From 13c1d16cb03032e036eeada2b709ad2c3a2537d7 Mon Sep 17 00:00:00 2001 From: AakashR003 Date: Sat, 28 Mar 2026 03:21:13 +0100 Subject: [PATCH 1/9] Add Validation Cases 1st commit --- iga/README.md | 13 +- iga/validation/README.md | 5 + iga/validation/buckling_analysis/README.md | 43 + .../data/Reference_Model.png | Bin 0 -> 14091 bytes .../source/ProjectParameters.json | 177 +++ .../source/geometry.cad.json | 1 + .../source/kratos_main_iga.py | 11 + .../buckling_analysis/source/materials.json | 21 + .../buckling_analysis/source/physics.iga.json | 50 + .../source/refinements.iga.json | 17 + .../README.md | 32 + .../data/LoadStep_vs_Displacement_XZ.png | Bin 0 -> 65991 bytes .../Reference_LoadStep_vs_Displacement_XZ.png | Bin 0 -> 24999 bytes .../data/Reference_Model.png | Bin 0 -> 24377 bytes .../source/ProjectParameters.json | 251 ++++ .../source/geometry.cad.json | 1190 +++++++++++++++++ .../source/kratos_main_iga.py | 11 + .../source/materials.json | 31 + .../source/physics.iga.json | 64 + .../source/refinements.iga.json | 30 + .../README.md | 26 + .../data/Reference_Model.png | Bin 0 -> 76225 bytes .../source/ProjectParameters.json | 193 +++ .../source/geometry.cad.json | 1013 ++++++++++++++ .../source/kratos_main_iga.py | 11 + .../source/materials.json | 21 + .../source/physics.iga.json | 50 + .../source/refinements.iga.json | 17 + .../README.md | 27 + .../data/Reference_Model.png | Bin 0 -> 45016 bytes .../source/ProjectParameters.json | 176 +++ .../source/geometry.cad.json | 507 +++++++ .../source/kratos_main_iga.py | 11 + .../source/materials.json | 21 + .../source/physics.iga.json | 50 + .../source/refinements.iga.json | 17 + 36 files changed, 4085 insertions(+), 2 deletions(-) create mode 100644 iga/validation/buckling_analysis/README.md create mode 100644 iga/validation/buckling_analysis/data/Reference_Model.png create mode 100644 iga/validation/buckling_analysis/source/ProjectParameters.json create mode 100644 iga/validation/buckling_analysis/source/geometry.cad.json create mode 100644 iga/validation/buckling_analysis/source/kratos_main_iga.py create mode 100644 iga/validation/buckling_analysis/source/materials.json create mode 100644 iga/validation/buckling_analysis/source/physics.iga.json create mode 100644 iga/validation/buckling_analysis/source/refinements.iga.json create mode 100644 iga/validation/cantilever_beam_multi_patch_non_linear/README.md create mode 100644 iga/validation/cantilever_beam_multi_patch_non_linear/data/LoadStep_vs_Displacement_XZ.png create mode 100644 iga/validation/cantilever_beam_multi_patch_non_linear/data/Reference_LoadStep_vs_Displacement_XZ.png create mode 100644 iga/validation/cantilever_beam_multi_patch_non_linear/data/Reference_Model.png create mode 100644 iga/validation/cantilever_beam_multi_patch_non_linear/source/ProjectParameters.json create mode 100644 iga/validation/cantilever_beam_multi_patch_non_linear/source/geometry.cad.json create mode 100644 iga/validation/cantilever_beam_multi_patch_non_linear/source/kratos_main_iga.py create mode 100644 iga/validation/cantilever_beam_multi_patch_non_linear/source/materials.json create mode 100644 iga/validation/cantilever_beam_multi_patch_non_linear/source/physics.iga.json create mode 100644 iga/validation/cantilever_beam_multi_patch_non_linear/source/refinements.iga.json create mode 100644 iga/validation/plate_with_hole_trimmed_patch_linear/README.md create mode 100644 iga/validation/plate_with_hole_trimmed_patch_linear/data/Reference_Model.png create mode 100644 iga/validation/plate_with_hole_trimmed_patch_linear/source/ProjectParameters.json create mode 100644 iga/validation/plate_with_hole_trimmed_patch_linear/source/geometry.cad.json create mode 100644 iga/validation/plate_with_hole_trimmed_patch_linear/source/kratos_main_iga.py create mode 100644 iga/validation/plate_with_hole_trimmed_patch_linear/source/materials.json create mode 100644 iga/validation/plate_with_hole_trimmed_patch_linear/source/physics.iga.json create mode 100644 