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

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. Content: Other Pergamon Titles of Interest , Page ii Front Matter , Page iii Copyright , Page iv PREFACE , Page v , S. Nemat-Nasser, K. Washizu SCIENTIFIC PROGRAM , Pages xiii-xvi LIST OF PARTICIPANTS , Pages xvii-xxii Remarks on Some Asymptotic Problems in Composite and in Perforated Materials , Pages 3-19 , J.L. Lions Mathematical and Computational Methods in Plasticity , Pages 20-28 , G. Strang, H. Matthies, R. Temam New Variational Irreversible Thermodynamics of Open Physical-Chemical Continua , Pages 29-39 , M.A. Biot SESSION A - COMPOSITES; EIGENVALUE PROBLEMS , Page 43 , G.M.L. Gladwell Macroscopic Behavior of Elastic Material with Periodically Spaced Rigid Inclusions , Pages 45-51 , F. Léné Variational Methods for Eigenvalue Problems in Composites , Pages 52-58 , C.O. Horgan, S. Nemat-Nasser Relationships Between Derivations of the Overall Properties of Composites by Perturbation Expansions and Variational Principles , Pages 59-66 , J.R. Willis Stabilization of the Lanczos Method and its Application to Structural Vibration , Pages 67-74 , M. Geradin Theory of Connectivity. A Unified Approach to Boundary Methods , Pages 77-82 , I. Herrera On Direct Discrete Methods and Their Application to Mechanics , Pages 83-94 , E.R.de Arantes e Oliveira Dependence of Solutions of Operator Equations of Mechanics on Design Variations , Pages 95-97 , E.J. Haug A Minimum Principle in Nonlinear Dynamics of Hardening Rigid-Plastic Bodies , Pages 98-102 , H. Stolarski Bounds for the Shear Center Coordinates of Prismatic Beams , Pages 105-114 , S. Nair Finite Deformation of Elastic Beams , Pages 115-120 , P.M. Pinsky, R.L. Taylor, K.S. Pister Generalization of the Hypercircle Method and Pointwise Error Bounds in Nonlinear Elasticity , Pages 121-126 , H. Stumpf Complementary Theorems of Solid Mechanics , Pages 127-135 , G. Wempner Stability Analysis of Structural Elastic Systems , Pages 136-138 , M. Como, A. Grimaldi Principle of Least Action and its Complementary Form , Pages 139-141 , B. Tabarrok Some Applications of Invariant Variational Principles in Mechanics of Solids , Pages 145-150 , G. Herrmann On Variational Principles for Non-Conservative Mechanical Systems with Follower Forces , Pages 151-155 , H.H.E. Leipholz General Use of the Lagrange Multiplier in Nonlinear Mathematical Physics , Pages 156-162 , M. Inokuti, H. Sekine, T. Mura Complementary Energy and Catastrophes , Pages 163-168 , M.J. Sewell A Study on the Geometrically Nonlinear Behavior of Beam Structures Using a Mixed Finite Element Procedure , Pages 169-174 , D. Karamanlidis, K. Knothe, O. Tsuzuki A Note on the Principle of Stationary Complementary Energy in Nonlinear Elasticity , Page 175 , K. Washizu SESSION E - FINITE ELEMENTS , Page 179 , Theodore H.H. Pian A New Discrete Element and its Variational Formulation , Pages 181-186 , T. Kawai Admissible and Inadmissible Simplifications of Variational Methods in Finite Element Analysis , Pages 187-198 , E. Haugeneder, H.A. Mang Incremental Finite Element Methods for Geometrically Nonlinear Elasto-Visco-Plastic Solids , Pages 199-204 , K.