Introduction to finite element analysis using MATLAB and Abaqus / Amar Khennane

By: Khennane, Amar [author]Contributor(s): Khennane, Amar [author]Material type: TextTextPublication details: Boca Raton : CRC Press, Taylor & Francis Group, c2013Description: xxix, 457 pages : illustrations ; 26 cmISBN: 9781466580206Subject(s): FINITE ELEMENT METHOD -- DATA PROCESSING | ENGINEERING MATHEMATICS | ABAQUS (ELECTRONIC RESOURCE)LOC classification: TA 347.F5 .K44 2013Online resources: Cover image
Contents:
Machine generated contents note: ch. 1 Introduction -- 1.1. Prologue -- 1.2. Finite Element Analysis and the User -- 1.3. Aim of the Book -- 1.4. Book Organization -- ch. 2 Bar Element -- 2.1. Introduction -- 2.2. One-Dimensional Truss Element -- 2.2.1. Formulation of the Stiffness Matrix: The Direct Approach -- 2.2.2. Two-Dimensional Truss Element -- 2.3. Global Stiffness Matrix Assembly -- 2.3.1. Discretization -- 2.3.2. Elements' Stiffness Matrices in Local Coordinates -- 2.3.3. Elements' Stiffness Matrices in Global Coordinates -- 2.3.3.1. Element 1 -- 2.3.3.2. Element 2 -- 2.3.3.3. Element 3 -- 2.3.4. Global Matrix Assembly -- 2.3.4.1. Only Element 1 Is Present -- 2.3.4.2. Only Element 2 Is Present -- 2.3.4.3. Only Element 3 Is Present -- 2.3.5. Global Force Vector Assembly -- 2.4. Boundary Conditions -- 2.4.1. General Case -- 2.5. Solution of the System of Equations -- 2.6. Support Reactions -- 2.7. Members' Forces -- 2.8.Computer Code: truss.m -- 2.8.1. Data Preparation. Contents note continued: 2.8.1.1. Nodes Coordinates -- 2.8.1.2. Element Connectivity -- 2.8.1.3. Material and Geometrical Properties -- 2.8.1.4. Boundary Conditions -- 2.8.1.5. Loading -- 2.8.2. Element Matrices -- 2.8.2.1. Stiffness Matrix in Local Coordinates -- 2.8.2.2. Transformation Matrix -- 2.8.2.3. Stiffness Matrix in Global Coordinates -- 2.8.2.4."Steering" Vector -- 2.8.3. Assembly of the Global Stiffness Matrix -- 2.8.4. Assembly of the Global Force Vector -- 2.8.5. Solution of the Global System of Equations -- 2.8.6. Nodal Displacements -- 2.8.7. Element Forces -- 2.8.8. Program Scripts -- 2.9. Problems -- 2.9.1. Problem 2.1 -- 2.9.2. Problem 2.2 -- 2.10. Analysis of a Simple Truss with Abaqus -- 2.10.1. Overview of Abaqus -- 2.10.2. Analysis of a Truss with Abaqus Interactive Edition -- 2.10.2.1. Modeling -- 2.10.2.2. Analysis -- 2.10.3. Analysis of a Truss with Abaqus Keyword Edition -- ch. 3 Beam Element -- 3.1. Introduction -- 3.2. Stiffness Matrix -- 3.3. Uniformly Distributed Loading. Contents note continued: 3.4. Internal Hinge -- 3.5.Computer Code: beam.m -- 3.5.1. Data Preparation -- 3.5.1.1. Nodes Coordinates -- 3.5.1.2. Element Connectivity -- 3.5.1.3. Material and Geometrical Properties -- 3.5.1.4. Boundary Conditions -- 3.5.1.5. Internal Hinges -- 3.5.1.6. Loading -- 3.5.1.7. Stiffness Matrix -- 3.5.2. Assembly and Solution of the Global System of Equations -- 3.5.3. Nodal Displacements -- 3.5.4. Element Forces -- 3.6. Problems -- 3.6.1. Problem 3.1 -- 3.6.2. Problem 3.2 -- 3.6.3. Problem 3.3 -- 3.7. Analysis of a Simple Beam with Abaqus -- 3.7.1. Interactive Edition -- 3.7.2. Analysis of a Beam