From 130991cbdb9d02f5bb220452e6baec4ace5ae43c Mon Sep 17 00:00:00 2001 From: rubenzorrilla Date: Wed, 4 Oct 2023 15:20:42 +0200 Subject: [PATCH 1/2] Anoeta stadium truss eigenvalue analysis --- .../README.md | 74 + .../data/anoeta_stadium_truss_eigenmode_1.gif | Bin 0 -> 612944 bytes .../data/anoeta_stadium_truss_eigenmode_2.gif | Bin 0 -> 478831 bytes .../data/anoeta_stadium_truss_eigenmode_3.gif | Bin 0 -> 676267 bytes .../data/anoeta_truss_1.png | Bin 0 -> 722833 bytes .../data/anoeta_truss_2.jpeg | Bin 0 -> 84226 bytes .../source/MainKratos.py | 83 + .../source/ProjectParameters.json | 78 + .../source/StructuralMaterials.json | 63 + .../source/anoeta_stadium_truss.mdpa | 2520 +++++++++++++++++ 10 files changed, 2818 insertions(+) create mode 100644 structural_mechanics/use_cases/anoeta_stadium_truss_eigenvalue_analysis/README.md create mode 100644 structural_mechanics/use_cases/anoeta_stadium_truss_eigenvalue_analysis/data/anoeta_stadium_truss_eigenmode_1.gif create mode 100644 structural_mechanics/use_cases/anoeta_stadium_truss_eigenvalue_analysis/data/anoeta_stadium_truss_eigenmode_2.gif create mode 100644 structural_mechanics/use_cases/anoeta_stadium_truss_eigenvalue_analysis/data/anoeta_stadium_truss_eigenmode_3.gif create mode 100644 structural_mechanics/use_cases/anoeta_stadium_truss_eigenvalue_analysis/data/anoeta_truss_1.png create mode 100644 structural_mechanics/use_cases/anoeta_stadium_truss_eigenvalue_analysis/data/anoeta_truss_2.jpeg create mode 100644 structural_mechanics/use_cases/anoeta_stadium_truss_eigenvalue_analysis/source/MainKratos.py create mode 100644 structural_mechanics/use_cases/anoeta_stadium_truss_eigenvalue_analysis/source/ProjectParameters.json create mode 100644 structural_mechanics/use_cases/anoeta_stadium_truss_eigenvalue_analysis/source/StructuralMaterials.json create mode 100644 structural_mechanics/use_cases/anoeta_stadium_truss_eigenvalue_analysis/source/anoeta_stadium_truss.mdpa diff --git a/structural_mechanics/use_cases/anoeta_stadium_truss_eigenvalue_analysis/README.md b/structural_mechanics/use_cases/anoeta_stadium_truss_eigenvalue_analysis/README.md new file mode 100644 index 00000000..25f47bfb --- /dev/null +++ b/structural_mechanics/use_cases/anoeta_stadium_truss_eigenvalue_analysis/README.md @@ -0,0 +1,74 @@ +# Example of eigenvalue analysis - Anoeta stadium truss + +**Author:** Jon Arambarri Rumayor - Rubén Zorrilla Martínez + +**Kratos version:** Current Head + +**Source files:** [Anoeta stadium truss eigenvalue analysis](https://github.com/KratosMultiphysics/Examples/tree/master/structural_mechanics/use_cases/anoeta_stadium_truss_eigenvalue_analysis/source) + +## Problem definition + +This example presents an eigenvalue analysis of the [Anoeta stadium](https://en.wikipedia.org/wiki/Anoeta_Stadium) roof structure. +More specifically, the example focuses on the truss structure that supports the plastic canopy that covers the tiers (see the figures below). + +

+ Anoeta stadium [1] +

+ +

+ Anoeta stadium [2] +

+ +The roof structure is conformed by two curved trusses of almost 200m aligned with the touch lines and two straight trusses of around 155m aligned with the goal lines. +The side trusses intersect the goal ones so the structure can be defined a spatial 3D truss. +While different cross-section areas are used, all the members are made of the same steel, which material properties are +- $E = 206.9$ GPa +- $\rho = 7850.0$ Kg/m^3^ + +Each member is meshed with a single truss element. +On top of these, nodal concentrated mass elements have been added in addition to the truss ones (see the [MainKratos.py](https://github.com/KratosMultiphysics/Examples/tree/master/structural_mechanics/use_cases/anoeta_stadium_truss_eigenvalue_analysis/source/MainKratos.py) file) in order to account for the weight of the plastic canopy. + +Current settings include the calculation of the first five eigenvalues. +If a different number is required, modify the *number_of_eigenvalues* field in the [ProjectParameters.json](https://github.com/KratosMultiphysics/Examples/tree/master/structural_mechanics/use_cases/anoeta_stadium_truss_eigenvalue_analysis/source/ProjectParameters.json). +Last but not least, it is important to mention that the use of the elimination builder and solver needs to be activated to avoid the singularity of the eigenvalue problem by keeping *use_block_builder* option as false in the builder and solver settings section. + +## Results + +By running the [MainKratos.py](https://github.com/KratosMultiphysics/Examples/tree/master/structural_mechanics/use_cases/anoeta_stadium_truss_eigenvalue_analysis/source/MainKratos.py) script the terminal outputs the fist five eigenvalues, which value is + +- $\lambda_{1} = 49.6942$ +- $\lambda_{2} = 54.461$ +- $\lambda_{3} = 66.1036$ +- $\lambda_{4} = 96.0785$ +- $\lambda_{5} = 112.096$ + +corresponding to the frequencies + +- $\f_{1} = 1.3813$ Hz +- $\f_{2} = 1.4374$ Hz +- $\f_{3} = 1.6349$ Hz +- $\f_{4} = 2.012$ Hz +- $\f_{5} = 2.0932$ Hz + +Complementary, a folder with the postprocess of the eigenmodes is also created. +The animation of the first three ones is shown below. + +

+ 1st eigenmode animation. +

+ +

+ 2st eigenmode animation. +

+ +

+ 3st eigenmode animation. +

+ +## References +[1] “Real Sociedad Amplía Los Derechos de Explotación de Anoeta Hasta 2074.” Palco23, Palco23, 17 Feb. 2022, www.palco23.com/clubes/real-sociedad-amplia-los-derechos-de-explotacion-de-anoeta-hasta-2074. + +[2] “La Real Sociedad Amplía El Derecho de Explotación de Anoeta Hasta 2074.” 2Playbook, 16 Feb. 2022, www.2playbook.com/clubes/real-sociedad-amplia-derecho-explotacion-anoeta-hasta-2074_6946_102.html. 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