A variational approach to structural analysis 1st Edition by David Wallerstein ISBN 9780471395935, 0471395935

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Product details: 

ISBN 10: 0471395935

ISBN 13:  9780471395935

Author: David V. Wallerstein

This textbook provides a comprehensive introduction to variational methods in structural analysis, bridging theory and practical applications. It emphasizes the principle of virtual work, complementary virtual work, and energy methods, serving as a foundation for finite element methods. The book is aimed at graduate students and engineering professionals in mechanical, civil, and aerospace engineering.

Table of contents: 

1. INTRODUCTION

2. PRELIMINARIES
    2.1 Variational Notation
    2.2 The Gradient
    2.3 Integration by Parts
    2.4 Stokes’s Theorem
    2.5 Green’s Theorem in the Plane
    2.6 Adjoint Equations
    2.7 Meaning of V²
    2.8 Total Differentials
    2.9 Legendre Transformation
    2.10 Lagrange Multipliers
    2.11 Differential Equations of Equilibrium
    2.12 Strain-Displacement Relations
    2.13 Compatibility Conditions of Strain
    2.14 Thermodynamic Considerations
    Problems

3. PRINCIPLE OF VIRTUAL WORK
    3.1 Virtual Work Definition
    3.2 Generalized Coordinates
    3.3 Virtual Work of a Deformable Body
    3.4 Thermal Stress, Initial Strain, and Initial Stress
    3.5 Some Constitutive Relationships
    3.6 Accounting for All Work
    3.7 Axially Loaded Members
    3.8 The Unit-Displacement Method
    3.9 Finite Elements for Axial Members
    3.10 Coordinate Transformations
    3.11 Review of the Simple Beam Theory
    3.12 Shear Stress in Simple Beams
    3.13 Shear Deflection in Straight Beams
    3.14 Beams with Initial Curvature
    3.15 Thermal Strain Correction in Curved Beams
    3.16 Shear and Radial Stress in Curved Beams
    3.17 Thin Walled Beams of Open Section
    3.18 Shear in Open Section Beams
    3.19 Slope-Deflection Equations
    3.20 Approximate Methods
    Problems

4. COMPLEMENTARY VIRTUAL WORK
    4.1 Complementary Virtual Work Definition
    4.2 Complementary Virtual Work of a Deformable Body
    4.3 Symmetry
    4.4 The Unit Load Method
    4.5 Force Elements
    4.6 Generalized Force-Displacement Transformations
    Problems

5. SOME ENERGY METHODS
    5.1 Conservative Forces and Potential Functions
    5.2 Stationary Potential Energy
    5.3 Castigliano’s First Theorem
    5.4 Complementary Energy
    5.5 Stationary Complementary Potential Energy
    5.6 Engesser-Crotti Theorem
    5.7 Variational Statements
    5.8 The Galerkin Method
    5.9 Derived Variational Principles
    Problems

6. SOME STATIC AND DYNAMIC STABILITY CONCEPTS
    6.1 Linear-Stability Analysis
    6.2 Geometric Measure of Strain
    6.3 A Beam with Initial Curvature Revisited
    6.4 Thin Walled Open Beams Revisited
    6.5 Some Stability Concepts
    6.6 Energy Criterion of Stability
    6.7 Stiffness
    6.8 Stiffening and Unstiffening Models
    6.9 Bifurcation Analysis
    6.10 Imperfection Analysis
    6.11 Circulatory Dynamic Stability
    6.12 Instationary Dynamic Stability
    Problems

7. REFERENCES

8. INDEX

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Tags: David Wallerstein, A variational approach, structural analysis