Analysis of Skeletal Structural Systems in the Elastic and Elastic-Plastic Range

Adam Borkowski

ISBN 10: 8301076879 / ISBN 13: 9788301076870

Published by Elsevier + PWN, 1988

About this Item

Cloth hardcover, vii + 223 pages, NOT ex-library. Gently age-toned with light internal creasing, book is clean and bright with unmarked text, free of inscriptions and stamps, firmly bound. Boards show gentle scratches and faint shelfworn marks. Edge-worn dust jacket shows shelfworn marks and short tears; creases on both flaps. -- The book presents applications of Mathematical Programming to non-linear static analysis of skeletal structures (trusses, frames, grillages, etc.). It is demonstrated that under the assumption of small displacements, a broad class of structural analysis problems exhibit the same internal structure. Such is the case with elastic analysis in the presence of unilateral supports or tension-only members, elastic-plastic analysis in both holonomic and non-holonomic formulations and, finally, ultimate load analysis. Throughout the book a clear and uniform methodology of presentation is used. First a complete set of governing relations is derived for a particular problem. Then that set is shown to be equivalent to a certain minimax problem (the saddle point problem), that in turn can be replaced by a pair of constrained extremum problems (dual MP-problems). Thus the complementary energy principles are established, furnishing the basis for the development of methods of numerical solution. Numerous examples illustrate the theory, while a catalog of finite elements and a collection of FORTRAN subroutines given in the Appendix allow the reader to gain his own experience in applying the proposed approach. -- Contents: Introduction; 1. Elements of Linear Algebra and Mathematical Programming [Systems of Linear Equations and Inequalities; Solutions of Systems of Linear Equations; Functions of Matrix Argument; Potentials of Systems of Equations and Inequalities; Dual Problems of Constrained Extremum] 2. Elements of Continuum Mechanics [Equations of Kinematics & Statics; Virtual Work Principle; Material Constitutive Relationships; Work and Energy] 3. Differential Description of an Element [Reduction of Dimensions of Physical Space; Dual Description of Kinematics and Statics; Physical Relations; Energy Expressions] 4. Discrete Description of an Element [Reduction of Dimensions of Mathematical Space; Dual Description of Kinematics and Statics; Physical Relationships; Energy Expressions] 5. Discrete Description of a Structure [Global Matrices of Dual Variables; Global Compatibility Equations; Classification of Skeletal Systems Based on Analysis of C; Global Physical Relationships (Structure Made of Linearly-Elastic Material; Structure Made of Elastic-Plastic or Rigid-Plastic Material); Global Energy Expressions] 6. Elastic Analysis [Formulation of the Problem and the Complete System of Equations; Direct Reduction of the Complete System by the Displacement Method or Force Method; Potential of the Complete System of Equations and Dual Energy Principles; Initial Strains and Kinematic Loads; Unilateral Supports; Tension-only Members] 7. Elastic-Plastic Analysis [Formulation of Problems. Complete Sets of Equations and Inequalities; Potential Function and Dual Energy Principles for the Incremental Problem; Potential Function and Dual Energy Principles when Unloading is Neglected; Structures Made of Elastic-Perfectly-Plastic or Rigid-Plastic Materials; Methods of Elastic-Plastic Analysis Employed in Practice (Kinematic Approach Using Elastic Solution; Tangent Stiffness Method; Initial Load Method)] 8. Ultimate Load Analysis [Formulation of the Problem and the Complete Set of Equations and Inequalities; Potential Function and Dual Energy Principles]; References; Appendix A. Catalogue of Elements; Appendix B. Subroutine SOLVE; Appendix C. Subroutine SIMPLEX; Appendix D. Subroutine MINIMUM; Index.

Seller Inventory # 010270

Bibliographic Details

• Title: Analysis of Skeletal Structural Systems in the Elastic and Elastic-Plastic Range
• Publisher: Elsevier + PWN
• Publication Date: 1988
• Language: English
• ISBN 10: 8301076879
• ISBN 13: 9788301076870
• Binding: Hardcover
• Edition: 1st Edition
• Condition: Very Good
• Dust Jacket Condition: Good

About this title

Synopsis

The purpose of this book is to provide a smooth transition from linear elasticity through the nonlinear behaviour induced by unilateral constraints to full-scale plasticity.

The book presents applications of Mathematical Programming to nonlinear static analysis of skeletal structures (trusses, frames, grillages etc.). It is demonstrated that under the assumption of small displacements, a broad class of structural analysis problems exhibit the same internal structure. Such is the case with elastic analysis in the presence of unilateral supports or tension-only members, elastic-plastic analysis in both holonomic and non-holonomic formulations and, finally, ultimate load analysis.

Throughout the book a clear and uniform methodology of presentation is used. First a complete set of governing relations is derived for a particular problem. Then that set is shown to be equivalent to a certain minimax problem (the saddle point problem), that in turn can be replaced by a pair of constrained extremum problems (dual MP-problems). Thus the complementary energy principles are established, furnishing the basis for the development of methods of numerical solution. Numerous examples illustrate the theory, while a catalogue of finite elements and a collection of FORTRAN subroutines given in the Appendix allow the reader to gain his own experience in applying the proposed approach.

Adam Borkowski, Professor and Head of the Adaptive Systems Laboratory at the Institute of Fundamental Technological Research in Warsaw, is the author of 40 papers on structural and solid mechanics and co-author of the monographs "Optimum Design of Elastic-Plastic Systems", "Structural Mechanics: A Computer-Oriented Approach", and "Structural Optimization by Mathematical Programming". His original contributions to the numerical analysis and design of structures have found many applications in engineering practice.