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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 - October 3, 2013
- Editor: S. Nemat-Nasser
- Language: English
- Paperback ISBN:9 7 8 - 1 - 4 8 3 1 - 1 3 4 1 - 8
- eBook ISBN:9 7 8 - 1 - 4 8 3 1 - 4 5 8 3 - 9
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… Read more
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Request a sales quoteVariational 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.
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: 428
- Language: English
- Edition: 1
- Published: October 3, 2013
- Imprint: Pergamon
- Paperback ISBN: 9781483113418
- eBook ISBN: 9781483145839
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S. Nemat-Nasser
Affiliations and expertise
La Jolla, CA, USARead Variational Methods in the Mechanics of Solids on ScienceDirect