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Add Validation Cases 1st commit
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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](https://github.com/KratosMultiphysics/Examples/blob/master/iga/validation/buckling_analysis/README.md)
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- [Cantilever Beam - Multi Patch - Geometric Non-Linear Analysis](https://github.com/KratosMultiphysics/Examples/blob/master/iga/validation/cantilever_beam_multi_patch_non_linear/README.md)
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- [Cantilever Beam - Single Patch - Geometric Non-Linear Analysis](https://github.com/KratosMultiphysics/Examples/blob/master/iga/validation/cantilever_beam_single_patch_non_linear/README.md)
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- [Plate with Hole - Trimmed Patch - Linear Analysis](https://github.com/KratosMultiphysics/Examples/blob/master/iga/validation/plate_with_hole_trimmed_patch_linear/README.md)
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- [Scordelis-Lo Roof - Single_Patch - Linear Analysis](https://github.com/KratosMultiphysics/Examples/blob/master/iga/validation/scordelis_lo_roof_single_patch_linear/README.md)

‎iga/validation/README.md‎

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This folder contains the validation cases:
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- [Buckling Analysis](buckling_analysis/README.md)
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- [Cantilever Beam - Multi Patch - Geometric Non-Linear Analysis](cantilever_beam_multi_patch_non_linear/README.md)
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- [Cantilever Beam - Single Patch - Geometric Non-Linear Analysis](cantilever_beam_single_patch_non_linear/README.md)
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- [Plate with Hole - Trimmed Patch - Linear Analysis](plate_with_hole_trimmed_patch_linear/README.md)
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- [Scordelis-Lo Roof - Single_Patch - Linear Analysis](scordelis_lo_roof_single_patch_linear/README.md)

‎iga/validation/buckling_analysis/README.md‎

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# Buckling Analysis
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**Author:** Aakash Ravichandran
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**Kratos version:** 10.2
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**Source files:** [Buckling Analysis](https://github.com/KratosMultiphysics/Examples/tree/master/iga/validation/buckling_analysis/source)
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## Problem definition
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This example presents the validation of buckling analysis in Kratos with IGA element.
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![Reference Model](data/Reference_Model.png)
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*Structural System [1]*
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The cantilever beam is modeled using single IGA patch with the Shell3pElement. The CAD model of both the patches is constructed with single span B-spline surfaces. The patch has an curve degree of 2 in both axes. Additional refinement is applied in Kratos by increasing the curve degree by 2 in both directions. Additional refinement is applied in Kratos, by increasing the curve degree to 4 in both directions 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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| Quantity | 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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| Buckling Mode Shape 1 | Buckling Mode Shape 2 |
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| :---: | :---: |
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| ![Buckling Mode Shape 1](data/Buckling_Mode_Shape_1.png) | ![Buckling Mode Shape 2](data/Buckling_Mode_Shape_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_Shape_3.png) | ![Buckling Mode Shape 4](data/Buckling_Mode_Shape_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/data/Reference_Model.png‎

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‎iga/validation/buckling_analysis/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_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_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_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_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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0,
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0
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],
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"interval": [
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0,
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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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0,
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0,
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0
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],
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"interval": [
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0,
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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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0,
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0
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],
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"interval": [
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0,
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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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}

