( + ABD_.append(opensg.compute_ABD_matrix( i, thick=self.layup_database["thick"], nlay=self.layup_database["nlay"], @@ -337,7 +355,229 @@ def generate_boundary_ABD(self): material_database=self.blade_mesh.material_database )) - # print('Computed',nphases,'ABD matrix') + print('Computed',nphases,'ABD matrix') + return ABD_ + + + # def plot(self): + # import pyvista + # pyvista.start_xvfb() + # u_topology, u_cell_types, u_geometry=dolfinx.plot.vtk_mesh(self.blade_mesh.mesh,self. mesh.blade_mesh.topology.dim) + # grid = pyvista.UnstructuredGrid(u_topology, u_cell_types, u_geometry) + # grid.cell_data["Marker"] = self.blade_mesh.subdomains.values[:] + # grid.set_active_scalars("Marker") + # u_plotter = pyvista.Plotter() + # u_plotter.add_mesh(grid) + # u_plotter.show_axes() + # #u_plotter.view_xy() # z is beam axis + # u_plotter.show() + + def compute_stiffness_EB(self, ABD): + # extract object data + mesh = self.mesh + frame = self.frame + subdomains = self.subdomains - # def ABD_matrix(i): - # return(as_tensor(ABD_[i])) \ No newline at end of file + D_eff = opensg.compute_stiffness_EB_blade_segment( + ABD, + mesh, + frame, + subdomains, + self.left_submesh, + self.right_submesh) + + return D_eff + + def compute_boundary_stiffness_timo(self, ABD): + + left_stiffness = opensg.compute_timo_boun( + ABD, + self.left_submesh["mesh"], + self.left_submesh_submesh["subdomains"], + self.left_submesh["frame"], + self.nullspace, # quad nullspace + self.left_submesh["nullspace"], + self.nphases)[1] + + right_stiffness = opensg.compute_timo_boun( + ABD, + self.right_submesh["mesh"], + self.right_submesh["subdomains"], + self.right_submesh["frame"], + self.nullspace, # quad nullspace + self.right_submesh["nullspace"], + self.nphases)[1] + + return left_stiffness, right_stiffness + +""" + def compute_stiffness_EB(self, ABD): + # extract object data + mesh = self.mesh + frame = self.frame + subdomains = self.subdomains + tdim=mesh.topology.dim + fdim = tdim - 1 + nphases = max(self.subdomains.values[:]) + 1 + + pp = mesh.geometry.x # point data + x_min, x_max=min(pp[:,0]), max(pp[:,0]) + # Initialize terms + e_l, V_l, dvl, v_l, x_l, dx_l = opensg.local_boun( + self.left_submesh["mesh"], self.left_submesh["frame"] ,self.left_submesh["subdomains"]) + + e_r, V_r, dvr, v_r, x_r, dx_r = opensg.local_boun( + self.right_submesh["mesh"], self.right_submesh["frame"] ,self.right_submesh["subdomains"]) + + self.left_submesh["nullspace"] = opensg.compute_nullspace(V_l) + self.right_submesh["nullspace"] = opensg.compute_nullspace(V_r) + + A_l = opensg.A_mat(ABD, e_l,x_l,dx_l,self.left_submesh["nullspace"],v_l,dvl, nphases) + A_r = opensg.A_mat(ABD, e_r,x_r,dx_r,self.right_submesh["nullspace"],v_r,dvr, nphases) + + V0_l = opensg.solve_boun(ABD, self.left_submesh, nphases) + + V0_r = opensg.solve_boun(ABD, self.right_submesh, nphases) + # The local_frame_l(self.left_submesh["mesh"]) can be replaced with frame_l, if we want to use mapped orientation from given direction cosine matrix (orien mesh data-yaml) + + # Quad mesh + e, V, dv, v_, x, dx = opensg.local_boun(mesh, frame, subdomains) + V0, Dle, Dhe, Dhd, Dld, D_ed, D_dd, D_ee, V1s = opensg.initialize_array(V) + mesh.topology.create_connectivity(1, 2) + self.left_submesh["mesh"].topology.create_connectivity(1, 1) + self.right_submesh["mesh"].topology.create_connectivity(1, 1) + + # Obtaining coefficient matrix AA and BB with and without bc applied. + # Note: bc is applied at boundary dofs. We define v2a containing all dofs of entire wind blade. + boundary_dofs = locate_dofs_topological(V, fdim, np.concatenate((self.right_submesh["entity_map"], self.left_submesh["entity_map"]), axis=0)) + F2=sum([dot(dot(as_tensor(ABD[i]), opensg.gamma_h(e,x,dv)), opensg.gamma_h(e,x,v_))*dx(i) for i in range(nphases)]) + v2a=Function(V) # b default, v2a has zero value for all. + bc = dolfinx.fem.dirichletbc(v2a, boundary_dofs) # This shows only boundary_dofs are taken for v2a under bc, which are zero (known) as input. + a = form(F2) + + B = assemble_matrix(a) # Obtain coefficient matrix without BC applied: BB + B.assemble() + ai, aj, av=B.getValuesCSR() + BB = csr_matrix((av, aj, ai)) + BB = BB.toarray() + + A = assemble_matrix(a,[bc]) # Obtain coefficient matrix with BC applied: AA + A.assemble() + ai, aj, av=A.getValuesCSR() + AA = csr_matrix((av, aj, ai)) + AA=AA.toarray() + avg=np.trace(AA)/len(AA) + + # averaging is done so that all terms are of same order. Note after appliying bc at [A=assemble_matrix(a,[bc])], the dofs of + # coefficientmatrix has only 1 replaced at that dofs. + for i,xx in enumerate(av): + if xx==1: + av[i]=avg + + AA_csr = csr_matrix((av, aj, ai)) + AAA = AA_csr.toarray() + AA = scipy.sparse.csr_matrix(AAA) + + # Assembly + # Running for 4 different F vector. However, F has bc applied to it where, stored known values of v2a is provided for each loop (from boun solve). + for p in range(4): # 4 