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.
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