added images and refined readme

Author: AakashR003

iga/validation/buckling_analysis/README.md

@@ -15,7 +15,7 @@ This example presents the validation of buckling analysis in Kratos with IGA ele
 *Structural System [1]*
 
 
-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.
+The cantilever beam is modeled using single NURBS patch with the Shell3pElement. The CAD model of both the patches is constructed with single span B-spline surfaces and has a curve degree of 2 in both axes. 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.
 
 ## Results
 
@@ -30,11 +30,11 @@ The buckling load factors are shown in table below. The corresponding buckling m
 
 | Buckling Mode Shape 1 | Buckling Mode Shape 2 |
 | :---: | :---: |
-| ![Buckling Mode Shape 1](data/Buckling_Mode_Shape_1.png) | ![Buckling Mode Shape 2](data/Buckling_Mode_Shape_2.png) |
+| ![Buckling Mode Shape 1](data/Buckling_Mode_1.png) | ![Buckling Mode Shape 2](data/Buckling_Mode_2.png) |
 
 | Buckling Mode Shape 3 | Buckling Mode Shape 4 |
 | :---: | :---: |
-| ![Buckling Mode Shape 3](data/Buckling_Mode_Shape_3.png) | ![Buckling Mode Shape 4](data/Buckling_Mode_Shape_4.png) |
+| ![Buckling Mode Shape 3](data/Buckling_Mode_3.png) | ![Buckling Mode Shape 4](data/Buckling_Mode_4.png) |
 
 
 

iga/validation/buckling_analysis/data/Buckling_Mode_1.png

@@ -15,7 +15,7 @@ This example presents the validation of geometric non-linear analysis of a canti
 *Structural System [1]*
 
 
-The cantilever beam is modeled using two connected IGA patches with the Shell3pElement. The CAD model of both the patches is constructed with single span B-spline surfaces. The first patch has an curve degree of 2 in both axes and the second patch has an curve degree of 3 in the longitudinal direction and 2 in the transverse direction. Additional refinement is applied in Kratos by increasing the curve degree by 1 in both directions for both patches. Furthermore, h-refinement is applied by inserting 4 knots longitudinally and 3 knots transversely in the first patch, alongside 12 knots longitudinally and 4 knots transversely in the second patch. Hence on the edge where two surfaces gets connected, in the first patch number of elements is 4 and in 2nd patch the number of elements is 5. Therefore they are nonconforming patches. 
+The cantilever beam is modeled using two connected NURBS patches with the Shell3pElement. The CAD model of both the patches is constructed with single span B-spline surfaces. The first patch has an curve degree of 2 in both axes and the second patch has an curve degree of 3 in the longitudinal direction and 2 in the transverse direction. Additional refinement is applied in Kratos by increasing the curve degree by 1 in both directions for both patches. Furthermore, h-refinement is applied by inserting 4 knots longitudinally and 3 knots transversely in the first patch, alongside 12 knots longitudinally and 4 knots transversely in the second patch. Hence on the edge where two surfaces gets connected, in the first patch number of elements is 4 and in 2nd patch the number of elements is 5. Therefore they are nonconforming patches. 
 
