+ + +References# + + +[hodges1990mixed] + + +Hodges. A mixed variational formulation based on exact intrinsic equations for dynamics of moving beams. International Journal of Solids and Structures, 26(11):1253-1273, 1990. + + + + + + + + +
+ + +GEBT# +GEBT (Geometrically Exact Beam Theory) is a code implementing the mixed variational formulation of the geometrically exact intrinsic beam theory developed by Prof. Hodges of Georgia Institute of Technology [hodges1990mixed], which captures all the geometrical nonlinearities obtainable by a beam model. +It is a companion code of VABS, a general-purpose cross-sectional analysis tool, to enable efficient yet high-fidelity analysis of slender structures, whether they are made of composite materials or not. +For effective design space explorations, we need to simplify the original nonlinear three-dimensional (3D) analysis of slender structures into a two-dimensional (2D) cross-sectional analysis and a one-dimensional (1D) nonlinear beam analysis. +This has been achieved using VABS along with GEBT. +VABS takes a finite element mesh of the cross-section including all the details of geometry and material as inputs to calculate the sectional properties including structural and inertial properties. +These properties are needed for GEBT to predict the global behavior of the slender structure. +The 3D pointwise displacement/strain/stress distribution within the structure can also be recovered by providing outputs from GEBT into VABS. + +Features# +GEBT adopts the mixed variational formulation of the geometrically exact beam theory of Prof. Hodges. +It uses the lowest possible shape functions and the element matrices are calculated exactly without numerical integration. +Since it is a mixed variational formulation, the complete set of variables can be directly calculated. +For example, for static analysis, we can obtain three displacements, three rotations, three forces, and three moments. +GEBT can treat an arbitrary assembly of beams made of arbitrary material and oriented arbitrarily in the 3D space. +GEBT uses dynamic link libraries (DLLs) to encapsulate the analysis capability so that it has true plug-n-play capability which is convenient for integration into other environments. +Now GEBT can be used both as a standalone application and a callable library. +A GEBT manual for developers can be requested separately. + + +Functionalities# +The most recent version of GEBT, GEBT 4.0, has the following functionalities: + +Static, both linear and nonlinear, analysis of beam assemblies with straight and/or initially curved/twisted members under prescribed concentrated or distributed forces/moments or displacements/rotations. +Static, both linear and nonlinear, analysis of beam assemblies with straight members and/or initially curved/twisted with linearly varying sectional properties. +Static, nonlinear, analysis of beam assemblies with straight and/or initially curved/twisted members under prescribed distributed or concentrated follower forces/moments. +Steady state of the dynamic response of beam assemblies with straight and/or initially curved/twisted members under prescribed distributed or concentrated dead or follower forces/moments. +Transient dynamic response of beam assemblies with straight and/or initially curved/twisted members under prescribed distributed or concentrated dead or follower forces/moments. +Sensitivities for the global beam responses for all the aforementioned analysis capabilities. + + +Contents: + +Conventions +Input Guide +Output Guide +References + + + + + + +