with Abaqus Keyword Edition -- ch. 4 Rigid Jointed Frames -- 4.1. Introduction -- 4.2. Stiffness Matrix of a Beam-Column Element -- 4.3. Stiffness Matrix of a Beam-Column Element in the Presence of Hinged End -- 4.4. Global and Local Coordinate Systems -- 4.5. Global Stiffness Matrix Assembly and Solution for Unknown Displacements -- 4.6.Computer Code: frame.m. Contents note continued: 4.6.1. Data Preparation -- 4.6.1.1. Nodes Coordinates -- 4.6.1.2. Element Connectivity -- 4.6.1.3. Material and Geometrical Properties -- 4.6.1.4. Boundary Conditions -- 4.6.1.5. Internal Hinges -- 4.6.1.6. Loading -- 4.6.2. Element Matrices -- 4.6.2.1. Stiffness Matrix in Local Coordinates -- 4.6.2.2. Transformation Matrix -- 4.6.2.3. Stiffness Matrix in Global Coordinates -- 4.6.2.4."Steering" Vector -- 4.6.2.5. Element Loads -- 4.6.3. Assembly of the Global Stiffness Matrix -- 4.6.4. Solution of the Global System of Equations -- 4.6.5. Nodal Displacements -- 4.6.6. Element Forces -- 4.7. Analysis of a Simple Frame with Abaqus -- 4.7.1. Interactive Edition -- 4.7.2. Keyword Edition -- ch. 5 Stress and Strain Analysis -- 5.1. Introduction -- 5.2. Stress Tensor -- 5.2.1. Definition -- 5.2.2. Stress Tensor-Stress Vector Relationships -- 5.2.3. Transformation of the Stress Tensor -- 5.2.4. Equilibrium Equations -- 5.2.5. Principal Stresses -- 5.2.6.von Mises Stress. Contents note continued: 5.2.7. Normal and Tangential Components of the Stress Vector -- 5.2.8. Mohr's Circles for Stress -- 5.2.9. Engineering Representation of Stress -- 5.3. Deformation and Strain -- 5.3.1. Definition -- 5.3.2. Lagrangian and Eulerian Descriptions -- 5.3.3. Displacement -- 5.3.4. Displacement and Deformation Gradients -- 5.3.5. Green Lagrange Strain Matrix -- 5.3.6. Small Deformation Theory -- 5.3.6.1. Infinitesimal Strain -- 5.3.6.2. Geometrical Interpretation of the Terms of the Strain Tensor -- 5.3.6.3.Compatibility Conditions -- 5.3.7. Principal Strains -- 5.3.8. Transformation of the Strain Tensor -- 5.3.9. Engineering Representation of Strain -- 5.4. Stress-Strain Constitutive Relations -- 5.4.1. Generalized Hooke's Law -- 5.4.2. Material Symmetries -- 5.4.2.1. Symmetry with respect to a Plane -- 5.4.2.2. Symmetry with respect to Three Orthogonal Planes -- 5.4.2.3. Symmetry of Rotation with respect to One Axis -- 5.4.3. Isotropic Material -- 5.4.3.1. Modulus of Elasticity. Contents note continued: 5.4.3.2. Poisson's Ratio -- 5.4.3.3. Shear Modulus -- 5.4.3.4. Bulk Modulus -- 5.4.4. Plane Stress and Plane Strain -- 5.5. Solved Problems -- 5.5.1. Problem 5.1 -- 5.5.2. Problem 5.2 -- 5.5.3. Problem 5.3 -- 5.5.4. Problem 5.4 -- 5.5.5. Problem 5.5 -- 5.5.6. Problem 5.6 -- 5.5.7. Problem 5.7 -- 5.5.8. Problem 5.8 -- ch. 6 Weighted Residual Methods -- 6.1. Introduction -- 6.2. General Formulation -- 6.3. Galerkin Method -- 6.4. Weak Form -- 6.5. Integrating by Part over Two and Three Dimensions (Green Theorem) -- 6.6. Rayleigh Ritz Method -- 6.6.1. Definition -- 6.6.2. Functional Associated with an Integral Form -- 6.6.3. Rayleigh Ritz Method -- 6.6.4. Example of a Natural Functional -- ch. 7 Finite Element Approximation -- 