| Description |
1 online resource (415 p.) |
| Contents |
Intro -- Foreword -- Preface -- Acknowledgements -- Editorial Note -- Contents -- Editors and Contributors -- 1 Introduction -- 1.1 History of Finite Element Method -- 1.2 Finite Element Method -- 1.2.1 Derive the Differential Equation and Obtain the Closed Form Solution -- 1.2.2 Analytical Solution -- 1.2.3 Finite Element Solution -- 1.3 Applications of FEA -- 1.3.1 Solid Mechanics -- 1.3.2 Heat Conduction -- 1.3.3 Fluid Flow Through Pipes -- 1.3.4 Electrostatics -- 1.4 Different Numerical Methods -- 1.4.1 Mesh Methods -- 1.4.2 Mesh Free Methods -- 1.4.3 Mixed Method |
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1.4.4 Advantages of Using FEM Over Other Methods -- 1.5 FEASTSMT© -- 1.6 Exercise Problems -- Bibliography -- 2 Linear Algebra -- 2.1 Introduction -- 2.2 Matrices -- 2.3 Special Matrices -- 2.4 Matrix Algebra -- 2.5 Linear Dependence and Rank of a Matrix -- 2.5.1 Properties of Rank -- 2.6 Solution of System of Linear Simultaneous Equations -- 2.6.1 Rouche's Theorem -- 2.6.2 Homogeneous System -- 2.7 Eigenvalues and Eigenvectors -- 2.7.1 Properties of Eigenvalues -- 2.7.2 Properties of Eigenvectors -- 2.8 Diagonalization of a Matrix -- 2.8.1 Diagonalization by Similarity Transformation |
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2.8.2 Diagonalization of a Real Symmetric Matrix by Orthogonal Reduction -- 2.9 Quadratic Forms -- 2.10 Solution Schemes of a System of Linear Simultaneous Equations -- 2.10.1 Direct Methods -- 2.10.2 Iterative Methods -- 2.11 Worked Out Examples -- 2.12 Exercise Problems -- Bibliography -- 3 Classical Approximate Solutions -- 3.1 Introduction -- 3.1.1 Brachistochrone -- 3.1.2 Geodesic -- 3.1.3 Isoperimetric -- 3.2 Mathematical Preliminaries -- 3.3 Classification of Partial Differential Equations -- 3.4 Boundary and Initial Conditions |
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3.5 Weak Formulation of Differential Equations and Rayleigh-Ritz Method -- 3.6 Weighted Residual Technique and Galerkin's Method -- 3.7 Link Between Classical Approximate Solution and Finite Element Method -- 3.8 Exercise -- Bibliography -- 4 Elementary Concepts in Elasticity -- 4.1 Equilibrium Equations -- 4.2 Kinematic Conditions -- 4.3 Strain-Displacement Equations -- 4.4 Constitutive Relations -- 4.5 Exercise Problems -- Bibliography -- 5 Finite Element Formulations -- 5.1 Introduction -- 5.2 Functional Overview of a Finite Element Solver -- 5.3 The Domain of Linear Structural Analysis |
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5.4 Displacement-Based FE Formulations -- 5.5 Classification of Structural Finite Elements -- 5.5.1 Three-Dimensional Elements -- 5.5.2 Two-Dimensional Elements -- 5.5.3 One-Dimensional Elements -- 5.6 Assumed Displacement Fields and Shape (Interpolation) Functions -- 5.7 Natural Coordinate System -- 5.8 Use of Principle of Minimum Potential Energy -- 5.9 Numerical Integration for Stiffness Matrix Computation -- 5.10 Transformation of Element Stiffness Matrices -- 5.11 Isoparametric Finite Element Formulations -- 5.12 Stiffness Matrix for Rod/Truss/Link Finite Element |
| Summary |
This textbook covers the basic concepts and applications of finite element analysis. It is specifically aimed at introducing this advanced topic to undergraduate-level engineering students and practicing engineers in a lucid manner. It also introduces a structural and heat transfer analysis software FEASTSMT which has wide applications in civil, mechanical, nuclear and automobile engineering domains. This software has been developed by generations of scientists and engineers of Vikram Sarabhai Space Centre and Indian Space Research Organisation. Supported with many illustrative examples, the textbook covers the classical methods of estimating solutions of mathematical models. The book is written in an easy-to-understand manner. This textbook also contains numeral exercise problems to aid self-learning of the students. The solutions to these problems are demonstrated using finite element software. Furthermore, the textbook contains several tutorials and associated online resources on usage of the FEASTSMT software. Given the contents, this textbook is highly useful for the undergraduate students of various disciplines of engineering. It is also a good reference book for the practicing engineers |
| Notes |
5.13 Stiffness Matrix for Three-Dimensional Solid Finite Element |
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Includes index |
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Online resource; title from PDF title page (SpringerLink, viewed October 24, 2023) |
| Subject |
Finite element method.
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Finite element method
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| Form |
Electronic book
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| Author |
Nair, S. Unnikrishnan
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Somanath, S
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| ISBN |
9789811979897 |
|
9811979898 |
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