load cases meaning + # Boundary + v2a = Function(V) + v2a = opensg.dof_mapping_quad(V, v2a,V_l,V0_l[:,p], self.left_submesh["facets"], self.left_submesh["entity_map"]) + v2a = opensg.dof_mapping_quad(V, v2a,V_r,V0_r[:,p], self.right_submesh["facets"], self.right_submesh["entity_map"]) + + # quad mesh + F2=sum([dot(dot(as_tensor(ABD[i]),opensg.gamma_e(e,x)[:,p]), opensg.gamma_h(e,x,v_))*dx(i) for i in range(nphases)]) + bc = dolfinx.fem.dirichletbc(v2a, boundary_dofs) + F = petsc.assemble_vector(form(rhs(F2))) + apply_lifting(F, [a], [[bc]]) # apply bc to rhs vector (Dhe) + set_bc(F, [bc]) + with F.localForm() as local_F: + for i in boundary_dofs: + for k in range(3): + # F[3*i+k]=avg*F[3*i+k] # normalize small terms + local_index = 3 * i + k + local_F[local_index] = avg * local_F[local_index] + + V0[:,p]= scipy.sparse.linalg.spsolve(AA, F, permc_spec=None, use_umfpack=True) # obtain sol: E* V1s = b* + Dhe[:,p]= scipy.sparse.csr_array(BB).dot(V0[:,p]) + + D1 = np.matmul(V0.T,-Dhe) + for s in range(4): + for k in range(4): + f = dolfinx.fem.form(sum([dot(dot(opensg.gamma_e(e,x).T,as_tensor(ABD[i])),opensg.gamma_e(e,x))[s,k]*dx(i) for i in range(nphases)])) + D_ee[s,k]=dolfinx.fem.assemble_scalar(f) + L = (x_max - x_min) + D_eff= D_ee + D1 + D_eff=D_eff/L # L is divided because of 3D shell mesh and corresponding beam length need to divided. + #--------------------------------------Printing Output Data--------------------------------------- + print(' ') + print('Stiffness Matrix') + np.set_printoptions(precision=4) + print(np.around(D_eff)) + + return D_eff +""" + + +class MeshData: + def __init__(self, mesh): + # What data is required to start? + + pass + + def add_submesh_attributes(self, + entity_map, + vertex_map, + geom_map, + submesh_facets): + pass + + def process_data(self): + pass + # what downstream data can be generated with the starting data? + + def process_data_with_args(self, args): + pass + # what data needs external information to be generated? + # how do we track that this data is not soley derived from the init data? + + # Mapping the orinetation data from quad mesh to boundary. The alternative is to use local_frame_1D(self.left_submesh["mesh"]). + # Either of both can be used in local_boun subroutine + + # self.left_submesh["subdomains"], self.left_submesh["frame"], self.left_submesh["facets"] = subdomains_boundary( + # self.left_submesh["mesh"], is_left_boundary, self.left_submesh["entity_map"]) + # self.right_submesh["subdomains"], self.right_submesh["frame"], self.right_submesh["facets"] = subdomains_boundary( + # self.right_submesh["mesh"], is_right_boundary, self.right_submesh["entity_map"]) + + +def _generate_submesh_subdomains(submesh_data, mesh_data): + mesh_data.mesh.topology.create_connectivity(2,1) # (quad mesh topology, boundary(1D) mesh topology) + cell_of_facet_mesh = mesh_data.mesh.topology.connectivity(2,1) + submesh_VV = dolfinx.fem.functionspace( + submesh_data.mesh, basix.ufl.element("DG", submesh_data.mesh.topology.cell_name(), 0, shape=(3, ))) + + submesh_e1 = dolfinx.fem.Function(submesh_VV) + submesh_e2 = dolfinx.fem.Function(submesh_VV) + submesh_n = dolfinx.fem.Function(submesh_VV) + + submesh_facets = dolfinx.mesh.locate_entities(submesh_data.mesh, self.fdim, submesh_marker) + submesh_subdomains = [] + for i, xx in enumerate(submesh_data.entity_map): + # assign subdomain + idx = int(np.where(cell_of_facet_mesh.array==xx)[0]/4) # 4 is for number of nodes in quad element + submesh_subdomains.append(mesh_data.subdomains.values[idx]) + # assign orientation + for j in range(3): + submesh_e1.x.array[3*i+j] = mesh_data.EE1.x.array[3*idx+j] + submesh_e2.x.array[3*i+j] = mesh_data.EE2.x.array[3*idx+j] + submesh_n.x.array[3*i+j] = mesh_data.N.x.array[3*idx+j] + + submesh_frame = [submesh_e1, submesh_e2, submesh_n] + submesh_subdomains = np.array(submesh_subdomains, dtype=np.int32) + submesh_num_cells = submesh_data.mesh.topology.index_map(submesh_data.mesh.topology.dim).size_local + submesh_cells = np.arange(submesh_num_cells, dtype=np.int32) + submesh_subdomains = dolfinx.mesh.meshtags( + submesh_data.mesh, submesh_data.mesh.topology.dim, submesh_cells, submesh_subdomains) + + return submesh_subdomains, submesh_frame, submesh_facets \ No newline at end of file diff --git a/opensg/solve.py b/opensg/solve.py index 15510b1..279c312 100644 --- a/opensg/solve.py +++ b/opensg/solve.py @@ -3,94 +3,22 @@ import numpy as np import dolfinx import basix -from dolfinx.fem import form, petsc, Function, functionspace -from ufl import TrialFunction, TestFunction, inner, lhs, rhs +from dolfinx.fem import form, petsc, Function, functionspace, apply_lifting, set_bc, locate_dofs_topological +from ufl import TrialFunction, TestFunction, inner, lhs, rhs, as_tensor, dot +from scipy.sparse import csr_matrix import petsc4py.PETSc +from dolfinx.fem.petsc import assemble_matrix +import opensg +import scipy + from