7.1. Introduction -- 7.2. General and Nodal Approximations -- 7.3. Finite Element Approximation -- 7.4. Basic Principles for the Construction of Trial Functions -- 7.4.1.Compatibility Principle -- 7.4.2.Completeness Principle. Contents note continued: 7.5. Two-Dimensional Finite Element Approximation -- 7.5.1. Plane Linear Triangular Element for C° Problems -- 7.5.1.1. Shape Functions -- 7.5.1.2. Reference Element -- 7.5.1.3. Area Coordinates -- 7.5.2. Linear Quadrilateral Element for C° Problems -- 7.5.2.1. Geometrical Transformation -- 7.5.2.2. Construction of a Trial Function over a Linear Quadrilateral Element -- 7.6. Shape Functions of Some Classical Elements for C° Problems -- 7.6.1. One-Dimensional Elements -- 7.6.1.1. Two-Nodded Linear Element -- 7.6.1.2. Three-Nodded Quadratic Element -- 7.6.2. Two-Dimensional Elements -- 7.6.2.1. Four-Nodded Bilinear Quadrilateral -- 7.6.2.2. Eight-Nodded Quadratic Quadrilateral -- 7.6.2.3. Three-Nodded Linear Triangle -- 7.6.2.4. Six-Nodded Quadratic Triangle -- 7.6.3. Three-Dimensional Elements -- 7.6.3.1. Four-Nodded Linear Tetrahedra -- 7.6.3.2. Ten-Nodded Quadratic Tetrahedra -- 7.6.3.3. Eight-Nodded Linear Brick Element -- 7.6.3.4. Twenty-Nodded Quadratic Brick Element. Contents note continued: ch. 8 Numerical Integration -- 8.1. Introduction -- 8.2. Gauss Quadrature -- 8.2.1. Integration over an Arbitrary Interval [a, b] -- 8.2.2. Integration in Two and Three Dimensions -- 8.3. Integration over a Reference Element -- 8.4. Integration over a Triangular Element -- 8.4.1. Simple Formulas -- 8.4.2. Numerical Integration over a Triangular Element -- 8.5. Solved Problems -- 8.5.1. Problem 8.1 -- 8.5.2. Problem 8.2 -- 8.5.3. Problem 8.3 -- ch. 9 Plane Problems -- 9.1. Introduction -- 9.2. Finite Element Formulation for Plane Problems -- 9.3. Spatial Discretization -- 9.4. Constant Strain Triangle -- 9.4.1. Displacement Field -- 9.4.2. Strain Matrix -- 9.4.3. Stiffness Matrix -- 9.4.4. Element Force Vector -- 9.4.4.1. Body Forces -- 9.4.4.2. Traction Forces -- 9.4.4.3. Concentrated Forces -- 9.4.5.Computer Codes Using the Constant Strain Triangle -- 9.4.5.1. Data Preparation -- 9.4.5.2. Nodes Coordinates -- 9.4.5.3. Element Connectivity -- 9.4.5.4. Material Properties. Contents note continued: 9.4.5.5. Boundary Conditions -- 9.4.5.6. Loading -- 9.4.5.7. Main Program -- 9.4.5.8. Element Stiffness Matrix -- 9.4.5.9. Assembly of the Global Stiffness Matrix -- 9.4.5.10. Solution of the Global System of Equations -- 9.4.5.11. Nodal Displacements -- 9.4.5.12. Element Stresses and Strains -- 9.4.5.13. Results and Discussion -- 9.4.5.14. Program with Automatic Mesh Generation -- 9.4.6. Analysis with Abaqus Using the CST -- 9.4.6.1. Interactive Edition -- 9.4.6.2. Keyword Edition -- 9.5. Linear Strain Triangle -- 9.5.1. Displacement Field -- 9.5.2. Strain Matrix -- 9.5.3. Stiffness Matrix -- 9.5.4.Computer Code: LST_PLANE_STRESS_MESH.m -- 9.5.4.1. Numerical Integration of the Stiffness Matrix -- 9.5.4.2.Computation of the Stresses and Strains -- 9.5.5. Analysis with Abaqus Using the 1st -- 9.5.5.1. Interactive Edition -- 9.5.5.2. Keyword Edition -- 9.6. The