| Description |
1 online resource (vii, 197 pages) : illustrations |
| Series |
CISM International Centre for Mechanical Sciences ; v. 597 |
|
Courses and lectures ; no. 597.
|
| Contents |
Intro; Preface; Contents; Engineering Notes on Concepts of the Finite Element Method for Elliptic Problems; 1 Introduction; 2 Introductory Example and Propaedeutic Remarks; 3 Classification of the Smoothness of Functions; 3.1 One-Dimensional Example; 3.2 H(div, calB) Hilbert Spaces; 4 Variational Formulations of Linear Elasticity; 4.1 Classical (Bubnov- )Galerkin Formulation; 4.2 Alternative Methods; 4.3 Mixed Variational Frameworks for Linear Elasticity; 5 Finite Element Method; 5.1 Conforming and Non-conforming Finite Elements; 5.2 Example of H-1-FEM for 1D Elliptic Problem |
|
6 Analysis of Mixed Finite Elements6.1 Theoretical Framework; 6.2 Treatment of Saddle Point Problems, Sensitization; 6.3 A Saddle Point Problem-Finite-Dimensional Case; A Sobolev and Hilbert Spaces; References; Sensitivity Analysis Based Automation of Computational Problems; 1 Introduction; 2 Automatic Code Generation with AceGen; 2.1 Hybrid Symbolic-Numerical System AceGen; 2.2 Simultaneous Simplification Procedure; 2.3 Typical Example of Automatic Code Generation with AceGen; 2.4 Automatic Differentiation; 2.5 Automatic Differentiation and Finite Element Method; 3 Sensitivity Analysis |
|
3.1 Design Velocity Field3.2 Arbitrary Sensitivity Parameters; 3.3 Sensitivity Analysis-Code Complexity of AceGen Codes; 4 Applications of Sensitivity Analysis; 4.1 Sensitivity Analysis Based Stochastic Analysis; 4.2 Asymptotic Numerical Methods; 4.3 Optimization; 4.4 Multi-scale Modeling; 5 Conclusions; References; Equilibrated Stress Reconstruction and a Posteriori Error Estimation for Linear Elasticity; 1 Introduction; 2 The Displacement-Pressure Approximations; 3 Stress Approximations; 4 Flux Equilibration; 5 Stress Equilibration; 6 Numerical Illustration; References |
|
A Concept for the Extension of the Assumed Stress Finite Element Method to Hyperelasticity1 Introduction; 2 Assumed Stress Elements in Linear Elasticity; 2.1 Equivalences to EAS Formulations; 3 Assumed Stress Elements for Hyperelasticity; 3.1 Continuum Mechanics; 3.2 Assumed Stress Elements in Hyperelasticity; 4 Remarks on EAS Methods for Finite Deformations; 5 Numerical Examples; 5.1 Bending Plate; 5.2 Cook's Membrane; 5.3 Hourglassing Test; 6 Conclusion; References; A Fully Nonlinear Beam Model of Bernoulli-Euler Type; 1 Introduction; 2 Geometrically Exact Bernoulli-Euler Rod Theory |
|
2.1 Kinematics2.2 Rodrigues Parameterization; 2.3 Incremental Description of the Rotation; 2.4 Strains; 2.5 Strain Rates; 2.6 Stresses; 2.7 Kinetics; 2.8 Weak Form of the Local Equilibrium Equation; 2.9 Statics; 3 Elastic Constitutive Equations; 4 Finite Element Implementation; 5 Conclusions; References; Isogeometric Analysis of Solids in Boundary Representation; 1 Introduction; 2 Parametrization; 3 Governing Equations; 4 Numerical Approximation; 4.1 Boundary Description; 4.2 Scaled Boundary Finite Element Equation; 4.3 NURBS-Based Hybrid Collocation-Galerkin Method |
| Summary |
This book presents new ideas in the framework of novel, finite element discretization schemes for solids and structure, focusing on the mechanical as well as the mathematical background. It also explores the implementation and automation aspects of these technologies. Furthermore, the authors highlight recent developments in mixed finite element formulations in solid mechanics as well as novel techniques for flexible structures at finite deformations. The book also describes automation processes and the application of automatic differentiation technique, including characteristic problems, automatic code generation and code optimization. The combination of these approaches leads to highly efficient numerical codes, which are fundamental for reliable simulations of complicated engineering problems. These techniques are used in a wide range of applications from elasticity, viscoelasticity, plasticity, and viscoplasticity in classical engineering disciplines, such as civil and mechanical engineering, as well as in modern branches like biomechanics and multiphysics |
| Bibliography |
Includes bibliographic references |
| Notes |
4.4 NURBS-Based Galerkin Method |
|
Print version record |
| Subject |
Finite element method.
|
|
Finite element method
|
| Form |
Electronic book
|
| Author |
Schröder, Jörg (Mechanical engineer)
|
|
Pimenta, Paulo de Mattos.
|
| ISBN |
9783030335205 |
|
3030335208 |
|
9783030335212 |
|
3030335216 |
|
9783030335229 |
|
3030335224 |
|