mpi4py import MPI import ufl -from contextlib import ExitStack - - -def ksp_solve(A, F, V): - """Krylov Subspace Solver for Aw = F - - Parameters - ---------- - A : array - stiffness matrix - F : array - Load or force vector - V : function space - _description_ - - Returns - ------- - array - solution vector (displacement field) - """ - w = Function(V) - ksp = petsc4py.PETSc.KSP() - ksp.create(comm=MPI.COMM_WORLD) - ksp.setOperators(A) - ksp.setType("preonly") - ksp.getPC().setType("lu") - ksp.getPC().setFactorSolverType("mumps") - ksp.getPC().setFactorSetUpSolverType() - ksp.getPC().getFactorMatrix().setMumpsIcntl(icntl=24, ival=1) # detect null pivots - ksp.getPC().getFactorMatrix().setMumpsIcntl( - icntl=25, ival=0 - ) # do not compute null space again - ksp.setFromOptions() - ksp.solve(F, w.vector) - w.vector.ghostUpdate( - addv=petsc4py.PETSc.InsertMode.INSERT, mode=petsc4py.PETSc.ScatterMode.FORWARD - ) - ksp.destroy() - return w - -def nullspace(V): - """Compute nullspace to restrict Rigid body motions - - Constructs a translational null space for the vector-valued function space V - and ensures that it is properly orthonormalized. - - Parameters - ---------- - V : functionspace - _description_ - - Returns - ------- - NullSpace - Nullspace of V - """ - # extract the Index Map from the Function Space - index_map = V.dofmap.index_map - - # initialize nullspace basis with petsc vectors - nullspace_basis = [ - dolfinx.la.create_petsc_vector(index_map, V.dofmap.index_map_bs) - for _ in range(4) - ] - - with ExitStack() as stack: - vec_local = [stack.enter_context(xx.localForm()) for xx in nullspace_basis] - basis = [np.asarray(xx) for xx in vec_local] - # identify the degrees of freedom indices for each subspace (x, y, z) - dofs = [V.sub(i).dofmap.list for i in range(3)] - # Build translational null space basis - for i in range(3): - basis[i][dofs[i]] = 1.0 - - # Create vector space basis and orthogonalize - dolfinx.la.orthonormalize(nullspace_basis) - - return petsc4py.PETSc.NullSpace().create(nullspace_basis, comm=MPI.COMM_WORLD) - - -def ABD_mat(ii, thick, nlay, angle, mat_names, material_database): +### ABD matrix computation +# @profile +# NOTE can pass in thick[ii], nlay[ii], etc instead of the dictionaries +def compute_ABD_matrix(ii, thick, nlay, angle, mat_names, material_database): """Compute the ABD matrix for a composite layup structure Constructs a local stiffness matrix for a composite laminate @@ -119,13 +47,13 @@ def ABD_mat(ii, thick, nlay, angle, mat_names, material_database): # initialization deg = 2 cell = ufl.Cell("interval") - elem = basix.ufl.element("Lagrange", "interval", 1, shape=(3,)) + elem = basix.ufl.element("Lagrange", "interval", 1, shape = (3,)) domain = ufl.Mesh(elem) # nodes (1D SG) th, s = [0], 0 # Reference starting point for k in thick[ii]: - s = s + k # Add the thickness of each layer + s = s - k # Add the thickness of each layer th.append(s) points = np.array(th) @@ -138,7 +66,7 @@ def ABD_mat(ii, thick, nlay, angle, mat_names, material_database): # Create mesh object dom = dolfinx.mesh.create_mesh(MPI.COMM_WORLD, cellss, points, domain) num_cells = dom.topology.index_map(dom.topology.dim).size_local - cells = np.arange(num_cells, dtype=np.int32) + cells = np.arange(num_cells, dtype = np.int32) # # Note: For a layup like layup1: containing 3 layers: @@ -147,28 +75,29 @@ def ABD_mat(ii, thick, nlay, angle, mat_names, material_database): # assigning each element as subdomain subdomain = dolfinx.mesh.meshtags(dom, dom.topology.dim, cells, cells) - x, dx = ufl.SpatialCoordinate(dom), ufl.Measure("dx")(domain=dom, subdomain_data=subdomain) - gamma_e = create_gamma_e(x) + x, dx = ufl.SpatialCoordinate(dom), ufl.Measure("dx")(domain = dom, subdomain_data = subdomain) + gamma_e = opensg.compute_utils.create_gamma_e(x) nphases = len(cells) # Creating FE function Space - V = functionspace(dom, basix.ufl.element("CG", "interval", deg, shape=(3,))) + V = functionspace(dom, basix.ufl.element("CG", "interval", deg, shape = (3,))) u, v = TrialFunction(V), TestFunction(V) # Weak form of energy - # dx is for integration - F2 = sum( - [inner(sigma( - vector=u, material_parameters=material_database[mat_names[ii][i]], - theta=angle[ii][i], Eps=gamma_e[:,0])[0], - eps(v)[0]) * dx(i) for i in range(nphases)] - ) + F2 = 0 + for j in range(nphases): + mat_name = mat_names[ii][j] + material_props = material_database[mat_name] + theta = angle[ii][j] + sigma_val = opensg.compute_utils.sigma(u, material_props, theta, Eps = gamma_e[:,0])[0] + inner_val = inner(sigma_val, opensg.compute_utils.eps(v)[0]) + F2 += inner_val * dx(j) # lhs gives left hand side of weak form : coeff matrix here A = petsc.assemble_matrix(form(lhs(F2))) A.assemble() - null = nullspace(V) + null = opensg.compute_utils.compute_nullspace(V) A.setNullSpace(null) # Set the nullspace xx = 3 * V.dofmap.index_map.local_range[1] # total dofs @@ -180,149 +109,312 @@ def ABD_mat(ii, thick, nlay, angle, mat_names, material_database): Eps = gamma_e[:, p] # weak form - F2 = sum([inner(sigma(u, i, Eps)[0], eps(v)[0]) * dx(i) for i in range(nphases)]) + F2 = 0 + for j in range(nphases): + mat_name = mat_names[ii][j] + material_props = material_database[mat_name] + theta = angle[ii][j] + sigma_val = opensg.compute_utils.sigma(u, material_props, theta, Eps)[0] + inner_val = inner(sigma_val, opensg.compute_utils.eps(v)[0]) + F2 += inner_val * dx(j) + + # F2 = sum([inner(sigma(u, i, Eps)[0], eps(v)[0]) * dx(i) for i in range(nphases)]) # rhs is used for getting right hand side of Aw = F; (which is F here) F = petsc.assemble_vector(form(rhs(F2))) - F.ghostUpdate(addv=petsc4py.PETSc.InsertMode.ADD, mode=petsc4py.PETSc.ScatterMode.REVERSE) + F.ghostUpdate(addv = petsc4py.PETSc.InsertMode.ADD, mode = petsc4py.PETSc.ScatterMode.REVERSE) null.remove(F) # Orthogonalize F to the null space of A^T - w = ksp_solve(A, F, V) + w = opensg.compute_utils.solve_ksp(A, F, V) Dhe[:, p] = F[:] # Dhe matrix formation V0[:, p] = w.vector[:] # V0 matrix formation - + + # NOTE: fixed.. D1 = np.matmul(V0.T, -Dhe) # Additional information matrix # Scalar assembly for each term of D_ee matrix for s in range(6): for k in range(6): - # Scalar assembly - f = dolfinx.fem.form(sum([Dee(i)[s, k] * dx(i) for i in range(nphases)])) + # f=dolfinx.fem.form(sum([opensg.compute_utils.Dee(x, u, material_props, theta, Eps)[s,k]*dx(i) for i in range(nphases)])) # Scalar assembly + f = 0 + for j in range(nphases): + mat_name = mat_names[ii][j] + material_props = material_database[mat_name] + theta = angle[ii][j] + dee_val = opensg.compute_utils.Dee(x, u, material_props, theta, Eps)[s, k] + f += dee_val * dx(j) + f = dolfinx.fem.form(f) D_ee[s, k] = dolfinx.fem.assemble_scalar(f) D_eff = D_ee + D1 return D_eff -def create_gamma_e(x): - """_summary_ + +### solve stiffness via EB method +# @profile +def compute_stiffness_EB_blade_segment( + ABD, # array + mesh, # + frame, # + subdomains, + l_submesh, # dictionary with mesh data for l boundary + r_submesh # dictionary with mesh data for r boundary + ): + """Computes the ABD stiffness matrix using the EB method for a blade segment Parameters ---------- - x : _type_ + ABD : _type_ _description_ - - Returns - ------- - _type_ + mesh : _type_ _description_ - """ - gamma_e = ufl.as_tensor([ - (1, 0, 0, x[0], 0, 0), - (0, 1, 0, 0, x[0], 0), - (0, 0, 0, 0, 0, 0), - (0, 0, 0, 0, 0, 0), - (0, 0, 0, 0, 0, 0), - (0, 0, 1, 0, 0, x[0]), - ]) - - return gamma_e - -def R_sig(C, t): - """Compute rotation matrix - - Parameters - ---------- - C : _type_ + frame : _type_ + _description_ + subdomains : _type_ _description_ - t : _type_ + l_submesh : _type_ + _description_ + r_submesh : _type_ _description_ Returns ------- - _type_ - _description_ + array + Stiffness matrix """ - th = np.deg2rad(t) - c, s, cs = np.cos(th), np.sin(th), np.cos(th) * np.sin(th) - R_Sig = np.array( - [ - (c**2, s**2, 0, 0, 0, -2 * cs), - (s**2, c**2, 0, 0, 0, 2 * cs), - (0, 0, 1, 0, 0, 0), - (0, 0, 0, c, s, 0), - (0, 0, 0, -s, c, 0), - (cs, -cs, 0, 0, 0, c**2 - s**2), - ] - ) - return np.matmul(np.matmul(R_Sig, C), R_Sig.transpose()) + tdim = mesh.topology.dim + fdim = tdim - 1 + nphases = max(subdomains.values[:]) + 1 + + pp = mesh.geometry.x # point data + x_min, x_max=min(pp[:,0]), max(pp[:,0]) + # Initialize terms + e_l, V_l, dvl, v_l, x_l, dx_l = opensg.local_boun( + l_submesh["mesh"], l_submesh["frame"], l_submesh["subdomains"]) + + e_r, V_r, dvr, v_r, x_r, dx_r = opensg.local_boun( + r_submesh["mesh"], r_submesh["frame"], r_submesh["subdomains"]) + + l_submesh["nullspace"] = opensg.compute_nullspace(V_l) + r_submesh["nullspace"] = opensg.compute_nullspace(V_r) -def Dee(i): - """ Simplifying gamma_e.T*C*gamma_e + A_l = opensg.A_mat(ABD, e_l, x_l, dx_l, l_submesh["nullspace"],v_l, dvl, nphases) + A_r = opensg.A_mat(ABD, e_r, x_r, dx_r, r_submesh["nullspace"],v_r, dvr, nphases) + + V0_l = opensg.solve_boun(ABD, l_submesh, nphases) + V0_r = opensg.solve_boun(ABD, r_submesh, nphases) + + # The local_frame_l(submesh["mesh"]) can be replaced with frame_l, if we want to use mapped orientation from given direction cosine matrix (orien mesh data-yaml) + + # Quad mesh + e, V, dv, v, x, dx = opensg.local_boun(mesh, frame, subdomains) + V0, Dle, Dhe, Dhd, Dld, D_ed, D_dd, D_ee, V1s = opensg.initialize_array(V) + mesh.topology.create_connectivity(1, 2) + l_submesh["mesh"].topology.create_connectivity(1, 1) + r_submesh["mesh"].topology.create_connectivity(1, 1) + + # Obtaining coefficient matrix AA and BB with and without bc applied. + # Note: bc is applied at boundary dofs. We define v2a containing all dofs of entire wind blade. + # NOTE: does order of right and left submesh matter here? + boundary_dofs = locate_dofs_topological(V, fdim, np.concatenate((r_submesh["entity_map"], l_submesh["entity_map"]), axis=0)) + F2=sum([dot(dot(as_tensor(ABD[i]), opensg.gamma_h(e,x,dv)), opensg.gamma_h(e,x,v))*dx(i) for