Bilinear Quadrilateral -- 9.6.1. Displacement Field -- 9.6.2. Strain Matrix -- 9.6.3. Stiffness Matrix. Contents note continued: 9.6.4. Element Force Vector -- 9.6.5.Computer Code: Q4_PLANE_STRESS.m -- 9.6.5.1. Data Preparation -- 9.6.5.2. Main Program -- 9.6.5.3. Integration of the Stiffness Matrix -- 9.6.5.4.Computation of the Stresses and Strains -- 9.6.5.5. Program with Automatic Mesh Generation -- 9.6.6. Analysis with Abaqus Using the Q4 Quadrilateral -- 9.6.6.1. Interactive Edition -- 9.6.6.2. Keyword Edition -- 9.7. The 8-Node Quadrilateral -- 9.7.1. Formulation -- 9.7.2. Equivalent Nodal Forces -- 9.7.3. Program Q8_PLANE_STRESS.m -- 9.7.3.1. Data Preparation -- 9.7.3.2. Main Program -- 9.7.3.3. Integration of the Stiffness Matrix -- 9.7.3.4. Results with the Coarse Mesh -- 9.7.3.5. Program with Automatic Mesh Generation -- 9.7.4. Analysis with Abaqus Using the Q8 Quadrilateral -- 9.8. Solved Problem with MATLAB® -- 9.8.1. Strip Footing with the CST Element -- 9.8.2. Strip Footing with the 1st Element -- 9.8.3. Bridge Pier with the Q8 Element -- ch. 10 Axisymmetric Problems -- 10.1. Definition. Contents note continued: 10.2. Strain-Displacement Relationship -- 10.3. Stress-Strain Relations -- 10.4. Finite Element Formulation -- 10.4.1. Displacement Field -- 10.4.2. Strain Matrix -- 10.4.3. Stiffness Matrix -- 10.4.4. Nodal Force Vectors -- 10.4.4.1. Body Forces -- 10.4.4.2. Surface Forces Vector -- 10.4.4.3. Concentrated Loads -- 10.4.4.4. Example -- 10.5. Programming -- 10.5.1.Computer Code: AXI_SYM_T6.m -- 10.5.1.1. Numerical Integration of the Stiffness Matrix -- 10.5.1.2. Results -- 10.5.2.Computer Code: AXI_SYM_Q8.m -- 10.5.2.1. Numerical Integration of the Stiffness Matrix -- 10.5.2.2. Results -- 10.6. Analysis with Abaqus Using the 8-Node Quadrilateral -- ch. 11 Thin and Thick Plates -- 11.1. Introduction -- 11.2. Thin Plates -- 11.2.1. Differential Equation of Plates Loaded in Bending -- 11.2.2. Governing Equation in terms of Displacement Variables -- 11.3. Thick Plate Theory or Mindlin Plate Theory -- 11.3.1. Stress-Strain Relationship. Contents note continued: 11.4. Linear Elastic Finite Element Analysis of Plates -- 11.4.1. Finite Element Formulation for Thin Plates -- 11.4.1.1. Triangular Element -- 11.4.1.2. Rectangular Element -- 11.4.2. Finite Element Formulation for Thick Plates -- 11.5. Boundary Conditions -- 11.5.1. Simply Supported Edge -- 11.5.2. Built-in or Clamped Edge -- 11.5.3. Free Edge -- 11.6.Computer Program for Thick Plates Using the 8-Node Quadrilateral -- 11.6.1. Main Program: Thick_plate_Q8.m -- 11.6.2. Data Preparation -- 11.6.2.1. Stiffness Matrices -- 11.6.2.2. Boundary Conditions -- 11.6.2.3. Loading -- 11.6.2.4. Numerical Integration of the Stiffness Matrix -- 11.6.3. Results -- 11.6.3.1. Determination of the Resulting Moments and Shear Forces -- 11.6.3.2. Contour Plots -- 11.7. Analysis with Abaqus -- 11.7.1. Preliminary -- 11.7.1.1. Three-Dimensional Shell Elements -- 11.7.1.2. Axisymmetric Shell Elements -- 11.7.1.3. Thick versus Thin Conventional Shell -- 11.7.2. Simply Supported Plate. Contents note continued: 11.7.3. Three-Dimensional Shells.
