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Merge pull request #156 from KratosMultiphysics/Add_IGA_Validation
Add IGA Validation Examples
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‎iga/README.md‎

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# Iga Examples
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This folder contains examples related to Isogeometric Analysis in Kratos.
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They are realized using the IgaApplication
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The Examples are continuously updated and extended
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## Use Cases
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- [External Boundary Circle (NURBS)](https://github.com/KratosMultiphysics/Examples/blob/master/iga/use_cases/external_boundary_circle_with_nurbs/README.md)
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- [IGA Single-Patch Shell in Membrane Action with Weak Supports and Line Load](https://github.com/KratosMultiphysics/Examples/blob/master/iga/use_cases/iga_shell_3p_single_patch/README.md)
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- [3D Laplacian on an Embedded Cube with SBM](https://github.com/KratosMultiphysics/Examples/blob/master/iga/use_cases/laplacian_3d_cube_sbm/README.md)
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## Validation Cases
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# Use Cases
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- [Buckling Analysis - Single Patch - Cantilever Beam](https://github.com/KratosMultiphysics/Examples/blob/master/iga/validation/buckling_analysis_single_patch_cantilever_beam/README.md)
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- [Geometric Linear Analysis - Single Patch - Scordelis-Lo Roof](https://github.com/KratosMultiphysics/Examples/blob/master/iga/validation/geometric_linear_analysis_single_patch_scordelis_lo_roof/README.md)
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- [Geometric Linear Analysis - Trimmed Patch - Plate with Hole](https://github.com/KratosMultiphysics/Examples/blob/master/iga/validation/geometric_linear_analysis_trimmed_patch_plate_with_hole/README.md)
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- [Geometric Non-Linear Analysis - Multi Patch - Cantilever Beam](https://github.com/KratosMultiphysics/Examples/blob/master/iga/validation/geometric_nonlinear_analysis_multi_patch_cantilever_beam/README.md)
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- [Geometric Non-Linear Analysis - Single Patch - Cantilever Beam](https://github.com/KratosMultiphysics/Examples/blob/master/iga/validation/geometric_nonlinear_analysis_single_patch_cantilever_beam/README.md)

‎iga/validation/README.md‎

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This folder contains the validation cases:
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- [Buckling Analysis - Single Patch - Cantilever Beam](buckling_analysis_single_patch_cantilever_beam/README.md)
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- [Geometric Linear Analysis - Single Patch - Scordelis-Lo Roof](geometric_linear_analysis_single_patch_scordelis_lo_roof/README.md)
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- [Geometric Linear Analysis - Trimmed Patch - Plate with Hole](geometric_linear_analysis_trimmed_patch_plate_with_hole/README.md)
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- [Geometric Non-Linear Analysis - Multi Patch - Cantilever Beam](geometric_nonlinear_analysis_multi_patch_cantilever_beam/README.md)
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- [Geometric Non-Linear Analysis - Single Patch - Cantilever Beam](geometric_nonlinear_analysis_single_patch_cantilever_beam/README.md)

‎iga/validation/buckling_analysis_single_patch_cantilever_beam/README.md‎

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# Buckling Analysis - Single Patch - Cantilever Beam
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**Author:** Aakash Ravichandran
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**Kratos version:** 10.2
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**Source files:** [Buckling Analysis - Single Patch - Cantilever Beam](https://github.com/KratosMultiphysics/Examples/tree/master/iga/validation/buckling_analysis_single_patch_cantilever_beam/source)
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## Problem definition
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This example presents the validation of buckling analysis in Kratos with Isogeometric Analysis.
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<div align="center">
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<img src="data/Reference_Model.png" alt="Displacement" width="600">
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*Structural System [1]*
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</div>
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The cantilever beam is modeled using single NURBS patch with the Shell3pElement. The CAD model is constructed with single span B-spline surfaces and has a curve degree of 2 in both directions of the plane. Additional refinement is applied in Kratos, by increasing the curve degree to 4 in both axes and inserting 4 knots in the width and 20 knots along the length of the beam.
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## Results
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The buckling load factors are shown in table below. The corresponding buckling modes are shown in image below.
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<div align="center">
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| | Reference | Kratos |
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| :--- | :--- | :--- |
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| $\lambda_{cr}^{(1)}$ | 4.1123 | 4.06977 |
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| $\lambda_{cr}^{(2)}$ | 16.449 | 16.1693 |
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| $\lambda_{cr}^{(3)}$ | 37.011 | 36.6759 |
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| $\lambda_{cr}^{(4)}$ | 102.81 | 102.106 |
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</div>
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| Buckling Mode Shape 1 | Buckling Mode Shape 2 |
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| :---: | :---: |
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| ![Buckling Mode Shape 1](data/Buckling_Mode_1.png) | ![Buckling Mode Shape 2](data/Buckling_Mode_2.png) |
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| Buckling Mode Shape 3 | Buckling Mode Shape 4 |
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| :---: | :---: |
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| ![Buckling Mode Shape 3](data/Buckling_Mode_3.png) | ![Buckling Mode Shape 4](data/Buckling_Mode_4.png) |
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## References
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1. Altair Engineering, Inc. (2026). *OS-V: 0080 Buckling of Shells and Composites with Offset*. In Altair OptiStruct Verification Problems. [link](https://help.altair.com/hwsolvers/os/topics/solvers/os/buckling_of_shells_and_composites_with_offset_verification_r.htm)