i in range(nphases)]) + v2a=Function(V) # b default, v2a has zero value for all. + bc = dolfinx.fem.dirichletbc(v2a, boundary_dofs) # This shows only boundary_dofs are taken for v2a under bc, which are zero (known) as input. + a = form(F2) + + B = assemble_matrix(a) # Obtain coefficient matrix without BC applied: BB + B.assemble() + ai, aj, av=B.getValuesCSR() + BB = csr_matrix((av, aj, ai)) + BB = BB.toarray() + + A = assemble_matrix(a,[bc]) # Obtain coefficient matrix with BC applied: AA + A.assemble() + ai, aj, av=A.getValuesCSR() + AA = csr_matrix((av, aj, ai)) + AA=AA.toarray() + avg=np.trace(AA)/len(AA) + + # averaging is done so that all terms are of same order. Note after appliying bc at [A=assemble_matrix(a,[bc])], the dofs of + # coefficientmatrix has only 1 replaced at that dofs. + for i,xx in enumerate(av): + if xx==1: + av[i]=avg + + AA_csr = csr_matrix((av, aj, ai)) + AAA = AA_csr.toarray() + AA = scipy.sparse.csr_matrix(AAA) - Parameters - ---------- - i : _type_ - _description_ + # Assembly + # Running for 4 different F vector. However, F has bc applied to it where, stored known values of v2a is provided for each loop (from boun solve). + for p in range(4): # 4 load cases meaning + # Boundary + v2a = Function(V) + v2a = opensg.dof_mapping_quad(V, v2a,V_l,V0_l[:,p], l_submesh["facets"], l_submesh["entity_map"]) + # NOTE: does this second call overwrite previous, or is the data combined? -klb + v2a = opensg.dof_mapping_quad(V, v2a,V_r,V0_r[:,p], r_submesh["facets"], r_submesh["entity_map"]) + + # quad mesh + F2=sum([dot(dot(as_tensor(ABD[i]),opensg.construct_gamma_e(e,x)[:,p]), opensg.gamma_h(e,x,v))*dx(i) for i in range(nphases)]) + bc = dolfinx.fem.dirichletbc(v2a, boundary_dofs) + F = petsc.assemble_vector(form(rhs(F2))) + apply_lifting(F, [a], [[bc]]) # apply bc to rhs vector (Dhe) + set_bc(F, [bc]) + with F.localForm() as local_F: + for i in boundary_dofs: + for k in range(3): + # F[3*i+k]=avg*F[3*i+k] # normalize small terms + local_index = 3 * i + k + local_F[local_index] = avg * local_F[local_index] + + V0[:,p]= scipy.sparse.linalg.spsolve(AA, F, permc_spec=None, use_umfpack=True) # obtain sol: E* V1s = b* + Dhe[:,p]= scipy.sparse.csr_array(BB).dot(V0[:,p]) + + D1 = np.matmul(V0.T,-Dhe) + gamma_e = opensg.construct_gamma_e(e,x) + q1 = gamma_e.T + q3 = gamma_e + + for s in range(4): + for k in range(4): + # f = dolfinx.fem.form(sum([dot(dot(opensg.construct_gamma_e(e,x).T,as_tensor(ABD[i])),opensg.construct_gamma_e(e,x))[s,k]*dx(i) for i in range(nphases)])) + form_list = [] + for i in range(nphases): + q2 = as_tensor(ABD[i]) + dot1 = dot(q1, q2) + dot2 = dot(dot1, q3) + q4 = dot2[s,k] + form_list.append(q4*dx(i)) + f = dolfinx.fem.form(sum(form_list)) + + D_ee[s,k]=dolfinx.fem.assemble_scalar(f) + L = (x_max - x_min) + D_eff= D_ee + D1 + D_eff=D_eff/L # L is divided because of 3D shell mesh and corresponding beam length need to divided. + #--------------------------------------Printing Output Data--------------------------------------- + print(' ') + print('Stiffness Matrix') + np.set_printoptions(precision=4) + print(np.around(D_eff)) + + return D_eff + - Returns - ------- - _type_ - _description_ - """ - C = sigma(u, i, Eps)[1] - x0 = x[0] - return ufl.as_tensor( - [ - (C[0, 0], C[0, 1], C[0, 5], x0 * C[0, 0], x0 * C[0, 1], x0 * C[0, 5]), - (C[1, 0], C[1, 1], C[1, 5], x0 * C[1, 0], x0 * C[1, 1], x0 * C[1, 5]), - (C[5, 0], C[5, 1], C[5, 5], x0 * C[5, 0], x0 * C[5, 1], x0 * C[5, 5]), - ( - x0 * C[0, 0], - x0 * C[0, 1], - x0 * C[0, 5], - x0 * x0 * C[0, 0], - x0 * x0 * C[0, 1], - x0 * x0 * C[0, 5], - ), - ( - x0 * C[1, 0], - x0 * C[1, 1], - x0 * C[1, 5], - x0 * x0 * C[1, 0], - x0 * x0 * C[1, 1], - x0 * x0 * C[1, 5], - ), - ( - x0 * C[5, 0], - x0 * C[5, 1], - x0 * C[5, 5], - x0 * x0 * C[5, 0], - x0 * x0 * C[5, 1], - x0 * x0 * C[5, 5], - ), - ] - ) +def compute_timo_boun(ABD, mesh, subdomains, frame, nullspace, sub_nullspace, nphases): -def sigma(vector, material_parameters, theta, Eps): - E1, E2, E3 = material_parameters["E"] - G12, G13, G23 = material_parameters["G"] - v12, v13, v23 = material_parameters["nu"] - S = np.zeros((6, 6)) - S[0, 0], S[1, 1], S[2, 2] = 1 / E1, 1 / E2, 1 / E3 - S[0, 1], S[0, 2] = -v12 / E1, -v13 / E1 - S[1, 0], S[1, 2] = -v12 / E1, -v23 / E2 - S[2, 0], S[2, 1] = -v13 / E1, -v23 / E2 - S[3, 3], S[4, 4], S[5, 5] = 1 / G23, 1 / G13, 1 / G12 - C = np.linalg.inv(S) - C = R_sig(C, theta) - s1 = ufl.dot(ufl.as_tensor(C), eps(vector)[1] + Eps) - return ufl.as_tensor([(s1[0], s1[5], s1[4]), (s1[5], s1[1], s1[3]), (s1[4], s1[3], s1[2])]), C - -def eps(vector): # (Gamma_h * w) - E1 = ufl.as_vector([0, 0, vector[2].dx(0), (vector[1].dx(0)), (vector[0].dx(0)), 0]) - ans = ufl.as_tensor([ - (E1[0], 0.5 * E1[5], 0.5 * E1[4]), - (0.5 * E1[5], E1[1], 0.5 * E1[3]), - (0.5 * E1[4], 0.5 * E1[3], E1[2]), - ]) - return