Summary: "This book introduces the theory of the finite element method using a balanced approach between its mathematical formulations and programming implementation. The computer implementation is carried out using MATLAB, while the practical applications are carried out in both MATLAB and Abaqus. All of the key steps are presented in great detail. MATLAB will allow the reader to focus on the finite element method by alleviating the programming burden. Detailed step-by-step procedures for solving sample problems with Abaqus interactive and keyword editions are provided at the end of each chapter"-- Provided by publisher.
Item type: Books
Tags from this library: No tags from this library for this title. Log in to add tags.
    Average rating: 0.0 (0 votes)
Item type Current library Home library Collection Shelving location Call number Copy number Status Date due Barcode
Books Books LRC - Main
National University - Manila
Computer Engineering General Circulation GC TA 347.F5 .K44 2013 (Browse shelf (Opens below)) c.1 Available NULIB000014039

Includes bibliographical references and index.

Machine generated contents note: ch. 1 Introduction --
1.1. Prologue --
1.2. Finite Element Analysis and the User --
1.3. Aim of the Book --
1.4. Book Organization --
ch. 2 Bar Element --
2.1. Introduction --
2.2. One-Dimensional Truss Element --
2.2.1. Formulation of the Stiffness Matrix: The Direct Approach --
2.2.2. Two-Dimensional Truss Element --
2.3. Global Stiffness Matrix Assembly --
2.3.1. Discretization --
2.3.2. Elements' Stiffness Matrices in Local Coordinates --
2.3.3. Elements' Stiffness Matrices in Global Coordinates --
2.3.3.1. Element 1 --
2.3.3.2. Element 2 --
2.3.3.3. Element 3 --
2.3.4. Global Matrix Assembly --
2.3.4.1. Only Element 1 Is Present --
2.3.4.2. Only Element 2 Is Present --
2.3.4.3. Only Element 3 Is Present --
2.3.5. Global Force Vector Assembly --
2.4. Boundary Conditions --
2.4.1. General Case --
2.5. Solution of the System of Equations --
2.6. Support Reactions --
2.7. Members' Forces --
2.8.Computer Code: truss.m --
2.8.1. Data Preparation. Contents note continued: 2.8.1.1. Nodes Coordinates --
2.8.1.2. Element Connectivity --
2.8.1.3. Material and Geometrical Properties --
2.8.1.4. Boundary Conditions --
2.8.1.5. Loading --
2.8.2. Element Matrices --
2.8.2.1. Stiffness Matrix in Local Coordinates --
2.8.2.2. Transformation Matrix --
2.8.2.3. Stiffness Matrix in Global Coordinates --
2.8.2.4."Steering" Vector --
2.8.3. Assembly of the Global Stiffness Matrix --
2.8.4. Assembly of the Global Force Vector --
2.8.5. Solution of the Global System of Equations --
2.8.6. Nodal Displacements --
2.8.7. Element Forces --
2.8.8. Program Scripts --
2.9. Problems --
2.9.1. Problem 2.1 --
2.9.2. Problem 2.2 --
2.10. Analysis of a Simple Truss with Abaqus --
2.10.1. Overview of Abaqus --
2.10.2. Analysis of a Truss with Abaqus Interactive Edition --
2.10.2.1. Modeling --
2.10.2.2. Analysis --
2.10.3. Analysis of a Truss with Abaqus Keyword Edition --
ch. 3 Beam Element --
3.1. Introduction --
3.2. Stiffness Matrix --
3.3. Uniformly Distributed Loading. Contents note continued: 3.4. Internal Hinge --
3.5.Computer Code: beam.m --
3.5.1. Data Preparation --
3.5.1.1. Nodes Coordinates --
3.5.1.2. Element Connectivity --
3.5.1.3. Material and Geometrical Properties --
3.5.1.4. Boundary Conditions --
3.5.1.5. Internal Hinges --
3.5.1.6. Loading --
3.5.1.7. Stiffness Matrix --
3.5.2. Assembly and Solution of the Global System of Equations --
