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Practical Programming of Finite Element Procedures for Solids and Structures with MATLAB®
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.
Front Cover -- Practical Programming of Finite Element Procedures for Solids and Structures with MATLAB® -- Copyright Page -- Dedication -- Contents -- Preface -- Aims and scope -- Subjects and contents -- 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 Multidimensional 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 -- 1.4.7.1 Matrix left division -- 1.4.7.2 QR solver -- 1.4.7.3 LU and LDL solvers -- 1.4.7.4 Cholesky solver -- 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 -- Exercises -- References -- 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 EXAMPLE 2.1: Determining the general form of the stiffness matrix -- 2.3 Plane trusses -- 2.3.1 Programming for the matrix analysis of plane trusses -- 2.3.2 Obtaining the internal forces of plane truss members -- 2.4 EXAMPLE 2.2: Matrix analysis of a plane truss -- 2.5 EXAMPLE 2.3: Matrix analysis of a plane truss -- 2.6 Space trusses -- 2.6.1 Programming for the matrix analysis of space trusses
2.6.2 Obtaining the internal forces of space truss members -- 2.7 EXAMPLE 2.4: Matrix analysis of a space truss -- 2.8 EXAMPLE 2.5: Matrix analysis of a space truss -- 2.9 Plane frames -- 2.9.1 Programming for the matrix analysis of plane frames -- 2.9.2 Obtaining the internal forces of plane frame members -- 2.10 EXAMPLE 2.6: Matrix analysis of a plane frame -- 2.11 EXAMPLE 2.7: Matrix analysis of a plane frame -- 2.12 Space frames -- 2.12.1 Programming for the matrix analysis of space frames -- 2.12.2 Obtaining the internal forces of space frame members
2.13 EXAMPLE 2.8: Matrix analysis of a space frame -- 2.14 EXAMPLE 2.9: Matrix analysis of a space frame -- 2.15 Grids -- 2.15.1 Programming for the matrix analysis of grids -- 2.15.2 Obtaining the internal forces of grid members -- 2.16 EXAMPLE 2.10: Matrix analysis of a grid structure -- 2.17 EXAMPLE 2.11: Matrix analysis of a grid structure -- 2.18 Special cases -- 2.18.1 Member loadings -- 2.18.1.1 Programming for frames with member loadings -- 2.19 EXAMPLE 2.12: Matrix analysis of a plane frame subjected to a distributed member loading -- 2.19.1 Support settlements
Description based upon print version of record.
2.19.1.1 Programming for frames with support settlement condition