 ## Results
 

iga/validation/buckling_analysis/data/Buckling_Mode_2.png

@@ -1,6 +1,6 @@
 {
     "problem_data": {
-        "problem_name": "Nonlinear_cantilever_beam_geometric_nonlinear_analysis",
+        "problem_name": "Cantilever_beam_geometric_nonlinear_analysis",
         "echo_level": 0,
         "parallel_type": "OpenMP",
         "start_time": 0,
@@ -53,7 +53,7 @@
                 "echo_level": 0,
                 "cad_model_part_name": "IgaModelPart",
                 "geometry_file_name": "geometry.cad.json",
-                "output_geometry_file_name": "Nonlinear_cantilever_beam_geometric_nonlinear_analysis_0.georhino.json"
+                "output_geometry_file_name": "Cantilever_beam_geometric_nonlinear_analysis_0.georhino.json"
             }
         },
         {
@@ -79,7 +79,7 @@
                 "kratos_module": "IgaApplication",
                 "python_module": "output_quadrature_domain_process",
                 "Parameters": {
-                    "output_file_name": "Nonlinear_cantilever_beam_geometric_nonlinear_analysis_shell_1_integrationdomain.json",
+                    "output_file_name": "Cantilever_beam_geometric_nonlinear_analysis_shell_1_integrationdomain.json",
                     "model_part_name": "IgaModelPart.StructuralAnalysis_1",
                     "output_geometry_elements": true,
                     "output_geometry_conditions": false
@@ -89,7 +89,7 @@
                 "kratos_module": "IgaApplication",
                 "python_module": "output_quadrature_domain_process",
                 "Parameters": {
-                    "output_file_name": "Nonlinear_cantilever_beam_geometric_nonlinear_analysis_support_2_integrationdomain.json",
+                    "output_file_name": "Cantilever_beam_geometric_nonlinear_analysis_support_2_integrationdomain.json",
                     "model_part_name": "IgaModelPart.Support_2",
                     "output_geometry_elements": false,
                     "output_geometry_conditions": true
@@ -99,7 +99,7 @@
                 "kratos_module": "IgaApplication",
                 "python_module": "output_quadrature_domain_process",
                 "Parameters": {
-                    "output_file_name": "Nonlinear_cantilever_beam_geometric_nonlinear_analysis_coupling_4_integrationdomain.json",
+                    "output_file_name": "Cantilever_beam_geometric_nonlinear_analysis_coupling_4_integrationdomain.json",
                     "model_part_name": "IgaModelPart.Coupling_4",
                     "output_geometry_elements": false,
                     "output_geometry_conditions": false,
@@ -211,7 +211,7 @@
                         "PK2_STRESS",
                         "INTERNAL_MOMENT"
                     ],
-                    "output_file_name": "Nonlinear_cantilever_beam_geometric_nonlinear_analysis_shell_1.post.res",
+                    "output_file_name": "Cantilever_beam_geometric_nonlinear_analysis_shell_1.post.res",
                     "model_part_name": "IgaModelPart.StructuralAnalysis_1",
                     "file_label": "step",
                     "output_control_type": "time",
@@ -226,7 +226,7 @@
                     "integration_point_results": [
                         "REACTION"
                     ],
-                    "output_file_name": "Nonlinear_cantilever_beam_geometric_nonlinear_analysis_support_2.post.res",
+                    "output_file_name": "Cantilever_beam_geometric_nonlinear_analysis_support_2.post.res",
                     "model_part_name": "IgaModelPart.Support_2",
                     "file_label": "step",
                     "output_control_type": "time",
@@ -239,7 +239,7 @@
                 "Parameters": {
                     "nodal_results": [],
                     "integration_point_results": [],
-                    "output_file_name": "Nonlinear_cantilever_beam_geometric_nonlinear_analysis_coupling_4.post.res",
+                    "output_file_name": "Cantilever_beam_geometric_nonlinear_analysis_coupling_4.post.res",
                     "model_part_name": "IgaModelPart.Coupling_4",
                     "file_label": "step",
                     "output_control_type": "time",

iga/validation/buckling_analysis/data/Buckling_Mode_3.png

@@ -0,0 +1,32 @@
+# Cantilever Beam - Multi Patch - Geometric Non-Linear Analysis
+
+**Author:** Aakash Ravichandran
+
+**Kratos version:** 10.4
+
+**Source files:** [Cantilever Beam - Single Patch - Geometric Non-Linear Analysis](https://github.com/KratosMultiphysics/Examples/tree/master/iga/validation/cantilever_beam_multi_patch_non_linear/source)
+
+## Problem definition
+
+This example presents the validation of geometric non-linear analysis of a cantilever beam subjected to a end shear force [1].
+
+![Reference Model](data/Reference_Model.png)
+
+*Structural System [1]*
+
+
+The cantilever beam is modeled using a single NURB patches with the Shell3pElement. The CAD model of the patches is constructed with single span B-spline surface. The patch has an curve degree of 3 in the longitudinal direction and 2 in the transverse direction. Additional refinement is applied in Kratos by increasing the curve degree by 1 in both directions for both patches. Furthermore, h-refinement is applied by inserting 10 knots longitudinally and 3 knots transversely in the patch. 
+
+## Results
+
+The load-displacement curve obtained at the free end is shown in [figure](data/LoadStep_vs_Displacement_XZ.png). This shows a good agreement with the reference [1] - Figure 2a and Table 2. 
+
+| Reference Force vs Displacement [1] | Force vs Displacement - From Kratos |
+| :---: | :---: |
+| ![Reference Force vs Displacement](data/Reference_LoadStep_vs_Displacement_XZ.png) | ![Kratos Force vs Displacement](data/LoadStep_vs_Displacement_XZ.png) |
+
+
+
+## References
+
+1. Sze, K. Y., Liu, X. H., & Lo, S. H. (2004). Popular benchmark problems for geometric nonlinear analysis of shells. *Finite Elements in Analysis and Design*, 40(11), 1551–1569. https://doi.org/10.1016/j.finel.2003.11.001