3.5.3. Nodal Displacements --
3.5.4. Element Forces --
3.6. Problems --
3.6.1. Problem 3.1 --
3.6.2. Problem 3.2 --
3.6.3. Problem 3.3 --
3.7. Analysis of a Simple Beam with Abaqus --
3.7.1. Interactive Edition --
3.7.2. Analysis of a Beam with Abaqus Keyword Edition --
ch. 4 Rigid Jointed Frames --
4.1. Introduction --
4.2. Stiffness Matrix of a Beam-Column Element --
4.3. Stiffness Matrix of a Beam-Column Element in the Presence of Hinged End --
4.4. Global and Local Coordinate Systems --
4.5. Global Stiffness Matrix Assembly and Solution for Unknown Displacements --
4.6.Computer Code: frame.m. Contents note continued: 4.6.1. Data Preparation --
4.6.1.1. Nodes Coordinates --
4.6.1.2. Element Connectivity --
4.6.1.3. Material and Geometrical Properties --
4.6.1.4. Boundary Conditions --
4.6.1.5. Internal Hinges --
4.6.1.6. Loading --
4.6.2. Element Matrices --
4.6.2.1. Stiffness Matrix in Local Coordinates --
4.6.2.2. Transformation Matrix --
4.6.2.3. Stiffness Matrix in Global Coordinates --
4.6.2.4."Steering" Vector --
4.6.2.5. Element Loads --
4.6.3. Assembly of the Global Stiffness Matrix --
4.6.4. Solution of the Global System of Equations --
4.6.5. Nodal Displacements --
4.6.6. Element Forces --
4.7. Analysis of a Simple Frame with Abaqus --
4.7.1. Interactive Edition --
4.7.2. Keyword Edition --
ch. 5 Stress and Strain Analysis --
5.1. Introduction --
5.2. Stress Tensor --
5.2.1. Definition --
5.2.2. Stress Tensor-Stress Vector Relationships --
5.2.3. Transformation of the Stress Tensor --
5.2.4. Equilibrium Equations --
5.2.5. Principal Stresses --
5.2.6.von Mises Stress. Contents note continued: 5.2.7. Normal and Tangential Components of the Stress Vector --
5.2.8. Mohr's Circles for Stress --
5.2.9. Engineering Representation of Stress --
5.3. Deformation and Strain --
5.3.1. Definition --
5.3.2. Lagrangian and Eulerian Descriptions --
5.3.3. Displacement --
5.3.4. Displacement and Deformation Gradients --
5.3.5. Green Lagrange Strain Matrix --
5.3.6. Small Deformation Theory --
5.3.6.1. Infinitesimal Strain --
5.3.6.2. Geometrical Interpretation of the Terms of the Strain Tensor --
5.3.6.3.Compatibility Conditions --
5.3.7. Principal Strains --
5.3.8. Transformation of the Strain Tensor --
5.3.9. Engineering Representation of Strain --
5.4. Stress-Strain Constitutive Relations --
5.4.1. Generalized Hooke's Law --
5.4.2. Material Symmetries --
5.4.2.1. Symmetry with respect to a Plane --
5.4.2.2. Symmetry with respect to Three Orthogonal Planes --
5.4.2.3. Symmetry of Rotation with respect to One Axis --
5.4.3. Isotropic Material --
5.4.3.1. Modulus of Elasticity. Contents note continued: 5.4.3.2. Poisson's Ratio --
5.4.3.3. Shear Modulus --
5.4.3.4. Bulk Modulus --
5.4.4. Plane Stress and Plane Strain --
5.5. Solved Problems --
5.5.1. Problem 5.1 --
5.5.2. Problem 5.2 --
5.5.3. Problem 5.3 --
5.5.4. Problem 5.4 --
5.5.5. Problem 5.5 --
5.5.6. Problem 5.6 --
5.5.7. Problem 5.7 --
5.5.8. Problem 5.8 --
ch. 6 Weighted Residual Methods --
6.1. Introduction --
6.2. General Formulation --
6.3. Galerkin Method --
6.4. Weak Form --
6.5. Integrating by Part over Two and Three Dimensions (Green Theorem) --
6.6. Rayleigh Ritz Method --
6.6.1. Definition --
6.6.2. Functional Associated with an Integral Form --
6.6.3. Rayleigh Ritz Method --
6.6.4. Example of a Natural Functional --
ch. 7 Finite Element Approximation --
7.1. Introduction --
7.2. General and Nodal Approximations --
