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

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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. N° de ref. del artículo 010270

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