Nonconvex Optimization in Mechanics: Algorithms, Heuristics and Engineering Applications by the F.E.M.: 21 (Nonconvex Optimization and Its Applications, 21) - Hardcover

Mistakidis, E.S.; Stavroulakis, Georgios E.

Hardcover

ISBN 10: 0792348125 ISBN 13: 9780792348122

Publisher: Kluwer Academic Publishers, 1997

Synopsis

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.

About this title

Review

`... 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)

Synopsis

This book presents, in a comprehensive way, the application of optimization algorithms and heuristics in engineering problems involving smooth and nonsmooth energy potentials. These problems arise in real-life modelling of civil engineering and engineering mechanics applications. Engineers will gain an insight into the theoretical justification of their methods and will find numerous extensions of the classical tools proposed for the treatment of novel applications with significant practical importance. Applied mathematicians and software developers will find a rigorous discussion of the links between applied optimization and mechanics which will enhance the interdisciplinary development of new methods and techniques. Among the large number of concrete applications are unilateral frictionless, frictional or adhesive contact problems, and problems involving complicated friction laws and interface geometries which are treated by the application of fractal geometry. The book should be of interest to researchers in mechanics, civil, mechanical and aeronautical engineers, as well as applied mathematicians.

It is suitable for advanced undergraduate and graduate courses in computational mechanics, focusing on nonlinear and nonsmooth applications, and as a source of examples for courses in applied optimization.

Edition details

• Publisher: Kluwer Academic Publishers
• Publication date: 1997
• Language: English
• ISBN 10: 0792348125
• ISBN 13: 9780792348122
• Binding: Hardcover
• Number of pages: 308