Variational Methods in the Mechanics of Solids

Variational Methods in the Mechanics of Solids

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

1st Edition - January 1, 1980

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  • Editor: S. Nemat-Nasser
  • eBook ISBN: 9781483145839

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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

Product details

  • No. of pages: 428
  • Language: English
  • Copyright: © Pergamon 1980
  • Published: January 1, 1980
  • Imprint: Pergamon
  • eBook ISBN: 9781483145839

About the Editor

S. Nemat-Nasser

Affiliations and Expertise

La Jolla, CA, USA

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