| Description |
xv, 528 pages : illustrations ; 24 cm |
| Series |
Prentice-Hall civil engineering and engineering mechanics series |
|
Prentice-Hall civil engineering and engineering mechanics series.
|
| Contents |
Matrices and Linear Algebra -- Elementary Concepts of Matrices -- Introduction to Matrices -- Special Matrices -- Matrix Equality, Addition, and Multiplication of a Scalar -- Multiplication of Matrices -- The Inverse Matrix -- Partitioning of Matrices, The Trace and Determinant of a Matrix -- Matrices and Vector Spaces -- Vector Spaces, Subspaces, and the Span of a Matrix -- Matrix Representation of Linear Transformation -- Change of Basis -- Matrix Representation of Variational Formulation -- The Eigenproblem Av = [lamda] v with A Being a Symmetric Matrix -- The Rayleigh Quotient and the Minimax Characterization of Eigenvalues -- Vector and Matrix Norms -- The Finite Element Methods -- Formulation of the Finite Element Method -- Formulation of the Finite Element Method -- Using the Principle of Virtual Displacements -- Displacement and Strain-Displacement Transformation Matrices for Plane Stress Analysis -- General Formulation -- Lumping of Structure Properties and Loads -- Specialization of the General Formulation -- Requirements for Monotonic Convergence -- Derivation of Generalized Coordinate Finite Element Models -- General Derivation and Specific Examples -- Spatial Isotropy -- Formulation and Calculation of Isoparametric Finite Element Matrices -- Isoparametric Derivation of Bar Element Stiffness Matrix -- General Isoparametric Formulation -- Formulation of Isoparametric Finite Element Matrices in Local Coordinate Systems -- Element Matrices in Global Coordinate System -- Convergence Considerations -- Associated Element Families -- Numerical Integration --Practical Considerations in Isoparametric Element Calculations -- Computer Program Implementation of Isoparametric Finite Elements -- Varational Formulation of the Finite Method -- Variational Formulation of Structural Mechanics Problems -- Ritz Solution -- Formulation of Field Problems-Example: Heat Transfer Analysis -- Nonconforming, Mixed, and Hybrid Finite Element Models; Finite Difference Differential and Energy Methods -- Implementation of the Finite Model -- Computer Program Organization for Calculation of Structure Matrices -- Nodal Point and Element Information Read-in -- Calculation of Element Stiffness, Mass, and Equivalent Nodal Loads -- Assemblage of Structural Matrices -- Calculation of Element Stresses -- Example Program STAP -- Data Input to Computer Program STAP --Listing of Program STAP -- Solution of Finite Element Equilibrium Equations -- Solution of Equilibrium Equations in Static Analysis -- Direct Solutions Using Algorithms Based on Gauss Elimination -- Introduction to Gauss Elimination -- The Gauss Elimination Solution -- Computer Implementation of Gauss Elimination -- Cholesky Factorization, Static Condensation, Substructures, and Frontal Solution -- Solution of Equations with Symmetric Nonpositive Definite Coefficient Matrices -- Direct Solutions Using Orthogonal Matrices -- The Givens Factorization -- The Householder Factorization -- The Gauss-Seidel Iterative Solution -- Solution Errors -- Solution of Equilibrium Equations in Dynamic Analysis -- Direct Integration Methods -- The Central Difference MEthod -- The Houbolt Method -- The Wilson [theta] Method -- The Newmark Method -- Mode Superposition -- Change of Basis to Modal Generalized Displacements -- Analysis with Damping Neglected -- Analysis with Damping Included -- Analsysis of Direct Integration Methods -- Direct Integration Approximation and Load Operators -- The Central Difference Method -- The Houbolt Method -- The Wilson [theta] Method -- The Newmark Method -- Stability Analysis -- Accuracy Analysis -- Preliminaries to the Solution of Eigenproblems -- Fundamental Facts Used in the Solution of Eigensystems -- Properties of the Eigenvectors -- The Characteristic Polynomials of the Eigenproblem K[phi] = [lambda]M[phi] and of Its Associated Constraint Problems -- Shifting -- Effect of Zero Mass -- Transformation of the Generalized Eigenproblem K[phi] = [lambda]M[phi] to a Standard Form -- Approximate Solution Techniques -- Static Condensation -- Rayleigh-Ritz Analysis -- Component Mode Synthesis -- Solution Errors -- Solution Methods for Eigenproblems -- Vector Iteration Methods -- Inverse Iteration -- Forward Iteration -- Shifting in Vector Iteration -- Rayleigh Quotient Iteration -- Matrix Deflation and Gram-Schmidt Orthogonalization -- Some Practical Considerations Concerning Vector Iterations -- Transformation Methods -- The Jacobi Method -- The Generalized Jacobi Method -- The Householder-QR-Inverse Iteration Solution -- Polynomial Iteration Techniques -- Explicit Polynomial Iteration -- Implicit Polynomial Iteration -- Methods Based on the Sturm Sequence Property -- Solution of Large Eigenproblems -- The Determinant Search Method -- Preliminary Considerations -- The Solution Algorithm -- Final Remarks Concerning the Determinant Search Solution -- The Subspace Iterations Method -- Preliminary Considerations -- Subspace Iteration -- Starting Iteration Vectors -- Convergence -- Final Remarks Concerning the Subspace Iteration Method -- Selection of Solution Technique |
| Analysis |
Mathematics Finite element methods For civil engineering |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Also issued online |
| Subject |
Finite element method.
|
|
Numerical analysis.
|
|
Finite element method.
|
|
Numerical analysis.
|
| Author |
Wilson, Edward L., 1931- author
|
| LC no. |
75046522 |
| ISBN |
0136271901 |
|
9780136271901 |
|
