New Trends in Thin Structures: Formulation, Optimization and Coupled Problems

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PREFACE

Table of Contents

A plate theory as a mean to compute precise 3D solution includung edge effects and related issues

1 Introduction

2 The classical theory of Laminated Plated or CLT

2.1 Description of the plate and of the constitutive relation

2.2 Basic assumptions of the CLT

2.3 The equations of the CLT in general forces

2.4 Formulation of the plate problem

3 Reconstruction of an approximation of the inner 3D solution from the plate solution

3.1 Reconstruction of a quasi-admissible stress field

3.2 Reconstruction of an associated approximation ofthe displacement field

3.3 Example of an isotropic plate loaed only on its lateral surfaces

3.4 Expression and properties of the plated for an isotropic plate loaed only on its lateral surfaces

3.5 Iterative reconstruction of the 3D expression of the displacement and stresses: principle adn notations

4 Edge effects analysis

4.1 Analysis of boundary conditions

4.2 Edge effects computation

4.3 Example with isotropic plate

5 Conclusions

Bibliography

A Fully Nonlinear Thin Shell Model of Kirchhoff-Love Type

1 Introduction

2 Nonlinear Kirchhoff shell theory

2.1 Kinematics

2.2 Strains

2.3 Stresses

2.4 Power

2.5 Weak form of the local equilibrium equation

2.6 Statics

2.7 Boundary conditions

2.7.1 Free and unloaded edges

2.7.2 Fixed but free to rotate edges

2.7.2 Clamped edges

2.8 Complete weak form of the equilibrium equations

2.9 Tangent weak form of the equilibrium equations

3 Elastic constitutive equations

3.1 Plane stress condition

3.2 General elastic isotropic material

3.3 Neo-Hookean material

3.4 Incompressible isotropic elastic material

4 Conclusions

Bibliography

A Bean Finite Element for Nonlinear Analysis of Shape Memory Alloy Devices

1 Introduction

2 Geometrically exact beam theory

2.1 Preliminaries: the rotation manifold

2.2 Reissner's beam model: kinematics

2.3 Reissner's beam model equilibrium

3 Total lagrangian finite element scheme

3.1 Consistent linearization

3.2 Remarks on the chosen finite element model

4 Shape Menory Alloy Constitutive Model

4.1 Time-discrete frame and solutions algorithm

5 Cross section integration algorithm

6 Numerical tests

6.1 Calibration of the proposed scheme

6.2 Cantilever beam

6.3 Elbow beam

6.4 Spring actuator

7 Consluding remarks

Bibliography

A Unifield Approach for the Nonlinear Dynamics of Rods and Shells Using an Exact Conserving Integration Algorithm

1 Introduction

2 Parameterization of the rotation field

3 Rod and Shell Dynamics

3.1 Kinematics

3.2 Strains

3.3 Stresses

3.4 External forces

3.5 Linear and angular momentum

3.6 Equations of motion

3.7 Weak form of the equations of motion

3.8 Internal and kinetic energy

4 Time increment

4.1 Incremental displacements and rotations

4.2 Incremental strains and strain rates

4.3 Increments of momentum, kinetic and strain energy

5 Time integration Algorithm

5.1 Time collocation of the equations of motion

5.2 Time approximations and algorithmic weak form

5.3 Conservation of linear and angular momentum

5.4 Conservation of energy

5.5 Tangent of the weak form

6 Finite element implementation and numerical examples

6.1 Large overall motion of an inclined beam

6.2 Free vibration of a beam in 3-D space

6.3 Dynamics of a satellite-like structure

6.4 Free vibration of a hemispherical shell

7 Conclusions

Bibliography

Advanced Numerical Methods for the Form Finding and Patterning of Membrane Structures

1 Introduction

2 "Correct" Continnum Mechanical Description of Membrane Structures

3 "Classical" Formfinding

3.1 Updated Reference Strategy

3.2 Prestress as shaping parameter

4 Optimezed cutting pattern generation

4.1 Method I: Least-squares optimization

4.2 Method II: Minimization of "stress difference" energy

4.3 Comparison of both methods

5 Intruducing cutting patterns in form finding and structural analysis

5.1 Form finding through cutting patterns

5.2 Structural analysis in consideration of cutting patterns

5.3 Conclusions

Bibliography

Contact between Beams and Shells

1 Introduction

2 Kinematics

2.1 Nomarl contact

2.2 Tangential contact

3 Variation of the Gap in Normal and Tangential Directions

4 Contact Contribution to Weak Form

4.1 Weak form

4.2 Constitutive relations

4.3 Algorithm for friction

5 Finite Element Formulation

6 Contact Search

7 Concluding Remarks

Bibliography

Advances in Computatonal Fluid-Thin-Walled-Structure Interaction Formulations and Solvers

1 Introduction

2 Problem definition

3 Artificial added mass effect

4 Efficient solver for FSI-block preconditionaled Newton-Krylov schemes

4.1 Block Gauss-Seidel process

4.2 Preconditioning based on Gauss-Seidel

4.3 AMG with block Gauss-Seidel smoothing

5 Examples of ALE-based FSI simulations

5.1 Elexible flag behind rigid obstacle

5.2 Abdominal Arotic Aneurysm

6 Robust formulation for large deformation FSI - an XFEM based fixed -gird approach

6.1 Introduction

6.2 Velocity and stress discontinuity across the fluid-structure interface

6.3 Fluid-interface coupling and interface discretization

6.4 Interface-structure coupling and FSI formulation

7 Conclusion

Bibliography

Advances in Subdivision Finite Elements for Thin Shells

1 Introduction

2 Subdivision Schemes for Smooth Interpolation

2.1 Univatiate B-Splines and Subdivision

2.2 Subdivision Surfaces

3 Thin-Shell Equations

3.1 Kinematics

3.2 Thin-shell Energy Functional and its Discretization

4 Examples

4.1 Pinched Cylinder

4.2 Pinched Square Tube

4.3 Spherical Panel with Stiffeners

4.4 Composite Plate

5 Conclusions

Bibliography