iga/validation/plate_with_hole_trimmed_patch_linear/source/refinements.iga.json create mode 100644 iga/validation/scordelis_lo_roof_single_patch_linear/README.md create mode 100644 iga/validation/scordelis_lo_roof_single_patch_linear/data/Reference_Model.png create mode 100644 iga/validation/scordelis_lo_roof_single_patch_linear/source/ProjectParameters.json create mode 100644 iga/validation/scordelis_lo_roof_single_patch_linear/source/geometry.cad.json create mode 100644 iga/validation/scordelis_lo_roof_single_patch_linear/source/kratos_main_iga.py create mode 100644 iga/validation/scordelis_lo_roof_single_patch_linear/source/materials.json create mode 100644 iga/validation/scordelis_lo_roof_single_patch_linear/source/physics.iga.json create mode 100644 iga/validation/scordelis_lo_roof_single_patch_linear/source/refinements.iga.json diff --git a/iga/README.md b/iga/README.md index 11e192c2..991d71b9 100644 --- a/iga/README.md +++ b/iga/README.md @@ -1,10 +1,19 @@ # Iga Examples +This folder contains examples related to Isogeometric Analysis in Kratos. + +They are realized using the IgaApplication + +The Examples are continuously updated and extended + ## Use Cases - [External Boundary Circle (NURBS)](https://github.com/KratosMultiphysics/Examples/blob/master/iga/use_cases/external_boundary_circle_with_nurbs/README.md) - [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) - [3D Laplacian on an Embedded Cube with SBM](https://github.com/KratosMultiphysics/Examples/blob/master/iga/use_cases/laplacian_3d_cube_sbm/README.md) ## Validation Cases - -# Use Cases +- [Buckling Analysis](https://github.com/KratosMultiphysics/Examples/blob/master/iga/validation/buckling_analysis/README.md) +- [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) +- [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) +- [Plate with Hole - Trimmed Patch - Linear Analysis](https://github.com/KratosMultiphysics/Examples/blob/master/iga/validation/plate_with_hole_trimmed_patch_linear/README.md) +- [Scordelis-Lo Roof - Single_Patch - Linear Analysis](https://github.com/KratosMultiphysics/Examples/blob/master/iga/validation/scordelis_lo_roof_single_patch_linear/README.md) diff --git a/iga/validation/README.md b/iga/validation/README.md index 78c1f8ac..f189f756 100644 --- a/iga/validation/README.md +++ b/iga/validation/README.md @@ -2,3 +2,8 @@ This folder contains the validation cases: +- [Buckling Analysis](buckling_analysis/README.md) +- [Cantilever Beam - Multi Patch - Geometric Non-Linear Analysis](cantilever_beam_multi_patch_non_linear/README.md) +- [Cantilever Beam - Single Patch - Geometric Non-Linear Analysis](cantilever_beam_single_patch_non_linear/README.md) +- [Plate with Hole - Trimmed Patch - Linear Analysis](plate_with_hole_trimmed_patch_linear/README.md) +- [Scordelis-Lo Roof - Single_Patch - Linear Analysis](scordelis_lo_roof_single_patch_linear/README.md) diff --git a/iga/validation/buckling_analysis/README.md b/iga/validation/buckling_analysis/README.md new file mode 100644 index 00000000..8d1cd681 --- /dev/null +++ b/iga/validation/buckling_analysis/README.md @@ -0,0 +1,43 @@ +# Buckling Analysis + +**Author:** Aakash Ravichandran + +**Kratos version:** 10.2 + +**Source files:** [Buckling Analysis](https://github.com/KratosMultiphysics/Examples/tree/master/iga/validation/buckling_analysis/source) + +## Problem definition + +This example presents the validation of buckling analysis in Kratos with IGA element. + +![Reference Model](data/Reference_Model.png) + +*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. + +## Results + +The buckling load factors are shown in table below. The corresponding buckling modes are shown in image below. + +| Quantity | Reference | Kratos | +| :--- | :--- | :--- | +| $\lambda_{cr}^{(1)}$ | 4.1123 | 4.06977 | +| $\lambda_{cr}^{(2)}$ | 16.449 | 16.1693 | +| $\lambda_{cr}^{(3)}$ | 37.011 | 36.6759 | +| $\lambda_{cr}^{(4)}$ | 102.81 | 102.106 | + +| 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 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) | + + + +## References + +1. Altair Engineering, Inc. (2026). *OS-V: 0080 Buckling of Shells and Composites with Offset*. In Altair OptiStruct Verification Problems. 