Practical Programming of Finite Element Procedures for Solids and Structures with MATLAB®
From Elasticity to Plasticity
- 1st Edition - September 22, 2023
- Imprint: Elsevier
- Authors: Salar Farahmand-Tabar, Kian Aghani
- Language: English
- Paperback ISBN:9 7 8 - 0 - 4 4 3 - 1 5 3 3 8 - 9
- eBook ISBN:9 7 8 - 0 - 4 4 3 - 1 5 7 8 1 - 3
Practical Programming of Finite Element Procedures for Solids and Structures with MATLAB®: From Elasticity to Plasticity provides readers with step-by-step programming proc… Read more
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Practical Programming of Finite Element Procedures for Solids and Structures with MATLAB®: From Elasticity to Plasticity provides readers with step-by-step programming processes and applications of the finite element method (FEM) in MATLAB®, as well as the underlying theory. The hands-on approach covers a number of structural problems such as linear analysis of solids and structural elements, as well as nonlinear subjects, including elastoplasticity and hyperelasticity. Each chapter begins with foundational topics to provide a solid understanding of the subject and then progresses to more complicated problems with supporting examples for constructing the appropriate program.
The book focuses on topics commonly encountered in civil, mechanical, and aerospace engineering, with special situations in structural analysis, 2D and 3D solids with various mesh elements, surface and body loading, incremental solution process, elastoplasticity, and finite deformation hyperelastic analysis each covered. Code that can be implemented and further extended is also provided.
- Covers both theory and practice of the finite element method (FEM)
- Takes a hands-on approach that provides a variety of both simple and complex problems for readers
- Includes MATLAB® codes that can be immediately implemented as well as extended by readers to improve their own FEM skills
- Provides special cases of structural analysis, elastoplasticity and hyperelasticity problems
Engineering students and researchers dealing with the finite element method, Finite Element analysts, structural designer and analyzer, part manufacturer, Undergraduates, higher educations, and advanced researchers
1. A brief overview of MATLAB® programming language 1.1 Introduction 1.2 Variables 1.3 Vectors 1.3.1 Vector operations 1.3.2 The linspace and logspace functions 1.4 Matrices 1.4.1 Singular, orthogonal, and positive definite matrices 1.4.2 Multi-dimensional matrices 1.4.3 Matrix operations 1.4.4 Matrix transpose and inverse 1.4.5 Concatenating matrices 1.4.6 Reshaping matrices 1.4.7 Solving the systems of linear equations in matrix form 1.5 Export and import data 1.6 Loops 1.6.1 The for loop 1.6.2 The while loop 1.7 Conditional statements 1.8 The switch function 1.9 2D and 3D plotting 1.10 Programming a function 1.10.1 Scripting 1.10.2 Functions 1.11 Chapter overview 2. Matrix analysis of framed structures 2.1 Introduction 2.1.1 Determining the Equation of the Stiffness Method 2.1.2 Forming the Stiffness Matrix of a Structural Member 2.1.3 Applying Boundary Conditions 2.2 Plane Trusses 2.2.1 Programming for the Matrix Analysis of Plane Trusses 2.2.2 Obtaining the Internal Forces of Plane Truss Members 2.3 Space Trusses 2.3.1 Programming for the Matrix Analysis of Space Trusses 2.3.2 Obtaining the Internal Forces of Space Truss Members 2.4 Plane Frames 2.4.1 Programming for the Matrix Analysis of Plane Frames 2.4.2 Obtaining the Internal Forces of Plane Frame Members 2.5 Space Frames 2.5.1 Programming for the Matrix Analysis of Space Frames 2.5.2 Obtaining the Internal Forces of Space Frame Members 2.6 Grids 2.6.1 Programming for the Matrix Analysis of Grids 2.6.2 Obtaining the Internal Forces of Grid Members 2.7 Special Cases 2.7.1 Member Loadings 2.7.2 Support Settlements 2.7.3 Temperature Variations 2.7.4 Non-Compliant Members 2.7.5 Released Members 2.7.6 Elastic Supports 2.8 Chapter Overview 3. Elastic analysis of structures using finite element procedure 3.1 Introduction to Finite Element Procedure 3.2 FEM Programming for Continuum Elements 3.2.1 One-Dimensional elements 3.2.2 Two-Dimensional elements 3.2.3 Three-Dimensional elements 3.3 FEM Programming for Structural Elements 3.3.1 Timoshenko Beam Theory 3.3.2 Mindlin-Reissner Plate Bending Theory 3.4 Chapter Overview 4. Elastoplastic analysis of structures using finite element procedure 4.1 Introduction 4.2 Basics 4.2.1 Stress invariants and deviatoric