Nonconvex Optimization in Mechanics: Algorithms, Heuristics and Engineering Applications by the F.E.M.

ISBN-13: 9781461376729 / Angielski / Miękka / 2013 / 288 str.

E. S. Mistakidis; Georgios E. Stavroulakis

Opis

Nonconvexity and nonsmoothness arise in a large class of engineering applica- tions. In many cases of practical importance the possibilities offered by opti- mization with its algorithms and heuristics can substantially improve the per- formance and the range of applicability of classical computational mechanics algorithms. For a class of problems this approach is the only one that really works. The present book presents in a comprehensive way the application of opti- mization algorithms and heuristics in smooth and nonsmooth mechanics. The necessity of this approach is presented to the reader through simple, represen- tative examples. As things become more complex, the necessary material from convex and nonconvex optimization and from mechanics are introduced in a self-contained way. Unilateral contact and friction problems, adhesive contact and delamination problems, nonconvex elastoplasticity, fractal friction laws, frames with semi- rigid connections, are among the applications which are treated in details here. Working algorithms are given for each application and are demonstrated by means of representative examples. The interested reader will find helpful references to up-to-date scientific and technical literature so that to be able to work on research or engineering topics which are not directly covered here.

Recenzje

`... The book is well written and organized. It presents an important contribution to the growing field of nonsmooth, nonconvex computational mechanics and engineering. The large number of algorithms and heuristics for nonsmooth optimization problems and the many examples give a comprehensive overview of this field.'
Pekka Neittaanmaki in Mathematical Reviews, 99b:73032
`... The publication of this book ... is a timely and authoritative introduction to the engineering applications of non-smooth/non-convex mechanics. Written by two relatively young experts in both applied mathematics and mechanics, this book presents both an excellent introduction and comprehensive applications for the wide range of non-smooth/non-convex engineering problems with emphasis on numerical optimization and computational mechanics. ... The publication of this book is definitely an important step in the development of non-smooth/non-convex mechanics ...'
Manohar Kamat, David Yang Gao in Applied Mechanics Reviews, 52:6 (1999)
`... the authors, who are well-known active researchers in the field, should be congratulated for having tackled the above difficult, useful and timely task and for having achieved their goals to a large extent, and very successfully. ... this book represents, in my opinion, a noteworthy addition to the literature on engineering mechanics and on its mathematical and numerical methodologies. It is bound to be very useful to researchers, industrial analysts and graduate students alike, in mechanics of materials and structures.'
Giulio Maier in Meccanica, 34:4 (1999)

Spis treści

Part I: Nonconvexity in Engineering Applications. 1. Nonconvexity in Engineering Applications. Part II: Applied Nonconvex Optimization Background. 2. Applied Nonconvex Optimization Background. Part III: Superpotential Modelling and Optimization in Mechanics with and without Convexity and Smoothness. 3. Convex Superpotential Problems. 4. Nonconvex Superpotential Problems. 5. Optimal Design Problems. Part IV: Computational Mechanics. Computer Implementation, Applications and Examples. 6. Computational Mechanics Algorithms. 7. Applications. Index.