‎iga/validation/buckling_analysis_single_patch_cantilever_beam/data/Buckling_Mode_1.png‎

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‎iga/validation/buckling_analysis_single_patch_cantilever_beam/data/Buckling_Mode_2.png‎

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‎iga/validation/buckling_analysis_single_patch_cantilever_beam/data/Buckling_Mode_3.png‎

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‎iga/validation/buckling_analysis_single_patch_cantilever_beam/data/Buckling_Mode_4.png‎

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‎iga/validation/buckling_analysis_single_patch_cantilever_beam/data/Reference_Model.png‎

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‎iga/validation/buckling_analysis_single_patch_cantilever_beam/source/ProjectParameters.json‎

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{
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"problem_data": {
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"problem_name": "Buckling_Analysis",
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"echo_level": 0,
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"parallel_type": "OpenMP",
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"start_time": 0,
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"end_time": 0.1
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},
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"solver_settings": {
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"model_part_name": "IgaModelPart",
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"domain_size": 1,
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"echo_level": 1,
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"buffer_size": 2,
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"analysis_type": "linear",
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"model_import_settings": {
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"input_type": "use_input_model_part"
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},
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"material_import_settings": {
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"materials_filename": "materials.json"
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},
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"time_stepping": {
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"time_step": 1
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},
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"rotation_dofs": false,
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"reform_dofs_at_each_step": false,
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"line_search": false,
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"compute_reactions": true,
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"clear_storage": false,
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"move_mesh_flag": true,
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"convergence_criterion": "residual_criterion",
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"displacement_relative_tolerance": 0.0001,
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"displacement_absolute_tolerance": 1E-09,
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"residual_relative_tolerance": 0.0001,
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"residual_absolute_tolerance": 1E-09,
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"max_iteration": 1,
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"builder_and_solver_settings" : {
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"advanced_settings": {},
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"use_block_builder": true,
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"use_lagrange_BS": false
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},
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"solver_type": "prebuckling",
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"buckling_settings" : {
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"initial_load_increment" : 1.0,
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"small_load_increment" : 0.0005,
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"path_following_step" : 0.5,
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"convergence_ratio" : 0.05,
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"make_matrices_symmetric" : true
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},
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"eigensolver_settings" : {
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"solver_type" : "eigen_eigensystem",
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"max_iteration" : 1000,
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"tolerance" : 1e-6,
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"number_of_eigenvalues" : 5,
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"echo_level" : 1
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},
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"auxiliary_variables_list": [],
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"auxiliary_dofs_list": [],
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"auxiliary_reaction_list": []
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},
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"modelers": [
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{
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"modeler_name": "CadIoModeler",
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"Parameters": {
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"echo_level": 0,
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"cad_model_part_name": "IgaModelPart",
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"geometry_file_name": "geometry.cad.json",
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"output_geometry_file_name": "Buckling_Analysis_kratos_0.georhino.json"
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}
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},
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{
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"modeler_name": "RefinementModeler",
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"Parameters": {
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"echo_level": 0,
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"physics_file_name": "refinements.iga.json"
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}
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},
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{
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"modeler_name": "IgaModeler",
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"Parameters": {
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"echo_level": 0,
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"cad_model_part_name": "IgaModelPart",
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"analysis_model_part_name": "IgaModelPart",
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"physics_file_name": "physics.iga.json"
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}
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}
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],
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"processes": {
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"additional_processes": [
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{
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"kratos_module": "IgaApplication",
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"python_module": "output_quadrature_domain_process",
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"Parameters": {
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"output_file_name": "Buckling_Analysis_kratos_shell_1_integrationdomain.json",
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"model_part_name": "IgaModelPart.StructuralAnalysis_1",
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"output_geometry_elements": true,
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"output_geometry_conditions": false
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}
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},
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{
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"kratos_module": "IgaApplication",
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"python_module": "output_quadrature_domain_process",
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"Parameters": {
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"output_file_name": "Buckling_Analysis_kratos_support_2_integrationdomain.json",
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"model_part_name": "IgaModelPart.Support_2",
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"output_geometry_elements": false,
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"output_geometry_conditions": true
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}
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},
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{
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"kratos_module": "IgaApplication",
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"python_module": "output_eigen_values_process",
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"Parameters": {
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"output_file_name": "Buckling_Analysis_kratos_eigen_values.post.res",
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"model_part_name": "IgaModelPart"
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}
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}
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],
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"dirichlet_process_list": [
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{
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"kratos_module": "KratosMultiphysics",
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"python_module": "assign_vector_variable_process",
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"Parameters": {
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"model_part_name": "IgaModelPart.Support_2",
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"variable_name": "DISPLACEMENT",
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"value": [
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0
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],
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"interval": [
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"End"
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]
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}
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},
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{
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"kratos_module": "KratosMultiphysics",
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"python_module": "assign_vector_variable_process",
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"Parameters": {
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"model_part_name": "IgaModelPart.Support_2_Rotational",
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"variable_name": "DISPLACEMENT",
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"value": [
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],
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"interval": [
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"End"
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]
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}
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}
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],
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"neumann_process_list": [
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{
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"kratos_module": "KratosMultiphysics",
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"python_module": "assign_vector_variable_to_conditions_process",
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"Parameters": {
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"model_part_name": "IgaModelPart.Load_3",
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"variable_name": "DEAD_LOAD",
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"value": [
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-5,
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],
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"interval": [
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"End"
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]
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}
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}
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]
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},
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"output_processes": {
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"output_process_list": []
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}
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}

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