7.3. Finite Element Approximation --
7.4. Basic Principles for the Construction of Trial Functions --
7.4.1.Compatibility Principle --
7.4.2.Completeness Principle. Contents note continued: 7.5. Two-Dimensional Finite Element Approximation --
7.5.1. Plane Linear Triangular Element for C° Problems --
7.5.1.1. Shape Functions --
7.5.1.2. Reference Element --
7.5.1.3. Area Coordinates --
7.5.2. Linear Quadrilateral Element for C° Problems --
7.5.2.1. Geometrical Transformation --
7.5.2.2. Construction of a Trial Function over a Linear Quadrilateral Element --
7.6. Shape Functions of Some Classical Elements for C° Problems --
7.6.1. One-Dimensional Elements --
7.6.1.1. Two-Nodded Linear Element --
7.6.1.2. Three-Nodded Quadratic Element --
7.6.2. Two-Dimensional Elements --
7.6.2.1. Four-Nodded Bilinear Quadrilateral --
7.6.2.2. Eight-Nodded Quadratic Quadrilateral --
7.6.2.3. Three-Nodded Linear Triangle --
7.6.2.4. Six-Nodded Quadratic Triangle --
7.6.3. Three-Dimensional Elements --
7.6.3.1. Four-Nodded Linear Tetrahedra --
7.6.3.2. Ten-Nodded Quadratic Tetrahedra --
7.6.3.3. Eight-Nodded Linear Brick Element --
7.6.3.4. Twenty-Nodded Quadratic Brick Element. Contents note continued: ch. 8 Numerical Integration --
8.1. Introduction --
8.2. Gauss Quadrature --
8.2.1. Integration over an Arbitrary Interval [a, b] --
8.2.2. Integration in Two and Three Dimensions --
8.3. Integration over a Reference Element --
8.4. Integration over a Triangular Element --
8.4.1. Simple Formulas --
8.4.2. Numerical Integration over a Triangular Element --
8.5. Solved Problems --
8.5.1. Problem 8.1 --
8.5.2. Problem 8.2 --
8.5.3. Problem 8.3 --
ch. 9 Plane Problems --
9.1. Introduction --
9.2. Finite Element Formulation for Plane Problems --
9.3. Spatial Discretization --
9.4. Constant Strain Triangle --
9.4.1. Displacement Field --
9.4.2. Strain Matrix --
9.4.3. Stiffness Matrix --
9.4.4. Element Force Vector --
9.4.4.1. Body Forces --
9.4.4.2. Traction Forces --
9.4.4.3. Concentrated Forces --
9.4.5.Computer Codes Using the Constant Strain Triangle --
9.4.5.1. Data Preparation --
9.4.5.2. Nodes Coordinates --
9.4.5.3. Element Connectivity --
9.4.5.4. Material Properties. Contents note continued: 9.4.5.5. Boundary Conditions --
9.4.5.6. Loading --
9.4.5.7. Main Program --
9.4.5.8. Element Stiffness Matrix --
9.4.5.9. Assembly of the Global Stiffness Matrix --
9.4.5.10. Solution of the Global System of Equations --
9.4.5.11. Nodal Displacements --
9.4.5.12. Element Stresses and Strains --
9.4.5.13. Results and Discussion --
9.4.5.14. Program with Automatic Mesh Generation --
9.4.6. Analysis with Abaqus Using the CST --
9.4.6.1. Interactive Edition --
9.4.6.2. Keyword Edition --
9.5. Linear Strain Triangle --
9.5.1. Displacement Field --
9.5.2. Strain Matrix --
9.5.3. Stiffness Matrix --
9.5.4.Computer Code: LST_PLANE_STRESS_MESH.m --
9.5.4.1. Numerical Integration of the Stiffness Matrix --
9.5.4.2.Computation of the Stresses and Strains --
9.5.5. Analysis with Abaqus Using the 1st --
9.5.5.1. Interactive Edition --
9.5.5.2. Keyword Edition --
9.6. The Bilinear Quadrilateral --
9.6.1. Displacement Field --
9.6.2. Strain Matrix --
9.6.3. Stiffness Matrix. Contents note continued: 9.6.4. Element Force Vector --
9.6.5.Computer Code: Q4_PLANE_STRESS.m --
9.6.5.1. Data Preparation --
9.6.5.2. Main Program --
9.6.5.3. Integration of the Stiffness Matrix --
9.6.5.4.Computation of the Stresses and Strains --
9.6.5.5. Program with Automatic Mesh Generation --