ans, E1 + mesh = opensg.local_frame_1D(mesh) + e, V_l, dv, v_, x, dx = opensg.compute_utils.local_boun(mesh,frame,subdomains) + mesh.topology.create_connectivity(1, 1) + V0,Dle,Dhe,Dhd,Dld,D_ed,D_dd,D_ee,V1s = opensg.compute_utils.initialize_array(V_l) + A_l = opensg.A_mat(e,x,dx,nullspace(V_l),v_,dv, nphases) + + for p in range(4): + Eps = opensg.compute_utils.gamma_e(e,x)[:,p] + F2 = sum([dot(dot(as_tensor(ABD[i]),Eps), opensg.compute_utils.gamma_h(e,x,v_))*dx(i) for i in range(nphases)]) + r_he = form(rhs(F2)) + F_l = petsc.assemble_vector(r_he) + F_l.ghostUpdate(addv = petsc4py.PETSc.InsertMode.ADD, mode = petsc4py.PETSc.ScatterMode.REVERSE) + sub_nullspace.remove(F_l) + w_l = opensg.compute_utils.solve_ksp(A_l,F_l,V_l) + Dhe[:,p]= F_l[:] + V0[:,p]= w_l.vector[:] + D1 = np.matmul(V0.T,-Dhe) + for s in range(4): + for k in range(4): + f = dolfinx.fem.form(sum([dot(dot(opensg.compute_utils.gamma_e(e,x).T,as_tensor(ABD[i])),opensg.compute_utils.gamma_e(e,x))[s,k]*dx(i) for i in range(nphases)])) + D_ee[s,k] = dolfinx.fem.assemble_scalar(f) + + D_eff= D_ee + D1 # Effective Stiffness Matrix (EB) + print('EB Computed') + F1 = sum([dot(dot(as_tensor(ABD[i]),opensg.compute_utils.gamma_l(e,x,v_)),opensg.compute_utils.gamma_l(e,x,dv))*dx(i) for i in range(nphases)]) + a1 = form(F1) + Dll = assemble_matrix(a1) + Dll.assemble() + ai, aj, av = Dll.getValuesCSR() + Dll= csr_matrix((av, aj, ai)).toarray() + + for p in range(4): + Eps = opensg.compute_utils.gamma_e(e,x)[:,p] + F1 = sum([dot(dot(as_tensor(ABD[i]),Eps),opensg.compute_utils.gamma_l(e,x,v_))*dx(i) for i in range(nphases)]) + Dle[:,p]= petsc.assemble_vector(form(F1))[:] + + Eps = opensg.compute_utils.gamma_d(e,x)[:,p] + F1 = sum([dot(dot(as_tensor(ABD[i]),Eps),opensg.compute_utils.gamma_h(e,x,v_))*dx(i) for i in range(nphases)]) + Dhd[:,p]= petsc.assemble_vector(form(F1))[:] + + Eps = opensg.compute_utils.gamma_d(e,x)[:,p] + F1 = sum([dot(dot(as_tensor(ABD[i]),Eps),opensg.compute_utils.gamma_l(e,x,v_))*dx(i) for i in range(nphases)]) + Dld[:,p]= petsc.assemble_vector(form(F1))[:] + + F_dhl = sum([dot(dot(as_tensor(ABD[i]),opensg.compute_utils.gamma_h(e,x,dv)),opensg.compute_utils.gamma_l(e,x,v_))*dx(i) for i in range(nphases)]) + a3 = form(F_dhl) + Dhl = assemble_matrix(a3) + Dhl.assemble() + ai, aj, av = Dhl.getValuesCSR() + Dhl = csr_matrix((av, aj, ai)).toarray() + for s in range(4): + for k in range(4): + f = dolfinx.fem.form(sum([dot(dot(opensg.compute_utils.gamma_e(e,x).T,as_tensor(ABD[i])),opensg.compute_utils.gamma_d(e,x))[s,k]*dx(i) for i in range(nphases)])) + D_ed[s,k] = dolfinx.fem.assemble_scalar(f) + + f = dolfinx.fem.form(sum([dot(dot(opensg.compute_utils.gamma_d(e,x).T,as_tensor(ABD[i])),opensg.compute_utils.gamma_d(e,x))[s,k]*dx(i) for i in range(nphases)])) + D_dd[s,k] = dolfinx.fem.assemble_scalar(f) + + #DhlTV0 + DhlV0 = np.matmul(Dhl.T,V0) + + #DhlTV0Dle + DhlTV0Dle = np.matmul(Dhl,V0)+Dle + + #V0DllV0 + V0DllV0 = np.matmul(np.matmul(V0.T,Dll),V0) + + # V1s + b = DhlTV0Dle-DhlV0-Dhd + + for p in range(4): + F = petsc4py.PETSc.Vec().createWithArray(b[:,p],comm = MPI.COMM_WORLD) + F.ghostUpdate(addv = petsc4py.PETSc.InsertMode.ADD, mode = petsc4py.PETSc.ScatterMode.REVERSE) + sub_nullspace.remove(F) + w_l = opensg.compute_utils.solve_ksp(A_l,F,V_l) + V1s[:,p]= w_l.vector[:] + + # Ainv + Ainv = np.linalg.inv(D_eff) + + # B_tim + B_tim= np.matmul(DhlTV0Dle.T,V0)+ D_ed+ np.matmul(V0.T,Dhd) + + # C_tim + C_tim= V0DllV0 + np.matmul(V1s.T,DhlV0 + DhlTV0Dle)+2*np.matmul(V0.T,Dld)+ D_dd+np.matmul(V1s.T,Dhd) + C_tim = 0.5*(C_tim+C_tim.T) + + # Ginv + Q_tim = np.matmul(Ainv,np.array([(0,0),(0,0),(0,-1),(1,0)])) + Ginv= np.matmul(np.matmul(Q_tim.T,(C_tim-np.matmul(np.matmul(B_tim.T,Ainv),B_tim))),Q_tim) + G_tim = np.linalg.inv(Ginv) + Y_tim= np.matmul(np.matmul(B_tim.T,Q_tim),G_tim) + A_tim= D_eff + np.matmul(np.matmul(Y_tim,Ginv),Y_tim.T) + + # Deff_srt + D = np.zeros((6,6)) + + D[4:6,4:6] = G_tim + D[0:4,4:6] = Y_tim + D[4:6,0:4] = Y_tim.T + D[0:4,0:4] = A_tim + + Deff_srt = np.zeros((6,6)) + Deff_srt[0,3:6] = A_tim[0,1:4] + Deff_srt[0,1:3] = Y_tim[0,:] + Deff_srt[0,0] = A_tim[0,0] + + Deff_srt[3:6,3:6] = A_tim[1:4,1:4] + Deff_srt[3:6,1:3] = Y_tim[1:4,:] + Deff_srt[3:6,0] = A_tim[1:4,0] + + Deff_srt[1:3,1:3] = G_tim + Deff_srt[1:3,3:6] = Y_tim.T[:,1:4] + Deff_srt[1:3,0] = Y_tim.T[:,0] + + return np.around(D_eff), np.around(Deff_srt) \ No newline at end of file diff --git a/opensg/tests/data/bar_urc_shell_mesh.yaml b/opensg/tests/data/bar_urc_shell_mesh.yaml new file mode 100644 index 0000000..fd0b750 --- /dev/null +++ b/opensg/tests/data/bar_urc_shell_mesh.yaml @@ -0,0 +1,324921 @@ +nodes: +- [-2.114282115869634, 0.769617524822445, 0.0] +- [-2.1373045369417625, 0.7019296545882159, 0.0] +- [-2.1167066220971087, 0.7646615948212594, 0.19157088122605342] +- [-2.1395410214162482, 0.6973523941350154, 0.19157088122605342] +- [-2.1191242928681033, 