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simulation = StructuralMechanicsAnalysis(model, parameters) + simulation.Run() diff --git a/iga/validation/plate_with_hole_trimmed_patch_linear/source/materials.json b/iga/validation/plate_with_hole_trimmed_patch_linear/source/materials.json new file mode 100644 index 00000000..319af392 --- /dev/null +++ b/iga/validation/plate_with_hole_trimmed_patch_linear/source/materials.json @@ -0,0 +1,21 @@ +{ + "properties": [ + { + "model_part_name": "IgaModelPart.StructuralAnalysis_1", + "properties_id": 1, + "Material": { + "name": "Steel", + "constitutive_law": { + "name": "LinearElasticPlaneStress2DLaw" + }, + "Variables": { + "THICKNESS": 0.1, + "YOUNG_MODULUS": 10e6, + "POISSON_RATIO": 0, + "DENSITY": 0 + }, + "Tables": {} + } + } + ] +} \ No newline at end of file diff --git a/iga/validation/plate_with_hole_trimmed_patch_linear/source/physics.iga.json b/iga/validation/plate_with_hole_trimmed_patch_linear/source/physics.iga.json new file mode 100644 index 00000000..0eca05fb --- /dev/null +++ b/iga/validation/plate_with_hole_trimmed_patch_linear/source/physics.iga.json @@ -0,0 +1,50 @@ +{ + "element_condition_list": [ + { + "brep_ids": [ + 2 + ], + "geometry_type": "GeometrySurface", + "iga_model_part": "StructuralAnalysis_1", + "parameters": { + "type": "element", + "name": "Shell3pElement", + "shape_function_derivatives_order": 3 + } + }, + { + "brep_id": 2, + "geometry_type": "GeometrySurfaceNodes", + "iga_model_part": "Support_2", + "parameters": { + "local_parameters": [ + 0, + -1 + ] + } + }, + { + "brep_id": 2, + "geometry_type": "GeometrySurfaceVariationNodes", + "iga_model_part": "Support_2_Rotational", + "parameters": { + "local_parameters": [ + 0, + -1 + ] + } + }, + { + "brep_ids": [ + 4 + ], + "geometry_type": "SurfaceEdge", + "iga_model_part": "Load_3", + "parameters": { + "type": "condition", + "name": "LoadCondition", + "shape_function_derivatives_order": 2 + } + } + ] +} \ No newline at end of file diff --git a/iga/validation/plate_with_hole_trimmed_patch_linear/source/refinements.iga.json b/iga/validation/plate_with_hole_trimmed_patch_linear/source/refinements.iga.json new file mode 100644 index 00000000..395afc34 --- /dev/null +++ b/iga/validation/plate_with_hole_trimmed_patch_linear/source/refinements.iga.json @@ -0,0 +1,17 @@ +{ + "refinements": [ + { + "brep_ids": [ + 2 + ], + "geometry_type": "NurbsSurface", + "model_part_name": "IgaModelPart", + "parameters": { + "insert_nb_per_span_u": 15, + "insert_nb_per_span_v": 15, + "increase_degree_u": 2, + "increase_degree_v": 2 + } + } + ] +} \ No newline at end of file diff --git a/iga/validation/scordelis_lo_roof_single_patch_linear/README.md b/iga/validation/scordelis_lo_roof_single_patch_linear/README.md new file mode 100644 index 00000000..ee953c82 --- /dev/null +++ b/iga/validation/scordelis_lo_roof_single_patch_linear/README.md @@ -0,0 +1,27 @@ +# Scordelis-Lo Roof - Single_Patch - Linear Analysis + +**Author:** Aakash Ravichandran + +**Kratos version:** 10.4 + +**Source files:** [Scordelis-Lo Roof - Single_Patch - Linear Analysis](https://github.com/KratosMultiphysics/Examples/tree/master/iga/validation/scordelis_lo_roof_single_patch_linear/source) + +## Problem definition + +This example presents the validation of Scordelis-Lo Roof with Shell3pElement in geometric linear analysis [1]. + +![Reference Model](data/Reference_Model.png) + +*Structural System [1]* + +Load = 90 per unit + +The roof is modeled using single IGA patch with the Shell3pElement. The CAD model is constructed with single span b-splines of curve degree 2 in both axis of the plate. Additional refinement is applied in Kratos, by increasing the curve degree to 4 and inserting 6 knots in each direction of the plate. + +## Results + +The displacement at point A is obtained as -0.3068 units, which is in agreement with the reference value of -0.3024 units. + +## References + +1. Josef M. Kiendl, *Isogeometric Analysis and Shape Optimal Design of Shell Structures*, PhD Dissertation, pp. 51–52. 