Energy Principles and Variational Methods in Applied Mechanics
A comprehensive guide to using energy principles and variational methods for solving problems in solid mechanics This book provides a systematic, highly practical introduction to the use of energy principles, traditional variational methods, and the finite element method for the solution of engineer...
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| Main Author: | |
|---|---|
| Format: | eBook |
| Language: | English |
| Published: |
Newark
John Wiley & Sons, Incorporated
2017
Wiley-Blackwell |
| Edition: | 3 |
| Subjects: | |
| ISBN: | 9781119087373, 1119087376 |
| Online Access: | Get full text |
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Table of Contents:
- 7.3 The First-Order Shear Deformation Plate Theory -- 7.4 Relationships between Bending Solutions of Classical and Shear Deformation Theories -- 7.5 Summary -- Problems -- Chapter 8: An Introduction to the Finite Element Method -- 8.1 Introduction -- 8.2 Finite Element Analysis of Straight Bars -- 8.3 Finite Element Analysis of the Bernoulli-Euler Beam Theory -- 8.4 Finite Element Analysis of the Timoshenko Beam Theory -- 8.5 Finite Element Analysis of the Classical Plate Theory -- 8.6 Finite Element Analysis of the First-Order Shear Deformation Plate Theory -- 8.7 Summary -- Problems -- Chapter 9: Mixed Variational and Finite Element Formulations -- 9.1 Introduction -- 9.2 Stationary Variational Principles -- 9.3 Variational Solutions Based on Mixed Formulations -- 9.4 Mixed Finite Element Models of Beams -- 9.5 Mixed Finite Element Models of the Classical Plate Theory -- 9.6 Summary -- Problems -- Chapter 10: Analysis of Functionally Graded Beams and Plates -- 10.1 Introduction -- 10.2 Functionally Graded Beams -- 10.3 Functionally Graded Circular Plates -- 10.4 A General Third-Order Plate Theory -- 10.5 Navier's Solutions -- 10.6 Finite Element Models -- 10.7 Summary -- Problems -- References -- Answers to Most Problems -- Index -- End User License Agreement
- Intro -- Title Page -- Copyright -- Table of Contents -- Dedication -- About the Author -- About the Companion Website -- Preface to the Third Edition -- Preface to the Second Edition -- Preface to the First Edition -- Chapter 1: Introduction and Mathematical Preliminaries -- 1.1 Introduction -- 1.2 Vectors -- 1.3 Tensors -- 1.4 Summary -- Problems -- Chapter 2: Review of Equations of Solid Mechanics -- 2.1 Introduction -- 2.2 Balance of Linear and Angular Momenta -- 2.3 Kinematics of Deformation -- 2.4 Constitutive Equations -- 2.5 Theories of Straight Beams -- 2.6 Summary -- Problems -- Chapter 3: Work, Energy, and Variational Calculus -- 3.1 Concepts of Work and Energy -- 3.2 Strain Energy and Complementary Strain Energy -- 3.3 Total Potential Energy and Total Complementary Energy -- 3.4 Virtual Work -- 3.5 Calculus of Variations -- 3.6 Summary -- Problems -- Chapter 4: Virtual Work and Energy Principles of Mechanics -- 4.1 Introduction -- 4.2 The Principle of Virtual Displacements -- 4.3 The Principle of Minimum Total Potential Energy and Castigliano's Theorem I -- 4.4 The Principle of Virtual Forces -- 4.5 Principle of Minimum Total Complementary Potential Energy and Castigliano's Theorem II -- 4.6 Clapeyron's, Betti's, and Maxwell's Theorems -- 4.7 Summary -- Problems -- Chapter 5: Dynamical Systems: Hamilton's Principle -- 5.1 Introduction -- 5.2 Hamilton's Principle for Discrete Systems -- 5.3 Hamilton's Principle for a Continuum -- 5.4 Hamilton's Principle for Constrained Systems -- 5.5 Rayleigh's Method -- 5.6 Summary -- Problems -- Chapter 6: Direct Variational Methods -- 6.1 Introduction -- 6.2 Concepts from Functional Analysis -- 6.3 The Ritz Method -- 6.4 Weighted-Residual Methods -- 6.5 Summary -- Problems -- Chapter 7: Theory and Analysis of Plates -- 7.1 Introduction -- 7.2 The Classical Plate Theory