9.6.6. Analysis with Abaqus Using the Q4 Quadrilateral --
9.6.6.1. Interactive Edition --
9.6.6.2. Keyword Edition --
9.7. The 8-Node Quadrilateral --
9.7.1. Formulation --
9.7.2. Equivalent Nodal Forces --
9.7.3. Program Q8_PLANE_STRESS.m --
9.7.3.1. Data Preparation --
9.7.3.2. Main Program --
9.7.3.3. Integration of the Stiffness Matrix --
9.7.3.4. Results with the Coarse Mesh --
9.7.3.5. Program with Automatic Mesh Generation --
9.7.4. Analysis with Abaqus Using the Q8 Quadrilateral --
9.8. Solved Problem with MATLAB® --
9.8.1. Strip Footing with the CST Element --
9.8.2. Strip Footing with the 1st Element --
9.8.3. Bridge Pier with the Q8 Element --
ch. 10 Axisymmetric Problems --
10.1. Definition. Contents note continued: 10.2. Strain-Displacement Relationship --
10.3. Stress-Strain Relations --
10.4. Finite Element Formulation --
10.4.1. Displacement Field --
10.4.2. Strain Matrix --
10.4.3. Stiffness Matrix --
10.4.4. Nodal Force Vectors --
10.4.4.1. Body Forces --
10.4.4.2. Surface Forces Vector --
10.4.4.3. Concentrated Loads --
10.4.4.4. Example --
10.5. Programming --
10.5.1.Computer Code: AXI_SYM_T6.m --
10.5.1.1. Numerical Integration of the Stiffness Matrix --
10.5.1.2. Results --
10.5.2.Computer Code: AXI_SYM_Q8.m --
10.5.2.1. Numerical Integration of the Stiffness Matrix --
10.5.2.2. Results --
10.6. Analysis with Abaqus Using the 8-Node Quadrilateral --
ch. 11 Thin and Thick Plates --
11.1. Introduction --
11.2. Thin Plates --
11.2.1. Differential Equation of Plates Loaded in Bending --
11.2.2. Governing Equation in terms of Displacement Variables --
11.3. Thick Plate Theory or Mindlin Plate Theory --
11.3.1. Stress-Strain Relationship. Contents note continued: 11.4. Linear Elastic Finite Element Analysis of Plates --
11.4.1. Finite Element Formulation for Thin Plates --
11.4.1.1. Triangular Element --
11.4.1.2. Rectangular Element --
11.4.2. Finite Element Formulation for Thick Plates --
11.5. Boundary Conditions --
11.5.1. Simply Supported Edge --
11.5.2. Built-in or Clamped Edge --
11.5.3. Free Edge --
11.6.Computer Program for Thick Plates Using the 8-Node Quadrilateral --
11.6.1. Main Program: Thick_plate_Q8.m --
11.6.2. Data Preparation --
11.6.2.1. Stiffness Matrices --
11.6.2.2. Boundary Conditions --
11.6.2.3. Loading --
11.6.2.4. Numerical Integration of the Stiffness Matrix --
11.6.3. Results --
11.6.3.1. Determination of the Resulting Moments and Shear Forces --
11.6.3.2. Contour Plots --
11.7. Analysis with Abaqus --
11.7.1. Preliminary --
11.7.1.1. Three-Dimensional Shell Elements --
11.7.1.2. Axisymmetric Shell Elements --
11.7.1.3. Thick versus Thin Conventional Shell --
11.7.2. Simply Supported Plate. Contents note continued: 11.7.3. Three-Dimensional Shells.

"This book introduces the theory of the finite element method using a balanced approach between its mathematical formulations and programming implementation. The computer implementation is carried out using MATLAB, while the practical applications are carried out in both MATLAB and Abaqus. All of the key steps are presented in great detail. MATLAB will allow the reader to focus on the finite element method by alleviating the programming burden. Detailed step-by-step procedures for solving sample problems with Abaqus interactive and keyword editions are provided at the end of each chapter"-- Provided by publisher.

There are no comments on this title.

to post a comment.

© 2021 NU LRC. All rights reserved.Privacy Policy I Powered by: KOHA