0.7597222974409591, 0.3831417624521066] +- [-2.1417733005059483, 0.6927365000718408, 0.3831417624521066] +- [-2.1215350963007604, 0.7547997269208557, 0.57471264367816] +- [-2.1440013615676565, 0.6880823595146998, 0.57471264367816] +- [-2.1239390005132206, 0.7498939775002599, 0.7662835249042133] +- [-2.1462251919581643, 0.6833903595795998, 0.7662835249042133] +- [-2.126335973623628, 0.7450051434184832, 0.9578544061302673] +- [-2.148444779034267, 0.6786608873825487, 0.9578544061302673] +- [-2.128725983750121, 0.7401333189148362, 1.1494252873563204] +- [-2.1506601101527543, 0.6738943300395535, 1.1494252873563204] +- [-2.1311089990108445, 0.7352785982286304, 1.3409961685823741] +- [-2.1528711726704217, 0.6690910746666222, 1.3409961685823741] +- [-2.1334849875239383, 0.7304410755991764, 1.5325670498084274] +- [-2.155077953944061, 0.664251508379762, 1.5325670498084274] +- [-2.135853917407546, 0.725620845265786, 1.7241379310344815] +- [-2.1572804413304656, 0.6593760182949808, 1.7241379310344815] +- [-2.138215756779808, 0.7208180014677696, 1.9157088122605357] +- [-2.1594786221864277, 0.6544649915282861, 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0.02, 0] + - [medium_density_foam, 0.025, 0] + - [glass_triax, 0.02, 0] + xDir: [-0.006858687942002506, 0.057685210811802, 2.0] + xyDir: [2.033134003091159, 1.4714660994440467, 0.0] +- type: shell + elementSet: 05_03_HP_LE + layup: + - [Gelcoat, 0.001, 0] + - [glass_triax, 0.02, 0] + - [glass_uni, 0.005, 0] + - [glass_triax, 0.02, 0] + xDir: [0.009664932696486161, 0.04002130865111442, 2.0] + xyDir: [0.028041913128936002, 0.10304031272524206, 0.0] +- type: shell + elementSet: 06_03_LP_LE + layup: + - [Gelcoat, 0.001, 0] + - [glass_triax, 0.02, 0] + - [glass_uni, 0.005, 0] + - [glass_triax, 0.02, 0] + xDir: [0.00854216206555991, 0.03947848878135851, 2.0] + xyDir: [0.017470469930023658, 0.10548820895941813, 0.0] +- type: shell + elementSet: 07_03_LP_LE_PANEL + layup: + - [Gelcoat, 0.001, 0] + - [glass_triax, 0.02, 0] + - [medium_density_foam, 0.02, 0] + - [glass_triax, 0.02, 0] + xDir: [-0.001400805237295577, -0.0126620838494097, 2.0] + xyDir: [-2.031314020096012, 2.614799777679697, 0.0] 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[-0.002162325810926665, 3.8791910100702444e-05, 0.9999976614184032, -0.022954812260697052, + -0.9997365035229354, -1.085411985048128e-05, 0.9997341651364944, -0.022954782049139047, + 0.002162646506706814] +- [-0.00221745734661887, 3.9636655558335404e-05, 0.9999975406529017, -0.022824730617278785, + -0.9997394818409164, -1.0986564121845272e-05, 0.999737022699052, -0.022824698845581096, + 0.002217784354698772] +- [-0.0022721771643253335, 4.045137336404789e-05, 0.9999974177839761, -0.022680995858780938, + -0.9997427530638922, -1.1094302130079533e-05, 0.9997401710633558, -0.022680962499769954, + 0.00227251013114327] +materials: +- name: Gelcoat + density: 1235.0 + elastic: + E: + - 3440000000.0 + - 3440000000.0 + - 3440000000.0 + nu: + - 0.3 + - 0.3 + - 0.3 + G: + - 1323000000.0 + - 1323000000.0 + - 1323000000.0 +- name: Adhesive + density: 1100.0 + elastic: + E: + - 3900000000.0 + - 3900000000.0 + - 3900000000.0 + nu: + - 0.3 + - 0.3 + - 0.3 + G: + - 1500000000.0 + - 1500000000.0 + - 1500000000.0 +- name: glass_uni + density: 1940.0 + elastic: + E: + - 43700000000.0 + - 16500000000.0 + - 15450000000.0 + nu: + - 0.262 + - 0.264 + - 0.35 + G: + - 3265000000.0 + - 3495000000.0 + - 3480000000.0 +- name: carbon_uni_industry_baseline + density: 1600.0 + elastic: + E: + - 157599000000.0 + - 9100000000.0 + - 9100000000.0 + nu: + - 0.3133 + - 0.3133 + - 0.47066 + G: + - 4131000000.0 + - 4131000000.0 + - 2689000000.0 +- name: glass_biax + density: 1940.0 + elastic: + E: + - 11023100000.0 + - 11023100000.0 + - 16047700000.0 + nu: + - 0.688074 + - 0.117173 + - 0.117173 + G: + - 13231400000.0 + - 3487480000.0 + - 3487480000.0 +- name: glass_triax + density: 1940.0 + elastic: + E: + - 28211400000.0 + - 16238800000.0 + - 15835500000.0 + nu: + - 0.497511 + - 0.18091 + - 0.27481 + G: + - 8248220000.0 + - 3491240000.0 + - 3491240000.0 +- name: medium_density_foam + density: 130.0 + elastic: + E: + - 142500000.0 + - 142500000.0 + - 142500000.0 + nu: + - 0.3194 + - 0.3194 + - 0.3194 + G: + - 54000000.0 + - 54000000.0 + - 54000000.0 +- name: resin + density: 1150.0 + elastic: + E: + - 1000000.0 + - 1000000.0 + - 1000000.0 + nu: + - 0.3 + - 0.3 + - 0.3 + G: + - 312500.0 + - 312500.0 + - 312500.0 +- name: steel + density: 7800 + elastic: + E: + - 200000000000.0 + - 200000000000.0 + - 200000000000.0 + nu: + - 0.3 + - 0.3 + - 0.3 + G: + - 79300000000.0 + - 79300000000.0 + - 79300000000.0 diff --git a/opensg/tests/test_workflow.py b/opensg/tests/test_workflow.py new file mode 100644 index 0000000..2b9d4e0 --- /dev/null +++ b/opensg/tests/test_workflow.py @@ -0,0 +1,34 @@ +import unittest +from os.path import abspath, dirname, join +import numpy as np +import opensg + +example_data_path = "" +testdir = dirname(abspath(str(__file__))) +datadir = join(testdir, "data") + +class TestExample(unittest.TestCase): + + # def setup + # def close + def setUp(self): + mesh_yaml = join(datadir, "bar_urc_shell_mesh.yaml") + mesh_data = opensg.load_yaml(mesh_yaml) + + self.blade_mesh = opensg.BladeMesh(mesh_data) + return super().setUp() + + def test_example(self): + # load expected values + # expected_ABD = np.loadtxt("") + # expected_stiffness = np.loadtxt("") + + section_mesh = self.blade_mesh.generate_segment_mesh(segment_index=1, filename="section.msh") + ABD = section_mesh.compute_ABD() + # assert np.isclsoe(ABD, expected_ABD).all() + + stiffness_matrix = section_mesh.compute_stiffness_EB(ABD) + assert stiffness_matrix.shape == (4,4) + # assert np.isclsoe(stiffness_matrix, expected_stiffness).all() + + diff --git a/opensg/timo.py b/opensg/timo.py deleted file mode 100644 index 504d657..0000000 --- a/opensg/timo.py +++ /dev/null @@ -1,101 +0,0 @@ - -import ufl -import opensg - - -def local_frame_1D(mesh): - t = ufl.Jacobian(mesh) - t1 = ufl.ufl.as_vector( - [t[0, 0], t[1, 0], t[2, 0]] - ) # [x2-x1,y2-y1,z2-z1] tangent vector for each element. - # Direction of tangenet vector about axis (1,0,0) depends on how we defined the mesh elements. - # For given example, final node-initial node --> clockwise direction about (1,0,0) axis. - - e2 = t1 / ufl.sqrt(ufl.dot(t1, t1)) # converting to unit vector - e1 = ufl.ufl.as_vector([1, 0, 0]) # Beam axis in x direction (global) - e3 = ufl.cross(e1, e2) # normal vector - e3 = e3 / ufl.sqrt(ufl.dot(e3, e3)) - return e1, e2, e3 - - - -def directional_derivative(e): - """Obtain the curvature of curved elements - - Directional derivative of e1 w.r.t. e2 --> d(e1)/d(e2) - ufl.grad (.)- is 3X1 vector --> [d(.)/dx ,d(.)/dy,d(.)/dz] - e2_1 shows derivative of e2 vector w.r.t. e1 vector - - Parameters - ---------- - e : _type_ - local element frame - - Returns - ------- - _type_ - _description_ - """ - # a3,1 - - e1, e2, e3 = e[0], e[1], e[2] - e1_1 = ufl.dot(e1, ufl.grad(e1)) - e1_2 = ufl.dot(e2, ufl.grad(e1)) - e2_1 = ufl.dot(e1, ufl.grad(e2)) - e2_2 = ufl.dot(e2, ufl.grad(e2)) - e3_1 = ufl.dot(e1, ufl.grad(e3)) - e3_2 = ufl.dot(e2, ufl.grad(e3)) - - # Initial Curvatures # - k11 = ufl.dot(e3_1, e1) - k12 = ufl.dot(e3_1, e2) - k21 = ufl.dot(e3_2, e1) - k22 = ufl.dot(e3_2, e2) - k13 = ufl.dot(e1_1, e2) - k23 = ufl.dot(e1_2, e2) - return k11, k12, k21, k22, k13, k23 - - -def local_grad(ee, q): - return ufl.dot(ee, ufl.grad(q)) - - -def ddot(w, d1): - return d1[0] * w[0] + d1[1] * w[1] + d1[2] * w[2] - - -def gamma_h(e, x, w): - d11 = ufl.as_vector([-k11 * d3[ii] + k13 * d2[ii] for ii in range(3)]) - d22 = ufl.as_vector([-k22 * d3[ii] - k23 * d1[ii] for ii in range(3)]) - d12 = ufl.as_vector([-k21 * d3[ii] + k23 * d2[ii] for ii in range(3)]) - d21 = ufl.as_vector([-k12 * d3[ii] - k13 * d1[ii] for ii in range(3)]) - - w_d1 = [opensg.local_grad(e[0], w[i]) for i in range(3)] - w_d2 = [opensg.local_grad(e[1], w[i]) for i in range(3)] - w_d11 = [opensg.local_grad(e[0], w_d1[i]) for i in range(3)] - w_d22 = [opensg.local_grad(e[1], w_d2[i]) for i in range(3)] - - w_d12 = [opensg.local_grad(e[1], w_d1[ii]) for ii in range(3)] - w_d21 = [opensg.local_grad(e[0], w_d2[ii]) for ii in range(3)] - w_11 = [opensg.local_grad(d11, w[ii]) for ii in range(3)] - w_22 = [opensg.local_grad(d22, w[ii]) for ii in range(3)] - w_12 = [opensg.local_grad(d12, w[ii]) for ii in range(3)] - w_21 = [opensg.local_grad(d21, w[ii]) for ii in range(3)] - - G1 = opensg.ddot(w_d1, d1) - G2 = opensg.ddot(w_d2, d2) - G3 = opensg.ddot(w_d1, d2) + opensg.ddot(w_d2, d1) - G4 = -k11 * G1 - k12 * 0.5 * G3 - opensg.ddot(w_d11, d3) + k13 * opensg.ddot(w_d2, d3) - G5 = -k22 * G2 - k21 * 0.5 * G3 - opensg.ddot(w_d22, d3) - k23 * opensg.ddot(w_d1, d3) - G6 = ( - -(k11 + k22) * 0.5 * G3 - - k12 * G2 - - k21 * G1 - + k23 * opensg.ddot(w_d2, d3) - - k13 * opensg.ddot(w_d1, d3) - - opensg.ddot(w_d12, d3) - - opensg.ddot(w_d21, d3) - ) - - E1 = as_tensor([G1, G2, G3, G4, G5, G6]) - return E1 \ No newline at end of file diff --git a/opensg/util.py b/opensg/util.py deleted file mode 100644 index f262dae..0000000 --- a/opensg/util.py +++ /dev/null @@ -1,9 +0,0 @@ -import numpy as np - - -def generate_boundary_markers(xmin, xmax): - def is_left_boundary(x): - return np.isclose(x[0], xmin) - def is_right_boundary(x): - return np.isclose(x[0], xmax) - return is_left_boundary, is_right_boundary \ No newline at end of file diff --git a/pyproject.toml b/pyproject.toml index 712355f..448f7a3 100644 --- a/pyproject.toml +++ b/pyproject.toml @@ -14,7 +14,8 @@ authors = [ # maintainers = [ # { name = "TODO", email = "TODO" }, # ] -requires-python = ">=3.9,<3.11" # this syntax might not work... +requires-python = ">=3.9" # this syntax might not work... +# requires-python = ">=3.9,<3.11" # this syntax might not work... # dependencies = [ # "numpy",