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Andreas Apostolatos
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README.md

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@@ -31,44 +31,44 @@ This folder contains the Live Script addressing the construction of the Finite E
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This folder contains the Live Script addressing the variational formulation and Finite Element approximation of the Timoshenko beam problem
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- **``main_Chapter2_ALinearStraightTimoshenkoBeamElement.mlx``**
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![ALinearStraightTimoshenkoBeamElementDeformation](https://user-images.githubusercontent.com/93076320/220361943-ae52101a-8bb4-4de6-a00a-9e8feb2cd3bd.png)
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![ALinearStraightTimoshenkoBeamElementDeformation](https://user-images.githubusercontent.com/93076320/220361943-ae52101a-8bb4-4de6-a00a-9e8feb2cd3bd.png){width=75%}
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- **``3_ReissnerMindlinPlate/``**\
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This folder contains the Live Scripts addressing the variational formulation and Finite Element approximation of the Reissner-Mindlin plate problem
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- **``3_ReissnerMindlinPlate.mlx``**
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![AReissnerMindlinPlateElementDeformation](https://user-images.githubusercontent.com/93076320/220361987-0e310c93-f57d-4ca3-bea9-c3ce2c922543.png)
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![AReissnerMindlinPlateElementDeformation](https://user-images.githubusercontent.com/93076320/220361987-0e310c93-f57d-4ca3-bea9-c3ce2c922543.png){width=75%}
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- **``4_TransverseShearLocking/``**\
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This folder contains the Live Scripts highlighting and addressing the transverse-shear locking:
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- **``main_Chapter4_Locking_Timoshenko_beam.mlx``**
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- **``main_Chapter4_Locking_ReissnerMindlin_cantilever_plate.mlx``**
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- **``main_Chapter4_Locking_ReissnerMindlin_TwoSidedClampedPlate.mlx``**
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![TransverseShearLocking](https://user-images.githubusercontent.com/93076320/220362061-f5e029b3-4302-474d-8b8d-12bc04d1c859.png)
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![TransverseShearLocking](https://user-images.githubusercontent.com/93076320/220362061-f5e029b3-4302-474d-8b8d-12bc04d1c859.png){width=75%}
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- **``5_WeakDirichletBoundaryConditions/``**\
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This folder contains the Live Script addressing the weak application of Dirichlet boundary conditions for the Timoshenko beam problem
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- **``main_Chapter5_WeakBoundaryConditions_TimoshenkoBeam.mlx``**
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![CrossSectionalRotationLagrangeMultipliers](https://user-images.githubusercontent.com/93076320/220362151-fe73acd1-d2c0-4d60-ac30-e645965bcfc2.png)
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![CrossSectionalRotationPenalty](https://user-images.githubusercontent.com/93076320/220362165-b120d68a-71e5-45bb-acb0-67af9ee5d8e0.png)
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![CrossSectionalRotationLagrangeMultipliers](https://user-images.githubusercontent.com/93076320/220362151-fe73acd1-d2c0-4d60-ac30-e645965bcfc2.png){width=75%}
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![CrossSectionalRotationPenalty](https://user-images.githubusercontent.com/93076320/220362165-b120d68a-71e5-45bb-acb0-67af9ee5d8e0.png){width=75%}
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- **``6_HellingerReissnerFormulation/``**\
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This folder contains the Live Scripts addressing the variational formulation of the Timoshenko beam problem by means of the Hellinger-Reissner principle
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- **``main_Chapter6_HellingerReissnerFormulation_TimoshenkoBeam.mlx``**
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- **``main_Chapter6_HellingerReissnerFormulation_TimoshenkoBeam_Study.mlx``**
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<img width="593" alt="HellingerReissner" src="https://user-images.githubusercontent.com/93076320/220362740-104ea5a5-9b12-4c1f-92b5-a52805b1f966.png">
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<img width="1186" alt="HellingerReissner" src="https://user-images.githubusercontent.com/93076320/220362740-104ea5a5-9b12-4c1f-92b5-a52805b1f966.png">
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![HellingerReissnerDisplacement](https://user-images.githubusercontent.com/93076320/220363390-79ca64ed-746b-4e46-8907-7a32b768c161.png)
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![HellingerReissnerDisplacement](https://user-images.githubusercontent.com/93076320/220363390-79ca64ed-746b-4e46-8907-7a32b768c161.png){width=75%}
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- **``AppexA_EfficiencyConsiderations/``**\
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This folder contains the Live Scripts demonstrating the runtime performance speedup by using page-wise computation of the element stiffness matrices and sparse assembly
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- **``main_AppexA_EfficiencyCondiderationsReissnerMindlinPlate.mlx``**
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- **``main_AppexA_EfficiencyCondiderationsTimoshenkoBeam.mlx``**
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![EfficiencyImprovement](https://user-images.githubusercontent.com/93076320/220362807-240cc55a-d464-4482-9da7-168b4b2d4bf8.png)
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![EfficiencyImprovement](https://user-images.githubusercontent.com/93076320/220362807-240cc55a-d464-4482-9da7-168b4b2d4bf8.png){width=75%}
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- **``TimoshenkoBeam/``**\
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This folder contains all functions needed for the Finite Element discretization of the Timoshenko beam problem

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