-D. Klee, E. Stein A Variational Approach to the Stability Analysis of Non-Gradient Discrete Systems , Pages 205-207 , S. Athel, M.S.El Naschie On the Monotony and the Convergence of a Special Class of Hybrid Finite Elements: The Mongrel Elements , Pages 208-213 , Nguyen Dang Hung Some Considerations on Accuracy of Arch Elements , Pages 214-217 , Y. Yamamoto, H. Ohtsubo Elastic-Plastic Torsion of Heterogeneous Cylindrical Bars , Pages 221-226 , H. Lanchon, D. Cioranescu, J.Saint Jean Paulin Homogenization Results for a Class of Nonlinear Stationary Diffusion Problems , Pages 227-231 , M. Artola, G. Duvaut SESSION G - FRACTURE, CONTACT, AND VARIATIONAL INEQUALITIES , Page 235 , E.A. Saibel On the Dynamic Deformation of a Bar Against an Obstacle , Pages 237-241 , C. Do Numerical Contact Elastostatics , Pages 242-248 , J.J. Kalker Variational Methods for Analysis of Stability of Interacting Cracks , Pages 249-253 , S. Nemat-Nasser Normal Dissipativity and Energy Criteria in Fracture , Pages 254-259 , Nguyen Quoc Son Use of Variational Methods for the Analysis of Contact Problems in Solid Mechanics , Pages 260-264 , J.T. Oden, N. Kikuchi Remarks on the Convergence of a Mixed Finite Element Method in Linear Elasticity , Pages 265-268 , L. Ascione, A. Grimaldi SESSION H - PLASTICITY I , Page 271 , J. Chandra Periodic Solutions in Plasticity and Viscoplasticity , Pages 273-277 , B. Halphen Variational Methods for Problems in Rigid-Plastic Structural Dynamics , Pages 278-285 , J.B. Martin Convergence to a Periodic Solution in Elastic Perfectly Plastic Structures , Pages 286-290 , C. Johnson, B. Mercier, J.C. Nédelec A Geometrical Facet of the Theory of Dislocations and Disclinations in a Cosserat Continuum , Pages 291-295 , S. Minagawa Minimum Theorems Concerning Cauchy and Periodic Problems for Maxwell Body , Pages 296-303 , B.J.P. Nayroles Existence and Regularity of Solutions for Plasticity Problems , Pages 304-309 , P-M. Suquet Variational Principles and Methods for Viscoelastic Plates and Shells , Pages 313-317 , J. Brilla Optimal Strain Paths in Linear Viscoelasticity: The Effect of the Past History , Pages 318-321 , M.E. Gurtin, L.F. Murphy Variational Methods in Creep Buckling of a Circular Cylindrical Shell with Varying Wall Thickness , Pages 322-326 , M.M. Kozarov, P.T. Kolev An Existence and Stability Theorem in Nonlinear Viscoelasticity , Pages 327-331 , M. Potier-Ferry SESSION J - OPTIMIZATION; PLASTICITY , Page 335 , Niels Olhoff Singular Solutions in Structural Optimization Problems , Pages 337-343 , E.F. Masur, Z. Mróz Optimal Control in the Theory of the Unilateral Von-Kármán-plates , Pages 344-348 , P.D. Panagiotopoulos Some Optimization Problems of Contact Bodies Within the Linear Theory of Elasticity , Pages 349-356 , I. Páczelt An Application of Optimal Structural Remodeling , Pages 357-358 , J.E. Taylor SESSION K - PLASTICITY II , Page 361 , E.H. Lee Rate Complementary Energy Principles; Finite Strain Plasticity Problems; and Finite Elements , Pages 363-367 , S.N. Atluri A Simple Convex Stress Rate-Strain Rate Relation in Plasticity not Relying on the Yield Surface Concept , Pages 368-373 , J. Christoffersen On the Application of a Variational Principle for Large-Displacement Elastic-Plastic Problems , Pages 374-377 , K.W. Neale SESSION L - FLOW, VISCOELASTICITY, AND PLASTICITY , Page 381 , H. Bufler Variational Formulation in Finite Deformation Elasto-Plasticity with Large Increments and Discontinuous Fields , Pages 383-386 , M. Kleiber A Variational Basis for “Upwind” Finite Elements , Pages 387-391 , T.J.R. Hughes, J.D. Atkinson A Variational Principle for Visco-Elastic Memory Fluids and its Use in Finite Element Analysis of Steady Flows , Pages 392-399 , B. Bernstein, D.S. Malkus On Minimum Principles in Plasticity , Pages 400-403 , P. Rafalski Index of Contributors , Pages 405-406