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Variational Methods in the Mechanics of Solids - 1st Edition - ISBN: 9780080247281, 9781483145839

Variational Methods in the Mechanics of Solids

1st Edition

Proceedings of the IUTAM Symposium on Variational Methods in the Mechanics of Solids Held at Northwestern University, Evanston, Illinois, U.S.A., 11-13 September 1978

Editor: S. Nemat-Nasser
eBook ISBN: 9781483145839
Imprint: Pergamon
Published Date: 1st January 1980
Page Count: 428
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Variational Methods in the Mechanics of Solids contains the proceedings of the International Union of Theoretical and Applied Mechanics Symposium on Variational Methods in the Mechanics of Solids, held at Northwestern University in Evanston, Illinois, on September 11-13, 1978. The papers focus on advances in the application of variational methods to a variety of mathematically and technically significant problems in solid mechanics. The discussions are organized around three themes: thermomechanical behavior of composites, elastic and inelastic boundary value problems, and elastic and inelastic dynamic problems. This book is comprised of 58 chapters and opens by addressing some questions of asymptotic expansions connected with composite and with perforated materials. The following chapters explore mathematical and computational methods in plasticity; variational irreversible thermodynamics of open physical-chemical continua; macroscopic behavior of elastic material with periodically spaced rigid inclusions; and application of the Lanczos method to structural vibration. Finite deformation of elastic beams and complementary theorems of solid mechanics are also considered, along with numerical contact elastostatics; periodic solutions in plasticity and viscoplasticity; and the convergence of the mixed finite element method in linear elasticity. This monograph will appeal to practitioners of mathematicians as well as theoretical and applied mechanics.

Table of Contents

Scientific Program

List of Participants

General Lectures

Remarks on Some Asymptotic Problems in Composite and in Perforated Materials

Mathematical and Computational Methods in Plasticity

New Variational Irreversible Thermodynamics of Open Physical-Chemical Continua

Session A: Composites; Eigenvalue Problems

Summary of Session A

Macroscopic Behavior of Elastic Material with Periodically Spaced Rigid Inclusions

Variational Methods for Eigenvalue Problems in Composites

Relationships between Derivations of the Overall Properties of Composites by Perturbation Expansions and Variational Principles

Stabilization of the Lanczos Method and Its Application to Structural Vibration

Session B: General Methods

Theory of Connectivity. A Unified Approach to Boundary Methods

On Direct Discrete Methods and Their Application to Mechanics

Dependence of Solutions of Operator Equations of Mechanics on Design Variations

A Minimum Principle in Nonlinear Dynamics of Hardening Rigid-Plastic Bodies

Session C: Elasticity

Bounds for the Shear Center Coordinates of Prismatic Beams

Finite Deformation of Elastic Beams

Generalization of the Hypercircle Method and Pointwise Error Bounds in Nonlinear Elasticity

Complementary Theorems of Solid Mechanics

Stability Analysis of Structural Elastic Systems

Principle of Least Action and Its Complementary Form

Session D: General Principles

Some Applications of Invariant Variational Principles in Mechanics of Solids

On Variational Principles for Non-Conservative Mechanical Systems with Follower Forces

General Use of the Lagrange Multiplier in Nonlinear Mathematical Physics

Complementary Energy and Catastrophes

A Study on the Geometrically Nonlinear Behavior of Beam Structures Using Mixed Finite Element Procedure

A Note on the Principle of Stationary Complementary Energy in Nonlinear Elasticity

Session E: Finite Elements

Summary of Session E

A New Discrete Element and Its Variational Formulation

Admissible and Inadmissible Simplifications of Variational Methods in Finite Element Analysis

Incremental Finite Element Methods for Geometrically Nonlinear Elasto-Visco-Plastic Solids

A Variational Approach to the Stability Analysis of Non-Gradient Discrete Systems

On the Monotony and the Convergence of a Special Class of Hybrid Finite Elements: The Mongrel Elements

Some Considerations on Accuracy of Arch Elements

Session F: Homogenization; Computational Methods

Elastic-Plastic Torsion of Heterogeneous Cylindrical Bars

Homogenization Results for a Class of Nonlinear Stationary Diffusion Problems

Session G: Fracture, Contact, and Variational Inequalities

Summary of Session G

On the Dynamic Deformation of a Bar Against an Obstacle

Numerical Contact Elastostatics

Variational Methods for Analysis of Stability of Interacting Cracks

Normal Dissipativity and Energy Criteria in Fracture

Use of Variational Methods for the Analysis of Contact Problems in Solid Mechanics

Remarks on the Convergence of the Mixed Finite Element Method in Linear Elasticity

Session H: Plasticity I

Summary of Session H

Periodic Solutions in Plasticity and Viscoplasticity

Variational Methods for Problems in Rigid-Plastic Structural Dynamics

Convergence to a Periodic Solution in Elastic Perfectly Plastic Structures

A Geometrical Facet of the Theory of Dislocations and Disclinations in a Cosserat Continuum

Minimum Theorems Concerning Cauchy and Periodic Problems for Maxwell Body

Existence and Regularity of Solutions for Plasticity Problems

Session I: Viscoelasticity

Variational Principles and Methods for Viscoelastic Plates and Shells

Optimal Strain Paths in Linear Viscoelasticity: The Effect of the Past History

Variational Methods in Creep Buckling of a Circular Cylindrical Shell with Varying Wall Thickness

An Existence and Stability Theorem in Nonlinear Viscoelasticity

Session J: Optimization; Plasticity

Summary of Session J

Singular Solutions in Structural Optimization Problems

Optimal Control in the Theory of the Unilateral von-Kárman-Plates

Some Optimization Problems of Contact Bodies within the Linear Theory of Elasticity

An Application of Optimal Structural Remodeling

Session K: Plasticity II

Summary of Session K

Rate Complementary Energy Principles; Finite Strain Plasticity Problems; and Finite Elements

A Simple Convex Stress Rate-Strain Rate Relation in Plasticity Not Relying on the Yield Surface Concept

On the Application of a Variational Principle for Large-Displacement Elastic-Plastic Problems

Session L: Flow, Viscoelasticity, and Plasticity

Summary of Session L

A Variational Principle for Visco-Elastic Memory Fluids and Its Use in Finite Analysis of Steady Flows

A Variational Basis for "Upwind" Finite Elements

Variational Formulation in Finite Deformation Elasto-Plasticity with Large Increments and Discontinuous Fields

On Minimum Principles in Plasticity

Index of Contributors


No. of pages:
© Pergamon 1980
1st January 1980
eBook ISBN:

About the Editor

S. Nemat-Nasser

Affiliations and Expertise

La Jolla, CA, USA

Ratings and Reviews