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| Bin 0 -> 21402 bytes .../data/Buckling_Mode_4.png | Bin 0 -> 34509 bytes .../README.md | 2 +- .../source/ProjectParameters.json | 16 +- .../README.md | 32 + .../data/LoadStep_vs_Displacement_XZ.png | Bin 0 -> 61918 bytes .../data/Model.png | Bin 0 -> 78218 bytes .../Reference_LoadStep_vs_Displacement_XZ.png | Bin 0 -> 24999 bytes .../data/Reference_Model.png | Bin 0 -> 24377 bytes .../source/ProjectParameters.json | 193 ++++++ .../source/geometry.cad.json | 558 ++++++++++++++++++ .../source/kratos_main_iga.py | 11 + .../source/materials.json | 21 + .../source/physics.iga.json | 1 + .../source/refinements.iga.json | 17 + .../README.md | 2 +- .../README.md | 4 +- 20 files changed, 848 insertions(+), 15 deletions(-) create mode 100644 iga/validation/buckling_analysis/data/Buckling_Mode_1.png create mode 100644 iga/validation/buckling_analysis/data/Buckling_Mode_2.png create mode 100644 iga/validation/buckling_analysis/data/Buckling_Mode_3.png create mode 100644 iga/validation/buckling_analysis/data/Buckling_Mode_4.png create mode 100644 iga/validation/cantilever_beam_single_patch_non_linear/README.md create mode 100644 iga/validation/cantilever_beam_single_patch_non_linear/data/LoadStep_vs_Displacement_XZ.png create mode 100644 iga/validation/cantilever_beam_single_patch_non_linear/data/Model.png create mode 100644 iga/validation/cantilever_beam_single_patch_non_linear/data/Reference_LoadStep_vs_Displacement_XZ.png create mode 100644 iga/validation/cantilever_beam_single_patch_non_linear/data/Reference_Model.png create mode 100644 iga/validation/cantilever_beam_single_patch_non_linear/source/ProjectParameters.json create mode 100644 iga/validation/cantilever_beam_single_patch_non_linear/source/geometry.cad.json create mode 100644 iga/validation/cantilever_beam_single_patch_non_linear/source/kratos_main_iga.py create mode 100644 iga/validation/cantilever_beam_single_patch_non_linear/source/materials.json create mode 100644 iga/validation/cantilever_beam_single_patch_non_linear/source/physics.iga.json create mode 100644 iga/validation/cantilever_beam_single_patch_non_linear/source/refinements.iga.json diff --git a/iga/validation/buckling_analysis/README.md b/iga/validation/buckling_analysis/README.md index 8d1cd681..6ffb4498 100644 --- a/iga/validation/buckling_analysis/README.md +++ b/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) | diff --git a/iga/validation/buckling_analysis/data/Buckling_Mode_1.png b/iga/validation/buckling_analysis/data/Buckling_Mode_1.png new file mode 100644 index 0000000000000000000000000000000000000000..19580627eeaa5996d63dc49e2ca9d4c03c2f3214 GIT binary patch literal 17421 zcmeHvc~q0v*Y1mG&??fFDwZf%t)+?*M^M73RYVY~h@eOkwJ0+pLnJXI6|1eN{2Z9X zKokL)0)m1h1h5oQ#xMqf1OXvoNFrpC#3bK&WAAsrb^pKX-aqJCHj;JD*?T|x*~8iI zi+}y<;bQoe=~oa08M+?)iU{!od?!5VZ7L_>W#EH~upO?R)I{i}SHd7$J8qgBnB9&Ws)(I5}`K z#6P6i&#y9=d!f+$w|o2V*e`KioUvB)_+>Be;oGaFClzP7D+=3w)bATI5-tAf&o=i! zvPQEe-cb>IaXfQ_@f%{>=A=d$W88E>=3i+yeKI*DmZ#XLv3~+!7SA6rkHI_- z=3`+#AI#^(`MLn-fq5RxV=&Ky`95*JSDwEwzOJKby6_67h0hOWjDc2v7ZBlX5GiW`=(6yT-Cj@qMrT zG_tPGxeI!4z$1^++tGK2e63F^Uo$;skh_^DIAy>nsc*D*E8TdKzWwv=9j z=c=oc+RXoIENe68Hoo*|Th)9Zt4a7=BXG=t;h(c=V*j`I`aMqO%qB-nlVbdQ3bY z$QGYHdqPsY8u&JLT3`A{UM=pq(Bbbb2kSfh?q?(gi%(X&n0MKa3t|IQZ@t$$`ih>h z{5%d?PLCURCegR7EFxdhc8PmG?h|Svy!hg_tdjt#EMDUakLFd)wkH}x{fi~dF{h?J zx2@sW4mG|m8&~ZH!8CdS2-{=6n{Ir^e3+5GJ3R5h?2%%>EQ#%+xo_xQcg*ExOq>t> zToSrdBY49c`)4O3L(+J!iA&JDOH^Cq4(3y)mD%m)?6dva41%=cn{OGh(0MJ2!aK=ZqwOs>S{Z8*B(K z=Uh0)#TQ-%)-&6w^=zuY%!OrX<|As7pRGgz8G9ucnU4uAan2!_i`3rg4=Z!{^~fdc zW>NccF*Q-~&m!hT_c8If@?KXbRdu7oUfT6a@IX5QOowpBOO~)h1FnlqKZ}!^?Vkr` zN1W>meSC_vj4-qOyg=UnTENh=ExDIrQesR+Pkk6~00+C#yJ$?6WK3bg4Jw$>8hV|~vr475)3=r$9%5EI+N_w3{%vCJ&tyeuU&u zU5h#Ad4dp75bsizQILe^{rZ6$c{WnOPw3dCjfEBKBPAPjmW;76$e$ zYr?6^V|)0pi|?