‎iga/validation/buckling_analysis/source/geometry.cad.json‎

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{"tolerances":{"model_tolerance":0.001},"version_number":1,"breps":[{"brep_id":1,"faces":[{"brep_id":2,"swapped_surface_normal":false,"surface":{"is_trimmed":true,"is_rational":false,"degrees":[2,2],"knot_vectors":[[0,0,0,2,2,2],[0,0,0,100,100,100]],"control_points":[[1,[0,0,0,1]],[2,[0,1,0,1]],[3,[0,2,0,1]],[4,[50,0,0,1]],[5,[50,1,0,1]],[6,[50,2,0,1]],[7,[100,0,0,1]],[8,[100,1,0,1]],[9,[100,2,0,1]]]},"boundary_loops":[{"loop_type":"outer","trimming_curves":[{"trim_index":0,"curve_direction":true,"parameter_curve":{"is_rational":false,"degree":1,"knot_vector":[0,0,2,2],"active_range":[0,2],"control_points":[[10,[0,0,0,1]],[11,[2,0,0,1]]]}},{"trim_index":1,"curve_direction":true,"parameter_curve":{"is_rational":false,"degree":1,"knot_vector":[0,0,100,100],"active_range":[0,100],"control_points":[[12,[2,0,0,1]],[13,[2,100,0,1]]]}},{"trim_index":2,"curve_direction":true,"parameter_curve":{"is_rational":false,"degree":1,"knot_vector":[0,0,2,2],"active_range":[0,2],"control_points":[[14,[2,100,0,1]],[15,[0,100,0,1]]]}},{"trim_index":3,"curve_direction":true,"parameter_curve":{"is_rational":false,"degree":1,"knot_vector":[0,0,100,100],"active_range":[0,100],"control_points":[[16,[0,100,0,1]],[17,[0,0,0,1]]]}}]}],"embedded_loops":[],"embedded_edges":[],"embedded_points":[]}],"edges":[{"brep_id":3,"3d_curve":{"degree":2,"knot_vector":[0,0,0,2,2,2],"active_range":[0,2],"control_points":[[18,[0,0,0,1]],[19,[0,1,0,1]],[20,[0,2,0,1]]]},"topology":[{"brep_id":2,"trim_index":0,"relative_direction":true}]},{"brep_id":4,"3d_curve":{"degree":2,"knot_vector":[0,0,0,100,100,100],"active_range":[0,100],"control_points":[[21,[0,2,0,1]],[22,[50,2,0,1]],[23,[100,2,0,1]]]},"topology":[{"brep_id":2,"trim_index":1,"relative_direction":true}]},{"brep_id":5,"3d_curve":{"degree":2,"knot_vector":[-2,-2,-2,0,0,0],"active_range":[-2,0],"control_points":[[24,[100,2,0,1]],[25,[100,1,0,1]],[26,[100,0,0,1]]]},"topology":[{"brep_id":2,"trim_index":2,"relative_direction":true}]},{"brep_id":6,"3d_curve":{"degree":2,"knot_vector":[-100,-100,-100,0,0,0],"active_range":[-100,0],"control_points":[[27,[100,0,0,1]],[28,[50,0,0,1]],[29,[0,0,0,1]]]},"topology":[{"brep_id":2,"trim_index":3,"relative_direction":true}]}],"vertices":[]}]}

‎iga/validation/buckling_analysis/source/kratos_main_iga.py‎

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import KratosMultiphysics
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import KratosMultiphysics.IgaApplication
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from KratosMultiphysics.StructuralMechanicsApplication.structural_mechanics_analysis import StructuralMechanicsAnalysis
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if __name__ == "__main__":
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with open("ProjectParameters.json",'r') as parameter_file:
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parameters = KratosMultiphysics.Parameters(parameter_file.read())
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model = KratosMultiphysics.Model()
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simulation = StructuralMechanicsAnalysis(model, parameters)
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simulation.Run()

‎iga/validation/buckling_analysis/source/materials.json‎

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{
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"properties": [
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{
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"model_part_name": "IgaModelPart.StructuralAnalysis_1",
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"properties_id": 1,
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"Material": {
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"name": "Steel",
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"constitutive_law": {
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"name": "LinearElasticPlaneStress2DLaw"
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},
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"Variables": {
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"THICKNESS": 1,
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"YOUNG_MODULUS": 1e6,
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"POISSON_RATIO": 0,
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"DENSITY": 1
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},
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"Tables": {}
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}
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}
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]
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}

‎iga/validation/buckling_analysis/source/physics.iga.json‎

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{
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"element_condition_list": [
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{
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"brep_ids": [
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2
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],
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"geometry_type": "GeometrySurface",
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"iga_model_part": "StructuralAnalysis_1",
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"parameters": {
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"type": "element",
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"name": "Shell3pElement",
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"shape_function_derivatives_order": 3
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}
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},
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{
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"brep_id": 2,
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"geometry_type": "GeometrySurfaceNodes",
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"iga_model_part": "Support_2",
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"parameters": {
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"local_parameters": [
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-1,
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0
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]
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}
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},
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{
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"brep_id": 2,
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"geometry_type": "GeometrySurfaceVariationNodes",
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"iga_model_part": "Support_2_Rotational",
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"parameters": {
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"local_parameters": [
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-1,
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0
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]
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}
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},
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{
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"brep_ids": [
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],
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"geometry_type": "SurfaceEdge",
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"iga_model_part": "Load_3",
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"parameters": {
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"type": "condition",
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"name": "LoadCondition",
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"shape_function_derivatives_order": 2
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}
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}
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]
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}

‎iga/validation/buckling_analysis/source/refinements.iga.json‎

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{
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"refinements": [
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{
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"brep_ids": [
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2
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],
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"geometry_type": "NurbsSurface",
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"model_part_name": "IgaModelPart",
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"parameters": {
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"insert_nb_per_span_u": 4,
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"insert_nb_per_span_v": 20,
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"increase_degree_u": 2,
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"increase_degree_v": 2
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}
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}
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]
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}

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