By David Yang Gao

ISBN-10: 0792361458

ISBN-13: 9780792361459

Inspired through useful difficulties in engineering and physics, drawing on quite a lot of utilized mathematical disciplines, this ebook is the 1st to supply, inside a unified framework, a self-contained entire mathematical idea of duality for normal non-convex, non-smooth structures, with emphasis on tools and purposes in engineering mechanics. subject matters lined contain the classical (minimax) mono-duality of convex static equilibria, the attractive bi-duality in dynamical platforms, the attention-grabbing tri-duality in non-convex difficulties and the advanced multi-duality typically canonical structures. A possibly strong sequential canonical twin transformation procedure for fixing totally nonlinear difficulties is constructed heuristically and illustrated through use of many fascinating examples in addition to broad purposes in a wide selection of nonlinear platforms, together with differential equations, variational difficulties and inequalities, limited international optimization, multi-well section transitions, non-smooth post-bifurcation, huge deformation mechanics, structural restrict research, differential geometry and non-convex dynamical platforms. With really coherent and lucid exposition, the paintings fills an enormous hole among the mathematical and engineering sciences. It indicates tips on how to use formal language and duality tips on how to version typical phenomena, to build intrinsic frameworks in numerous fields and to supply rules, innovations and strong tools for fixing non-convex, non-smooth difficulties bobbing up clearly in engineering and technology. a lot of the booklet includes fabric that's new, either in its demeanour of presentation and in its examine improvement. A self-contained appendix presents a few beneficial history from straightforward useful research. viewers: The e-book could be a worthwhile source for college students and researchers in utilized arithmetic, physics, mechanics and engineering. the total quantity or chosen chapters is additionally urged as a textual content for either senior undergraduate and graduate classes in utilized arithmetic, mechanics, common engineering technology and different parts within which the notions of optimization and variational tools are hired.