`Pm8Vh#i|iR))az4E_`|jnRTv9r9>16onE-lk(Q8TP1^nQt!AQ3~`S4>YT=l}h_X0bqB=>k~gxe>HGfBCpq-LSN zsOX}PT`~UMH~P^)D~{iHGzkOPxXB6itk(bKc^jtm9Shm+DGPtOmOGQaPRvFb)bG;T z!vw$d&%(g9gMz>Kv(hML$33>CfnautAUljr1+KFe)T@{|@`v@zNWUiLX+OrO;|;>~ z_&sSQax&hn2W*F2);j4=d88K%bbT*Ft{6{FrL~7uoYP~x8$vyElVtjd%J}l|zRYXP z(enMgM@$3RcuX*C$x>t5@3(}Hu*+s2oFutL@>|Cac<#kA_EOrWy7|=}Bzon~PT1o) zd{HKc8J+Jh|IFLaKE=Io+EjGAeMMZohnigytvks0TiWl%BaiOvYsU{B9h^(QXoLCB zH8cZgpWhzW?pNUKNX}>BIxv0A=|5P=*xX^!r^}Hl{*8ULrpq{=ZD0)g)-DXB&==)1 z2&sRgHQ6s8*&_V0e^`klHh)jcVm@`?$8<)qfTxJVkJa^$)o06*v3Ugi(=B? zjx-g?Q7htNGBbUi!U~)P<q7Tg|q|Bh1PoySX_^uKsa&o-g~B2Boh6y~tp4k*el zny{YZ)f@6LUQfkqxuLP=}Q;7u@P;0>jo1U~4^hX{xG5^AKO3c`PE55^fr8p;Ma&63E+T z6X6Q3KRK>xfE>qAJ0@1|t2O(uu^a3y-4C9p`W>-2I&=Y8(}xhaX#$2ZRX7gz&ZLlh zo}uow_Vfvfe+-t^9r(#fzw~Mq@j+C3B{~1)Xmf*M>XRwd7JPk9P!2@J@6=P?_1Q95 zXfi$GqoCJr7na1Td~Q_F4J~VW+Xc&V2D0o{$7F`Di-~~6?Xu zL^L}5w-Ue7vct8^K_Pa_?6?>SK#d36ob2>WDKk$8qItr~mH5Gv%f!xDy9bZZddgjv z2*G|s

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a/iga/validation/cantilever_beam_multi_patch_non_linear/README.md b/iga/validation/cantilever_beam_multi_patch_non_linear/README.md index ca805f2f..e404d155 100644 --- a/iga/validation/cantilever_beam_multi_patch_non_linear/README.md +++ b/iga/validation/cantilever_beam_multi_patch_non_linear/README.md @@ -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 diff --git a/iga/validation/cantilever_beam_multi_patch_non_linear/source/ProjectParameters.json b/iga/validation/cantilever_beam_multi_patch_non_linear/source/ProjectParameters.json index e519cceb..8325e4d1 100644 --- a/iga/validation/cantilever_beam_multi_patch_non_linear/source/ProjectParameters.json +++ b/iga/validation/cantilever_beam_multi_patch_non_linear/source/ProjectParameters.json @@ -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", diff --git a/iga/validation/cantilever_beam_single_patch_non_linear/README.md b/iga/validation/cantilever_beam_single_patch_non_linear/README.md new file mode 100644 index 00000000..f7ac4332 --- /dev/null +++ b/iga/validation/cantilever_beam_single_patch_non_linear/README.md @@ -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). 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z(Ge;e)-HwD&O^&{CHO|L(P*zz+;?y$rx#dIY!K^WbpkMfaiDJ5?tdVQ9M6O9w{o$s z<|?19tgeP)f)CX=waIN}V$D1#R1`+%)OqBd4kc6h@y*W4+*-a)%NDSpc7%4}XlQ@! z!;bulD6%DlvaPW{LFpe}`HEFAw%Wg(?oto8*YKV0=ewvSC29jLre2K=H}Q6Z?Iq<+ zLa?IXQo(FHkOu0J>z*5E53;x#c5gwXj0!u}5!o!eUB?;`de vK%f7=v(*19FIWnAh1BnFT~6M0TBfo1%3#mA9lXHZQ+DszxBZ#E<< Date: Mon, 30 Mar 2026 16:13:32 +0200 Subject: [PATCH 3/9] name change --- .../buckling_analysis/source/ProjectParameters.json | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/iga/validation/buckling_analysis/source/ProjectParameters.json b/iga/validation/buckling_analysis/source/ProjectParameters.json index 66ab94fd..bc7833c4 100644 --- a/iga/validation/buckling_analysis/source/ProjectParameters.json +++ b/iga/validation/buckling_analysis/source/ProjectParameters.json @@ -64,7 +64,7 @@ "echo_level": 0, "cad_model_part_name": "IgaModelPart", "geometry_file_name": "geometry.cad.json", - "output_geometry_file_name": "Buckling_Analysis_0.georhino.json" + "output_geometry_file_name": "Buckling_Analysis_kratos_0.georhino.json" } }, { @@ -90,7 +90,7 @@ "kratos_module": "IgaApplication", "python_module": "output_quadrature_domain_process", "Parameters": { - "output_file_name": "Buckling_Analysis_shell_1_integrationdomain.json", + "output_file_name": "Buckling_Analysis_kratos_shell_1_integrationdomain.json", "model_part_name": "IgaModelPart.StructuralAnalysis_1", "output_geometry_elements": true, "output_geometry_conditions": false @@ -100,7 +100,7 @@ "kratos_module": "IgaApplication", "python_module": "output_quadrature_domain_process", "Parameters": { - "output_file_name": "Buckling_Analysis_support_2_integrationdomain.json", + "output_file_name": "Buckling_Analysis_kratos_support_2_integrationdomain.json", "model_part_name": "IgaModelPart.Support_2", "output_geometry_elements": false, "output_geometry_conditions": true @@ -110,7 +110,7 @@ "kratos_module": "IgaApplication", "python_module": "output_eigen_values_process", "Parameters": { - "output_file_name": "Buckling_Analysis_eigen_values.post.res", + "output_file_name": "Buckling_Analysis_kratos_eigen_values.post.res", "model_part_name": "IgaModelPart" } } From e57e0f209f7172fb9beb8b1bd3e633fcf619d824 Mon Sep 17 00:00:00 2001 From: AakashR003 Date: Mon, 30 Mar 2026 16:24:32 +0200 Subject: [PATCH 4/9] name change --- .../source/ProjectParameters.json | 14 +++++++------- .../source/ProjectParameters.json | 12 ++++++------ .../source/ProjectParameters.json | 10 +++++----- .../source/ProjectParameters.json | 10 +++++----- 4 files changed, 23 insertions(+), 23 deletions(-) diff --git a/iga/validation/cantilever_beam_multi_patch_non_linear/source/ProjectParameters.json b/iga/validation/cantilever_beam_multi_patch_non_linear/source/ProjectParameters.json index 8325e4d1..cb26fcc7 100644 --- a/iga/validation/cantilever_beam_multi_patch_non_linear/source/ProjectParameters.json +++ b/iga/validation/cantilever_beam_multi_patch_non_linear/source/ProjectParameters.json @@ -53,7 +53,7 @@ "echo_level": 0, "cad_model_part_name": "IgaModelPart", "geometry_file_name": "geometry.cad.json", - "output_geometry_file_name": "Cantilever_beam_geometric_nonlinear_analysis_0.georhino.json" + "output_geometry_file_name": "Cantilever_beam_geometric_nonlinear_analysis_kratos_0.georhino.json" } }, { @@ -79,7 +79,7 @@ "kratos_module": "IgaApplication", "python_module": "output_quadrature_domain_process", "Parameters": { - "output_file_name": "Cantilever_beam_geometric_nonlinear_analysis_shell_1_integrationdomain.json", + "output_file_name": "Cantilever_beam_geometric_nonlinear_analysis_kratos_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": "Cantilever_beam_geometric_nonlinear_analysis_support_2_integrationdomain.json", + "output_file_name": "Cantilever_beam_geometric_nonlinear_analysis_kratos_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": "Cantilever_beam_geometric_nonlinear_analysis_coupling_4_integrationdomain.json", + "output_file_name": "Cantilever_beam_geometric_nonlinear_analysis_kratos_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": "Cantilever_beam_geometric_nonlinear_analysis_shell_1.post.res", + "output_file_name": "Cantilever_beam_geometric_nonlinear_analysis_kratos_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": "Cantilever_beam_geometric_nonlinear_analysis_support_2.post.res", + "output_file_name": "Cantilever_beam_geometric_nonlinear_analysis_kratos_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": "Cantilever_beam_geometric_nonlinear_analysis_coupling_4.post.res", + "output_file_name": "Cantilever_beam_geometric_nonlinear_analysis_kratos_coupling_4.post.res", "model_part_name": "IgaModelPart.Coupling_4", "file_label": "step", "output_control_type": "time", diff --git a/iga/validation/cantilever_beam_single_patch_non_linear/source/ProjectParameters.json b/iga/validation/cantilever_beam_single_patch_non_linear/source/ProjectParameters.json index c50c6199..d35dd4e5 100644 --- a/iga/validation/cantilever_beam_single_patch_non_linear/source/ProjectParameters.json +++ b/iga/validation/cantilever_beam_single_patch_non_linear/source/ProjectParameters.json @@ -1,6 +1,6 @@ { "problem_data": { - "problem_name": "NonlinearCant_kratos", + "problem_name": "Cantilever_beam_geometric_nonlinear_analysis_kratos", "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": "NonlinearCant_kratos_0.georhino.json" + "output_geometry_file_name": "Cantilever_beam_geometric_nonlinear_analysis_kratos_0.georhino.json" } }, { @@ -79,7 +79,7 @@ "kratos_module": "IgaApplication", "python_module": "output_quadrature_domain_process", "Parameters": { - "output_file_name": "NonlinearCant_kratos_shell_1_integrationdomain.json", + "output_file_name": "Cantilever_beam_geometric_nonlinear_analysis_kratos_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": "NonlinearCant_kratos_support_2_integrationdomain.json", + "output_file_name": "Cantilever_beam_geometric_nonlinear_analysis_kratos_support_2_integrationdomain.json", "model_part_name": "IgaModelPart.Support_2", "output_geometry_elements": false, "output_geometry_conditions": true @@ -166,7 +166,7 @@ "PK2_STRESS", "INTERNAL_MOMENT" ], - "output_file_name": "NonlinearCant_kratos_shell_1.post.res", + "output_file_name": "Cantilever_beam_geometric_nonlinear_analysis_kratos_shell_1.post.res", "model_part_name": "IgaModelPart.StructuralAnalysis_1", "file_label": "step", "output_control_type": "time", @@ -181,7 +181,7 @@ "integration_point_results": [ "REACTION" ], - "output_file_name": "NonlinearCant_kratos_support_2.post.res", + "output_file_name": "Cantilever_beam_geometric_nonlinear_analysis_kratos_support_2.post.res", "model_part_name": "IgaModelPart.Support_2", "file_label": "step", "output_control_type": "time", diff --git a/iga/validation/plate_with_hole_trimmed_patch_linear/source/ProjectParameters.json b/iga/validation/plate_with_hole_trimmed_patch_linear/source/ProjectParameters.json index 8b8467c6..c59b9f7d 100644 --- a/iga/validation/plate_with_hole_trimmed_patch_linear/source/ProjectParameters.json +++ b/iga/validation/plate_with_hole_trimmed_patch_linear/source/ProjectParameters.json @@ -53,7 +53,7 @@ "echo_level": 0, "cad_model_part_name": "IgaModelPart", "geometry_file_name": "geometry.cad.json", - "output_geometry_file_name": "Plate_with_hole_trimmed_patch_linear_0.georhino.json" + "output_geometry_file_name": "Plate_with_hole_trimmed_patch_linear_kratos_0.georhino.json" } }, { @@ -79,7 +79,7 @@ "kratos_module": "IgaApplication", "python_module": "output_quadrature_domain_process", "Parameters": { - "output_file_name": "Plate_with_hole_trimmed_patch_linear_shell_1_integrationdomain.json", + "output_file_name": "Plate_with_hole_trimmed_patch_linear_kratos_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": "Plate_with_hole_trimmed_patch_linear_support_2_integrationdomain.json", + "output_file_name": "Plate_with_hole_trimmed_patch_linear_kratos_support_2_integrationdomain.json", "model_part_name": "IgaModelPart.Support_2", "output_geometry_elements": false, "output_geometry_conditions": true @@ -166,7 +166,7 @@ "PK2_STRESS", "INTERNAL_MOMENT" ], - "output_file_name": "Plate_with_hole_trimmed_patch_linear_shell_1.post.res", + "output_file_name": "Plate_with_hole_trimmed_patch_linear_kratos_shell_1.post.res", "model_part_name": "IgaModelPart.StructuralAnalysis_1", "file_label": "step", "output_control_type": "time", @@ -181,7 +181,7 @@ "integration_point_results": [ "REACTION" ], - "output_file_name": "Plate_with_hole_trimmed_patch_linear_support_2.post.res", + "output_file_name": "Plate_with_hole_trimmed_patch_linear_kratos_support_2.post.res", "model_part_name": "IgaModelPart.Support_2", "file_label": "step", "output_control_type": "time", diff --git a/iga/validation/scordelis_lo_roof_single_patch_linear/source/ProjectParameters.json b/iga/validation/scordelis_lo_roof_single_patch_linear/source/ProjectParameters.json index 489c8053..67002d6a 100644 --- a/iga/validation/scordelis_lo_roof_single_patch_linear/source/ProjectParameters.json +++ b/iga/validation/scordelis_lo_roof_single_patch_linear/source/ProjectParameters.json @@ -53,7 +53,7 @@ "echo_level": 0, "cad_model_part_name": "IgaModelPart", "geometry_file_name": "geometry.cad.json", - "output_geometry_file_name": "Scordelis_Lo_roof_single_patch_linear_analysis_0.georhino.json" + "output_geometry_file_name": "Scordelis_Lo_roof_single_patch_linear_analysis_kratos_0.georhino.json" } }, { @@ -79,7 +79,7 @@ "kratos_module": "IgaApplication", "python_module": "output_quadrature_domain_process", "Parameters": { - "output_file_name": "Scordelis_Lo_roof_single_patch_linear_analysis_shell_1_integrationdomain.json", + "output_file_name": "Scordelis_Lo_roof_single_patch_linear_analysis_kratos_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": "Scordelis_Lo_roof_single_patch_linear_analysis_support_2_integrationdomain.json", + "output_file_name": "Scordelis_Lo_roof_single_patch_linear_analysis_kratos_support_2_integrationdomain.json", "model_part_name": "IgaModelPart.Support_2", "output_geometry_elements": false, "output_geometry_conditions": true @@ -149,7 +149,7 @@ "PK2_STRESS", "INTERNAL_MOMENT" ], - "output_file_name": "Scordelis_Lo_roof_single_patch_linear_analysis_shell_1.post.res", + "output_file_name": "Scordelis_Lo_roof_single_patch_linear_analysis_kratos_shell_1.post.res", "model_part_name": "IgaModelPart.StructuralAnalysis_1", "file_label": "step", "output_control_type": "time", @@ -164,7 +164,7 @@ "integration_point_results": [ "REACTION" ], - "output_file_name": "Scordelis_Lo_roof_single_patch_linear_analysis_support_2.post.res", + "output_file_name": "Scordelis_Lo_roof_single_patch_linear_analysis_kratos_support_2.post.res", "model_part_name": "IgaModelPart.Support_2", "file_label": "step", "output_control_type": "time", From 7242b453c0b0f2588b862bdb3729191ce8384528 Mon Sep 17 00:00:00 2001 From: AakashR003 Date: Mon, 30 Mar 2026 17:15:18 +0200 Subject: [PATCH 5/9] added_displacement images --- .../README.md | 2 ++ .../data/Model.png | Bin 0 -> 60573 bytes .../README.md | 2 ++ .../README.md | 2 ++ .../data/Model.png | Bin 0 -> 158157 bytes .../README.md | 2 ++ .../data/Model.png | Bin 0 -> 255503 bytes 7 files changed, 8 insertions(+) create mode 100644 iga/validation/cantilever_beam_multi_patch_non_linear/data/Model.png create mode 100644 iga/validation/plate_with_hole_trimmed_patch_linear/data/Model.png create mode 100644 iga/validation/scordelis_lo_roof_single_patch_linear/data/Model.png diff --git a/iga/validation/cantilever_beam_multi_patch_non_linear/README.md b/iga/validation/cantilever_beam_multi_patch_non_linear/README.md index e404d155..11f70e5a 100644 --- a/iga/validation/cantilever_beam_multi_patch_non_linear/README.md +++ b/iga/validation/cantilever_beam_multi_patch_non_linear/README.md @@ -21,6 +21,8 @@ The cantilever beam is modeled using two connected NURBS patches with the Shell3 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. +![Displacement](data/Model.png) + | 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) | diff --git a/iga/validation/cantilever_beam_multi_patch_non_linear/data/Model.png b/iga/validation/cantilever_beam_multi_patch_non_linear/data/Model.png new file mode 100644 index 0000000000000000000000000000000000000000..d7976f05c3bbf589fe6ca2e1b2ca55748b6bfbd0 GIT binary patch literal 60573 zcmeFZi(67z`#!Fj+C=I!m6XTNyuM}Sfo3W-4WzNO$w@nSDi7#5jan(12NXms$9&V& zw`t62Od-uQ#Z#e>3XGaM=_IJ3<^e=A@C2wJ3JBlj%=`Nze%Cc#m+ZCohP@Yiuk}3l zeLwf+-UTlYgY72UwY0PhzCC;Tl9rZ!x|Y^fr)^unmWT$w-C&^|f63z;t=c}bS+KG- z;?((5T3QYH5LK8iSpO{c?3H*eEyx#}|Jnl+X(}zPg|ELoeaa^}WMM)#_E{EQ!`J+I z=b6>fqeqJ$KYsk7A>3=~$gw}8NKtO*f4h6){Gq6yzcGpY`FT`FsHe@z<;NfL7M+^p zns(9L1jfI5&qOtDOk*4~a=Uy7&Y}<7W=z^Bk$Ny-Z@7fx< z+5E#s`?vd_u{WFl_1|)A-!76iX#QW_*2u39Aay_!8S)wXhwsw$Kr_Ad3)0(PwG2R0 zD`h|O;aA!wo6Y5O=?B8M9NTPuEcoZZ|6GcHMg^D(|4fj7V#PmU^PddzPcr=nSNsF9 z{z04n;NyR&!atz!9|HLgm;Ogq0Fm$?h2xQ+a3er zJoqc(Tck>U8P!yO_IvA>$cGK@dv*Wb@#-;oRTI7Ci0d}?59C$FK z6vtiZ!pJzB8?~RwRRaGydJ}dcu`!r{m)$k3a^&t6eJZ+v<3p-p*o(49fmJXw7wqGmEfB{odH z0Uy0n<=%#tSNZ#)mX;+}I}mj?_H`jiQL+KgDk#c_F1ZscAfn*n@wwLm9~Pn-JM@^d z%e&G76D0dJyeiAm55B;j`%>RO->DV5_LSph^cj;NImO8^+~HcK^TJIB@5Rwst&Y~ThT^4vu@ zW8=P^|%T47+!!cD{R&>c|T+yUI z?#KM#l8GCIbKDkR`GnP4T~(F{1z$*?em8 z=Vi^k9l^LOvh~7D!iC|WFGM|%D*q=ax=J;7P2dBAw_y7pb0DnBkXWotb-7wld3v_0zn2f>3b(Q|C ze1@f}f%wW>_Jm#?v3La@E}z@i;_E$8j-Bh{Tu!PgX$_ZsG%tZiWkuwTDIQNZVHG1a z>V!Xyz0F^BzUoHrS$I56O>JhlnlsO|R$L!DIbwNZY~ih<#3^mi+H2&PdiCu?2i&Lk zcGVF#gW)&E=3bBavv>_yejg{tWb6f&Z^&7pR+qFaz7pKrkX{Kyq$qyOCpNteuZRg6 zi|Y5vPwMI-Y)kqP9}&I0_MzxxnpgdKOIOUGb>GCXH8bK#!eA(&HT0ErMlkKeLumAB zcPJFS+U@CpoBR14vH95OwIa>z@;gmJr?Izw%dMPpji$8K^*~qLq65En>^T-s zF>R{h(xPS0qpKa!P?2tb2rXE4W-O~^|40%)WPGHlzv*6+>{VOLhq=drO*>Ylc7dwd zGl3@)dp~*8BUfA*k*~T@^-Gp9+_i=xN38Udf#vI{j;xG{);2fCXvyUHdDny$h0)zW z@$F<-faW%|7P_ELhFx`BGZW+bo8{b>UeT}+K}oEqDCOJwL{Umq{eF2XnNjG0>-<@X zqKhoKw2L&yXla%sS{gv{;I;Ct&|C@M5&ikXQ^z{ZWYI8T^4y zD_n4D^jkQg;UiZLOA)%w!=-##2mXf*eb<*iT_b@?DphEgdOzxG#^ahoL2Z6gnmg zJ?CAe^E^QACv)R-%4JcH>{Dq}G! 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