stresses 4.2.2 Strain invariants and deviatoric strains 4.2.3 Voigt notation 4.2.4 Haigh–Westergaard stress space 4.3 Elastoplasticity 4.3.1 Plastic flow rule 4.3.2 Yield function 4.4 Yield criteria 4.4.1 Von Mises yield criterion 4.4.2 Tresca yield criterion 4.4.3 Evolution of the yield surface 4.5 Hardening laws 4.5.1 Perfect-plasticity 4.5.2 Isotropic hardening 4.5.3 Kinematic hardening 4.5.4 Combined/Mixed kinematic and isotropic hardening 4.6 Stress integration using the von Mises yield criterion 4.6.1 Material with kinematic hardening 4.6.2 Material with isotropic hardening 4.6.3 Material with combined kinematic/isotropic hardening 4.6.4 Material with power-law Isotropic hardening 4.7 Solving non-linear problems 4.7.1 Incremental iterative solution method 4.7.2 General steps 4.7.3 Plasticity algorithm 4.8 Finite Element programming considering the non-linear behavior of materials 4.8.1 Materials with kinematic hardening 4.8.2 Materials with isotropic hardening 4.8.3 Materials with combined isotropic/kinematic hardening 4.8.4 Materials with power-law isotropic hardening 4.9 Extension to Three-Dimensional Elements 4.10 Elastoplastic tangent operator 4.10.1 Tangent operator for one-dimensional elastoplasticity 4.10.2 Tangent operator for multi-dimensional elastoplasticity 4.11 Convergence 4.11.1 rate of convergence 4.12 Chapter overview 5. Finite deformation and hyperelasticity 5.1 Introduction 5.2 Strain and stress measures in finite deformation 5.2.1 Deformation gradient 5.2.2 Lagrangian strain 5.2.3 Cauchy and Piola-Kirchhoff stresses 5.3 Analysis procedures 5.3.1 Introduction to linearization of the equilibrium equation 5.3.2 Total Lagrangian (TL) formulation 5.3.3 Updated Lagrangian (UL) formulation 5.4 Hyperelastic Materials 5.4.1 Strain energy density potential 5.4.2 The F-bar deformation gradient 5.4.3 Types of the strain energy density potential 5.4.4 Obtaining the Cauchy stress for the neo-Hookean, Mooney–Rivlin, and Yeoh models 5.4.5 Fitting hyperelastic material constants from test data 5.4.6 Programming for hyperelastic materials using the neo-Hookean model 5.5 Chapter overview 6. Finite strain 6.1 Introduction 6.2 Finite rotation and objective rates 6.2.1 Objective stress rates 6.2.2 Analysis procedures with the TL formulation and Jaumann stress rate 6.2.3 Analysis procedures with the UL formulation and Jaumann rate 6.2.4 Extension to elastoplasticity 6.3 Finite deformation elastoplasticity 6.3.1 Multiplicative decomposition 6.3.2 Formulation of the Finite deformation elastoplasticity 6.3.3 Integration procedure 6.3.4 Consistent tangent matrix 6.4 Chapter overview 7. Solution to systems of linear equations 7.1 Introduction 7.2 Solution to systems of linear equations 7.2.1 Direct methods 7.2.2 Iterative methods 7.3 Solution to eigen-problems 7.3.1 Transformation methods 7.3.2 Vector iteration methods 7.3.3 Implicit polynomial iteration method 7.3.4 Lanczos iteration method 7.3.5 Subspace iteration method 7.4 Chapter overvie
- Edition: 1
- Published: September 22, 2023
- Imprint: Elsevier
- Language: English
SF
Salar Farahmand-Tabar
Salar Farahmand-Tabar is a structural engineering researcher and university lecturer. His research interests include computational mechanics, structural optimization, bridge engineering, and more. He strives to contribute to structure advancements through the practical use of computational intelligence and optimization in the field of computational mechanics, using programming languages such as MATLAB® and Python. He has published papers in international journals in the field, and collaborates with prestigious journals as a reviewer.
Affiliations and expertise
Department of Civil Engineering, Faculty of Engineering, University of Zanjan, IranKA
Kian Aghani
Kian Aghani contributes to the field of structural engineering as a lecturer and researcher, concentrating on computational mechanics, finite element (FE) procedures, structural analysis, and structure retrofitting. In addition, he works as an FE analyst, specializing in the FE modeling of structural members. He enjoys programming, such as writing Fortran, Python, and MATLAB® subroutines. He strives contributing to technological improvements in engineering by utilizing his skills as an accomplished programmer.
Affiliations and expertise
Department of Civil Engineering, Sahand University of Technology, IranRead Practical Programming of Finite Element Procedures for Solids and Structures with MATLAB® on ScienceDirect