Nonsmooth/Nonconvex Mechanics: Modeling, Analysis and Numerical Methods: 50 (Nonconvex Optimization and Its Applications, 50) - Hardcover

Hardcover

ISBN 10: 0792367863 ISBN 13: 9780792367864

Publisher: Springer, 2001

Synopsis

Nonsmoothness and nonconvexity arise in numerous applications of mechan­ ics and modeling due to the need for studying more and more complicated phe­ nomena and real life applications. Mathematicians have started to provide the necessary tools and theoretical results underpinning these applications. Ap­ plied mathematicians and engineers have begun to realize the benefits of this new area and are adopting, increasingly, these new tools in their work. New computational tools facilitate numerical applications and enable the theory to be tested, and the resulting feedback poses new theoretical questions. Because of the upsurge in activity in the area of nonsmooth and noncon­ vex mechanics, Professors Gao and Ogden, together with the late Professor P.D. Panagiotopoulos, had planned to organize a Minisymposium with the title Nonsmooth and Nonconvex Mechanics within the ASME 1999 Mechanics & Materials Conference, June 27-30 1999, Blacksburg, Virginia. After the unex­ pected death of Professor Panagiotopoulos the first two editors invited the third editor (Professor Stavroulakis) to join them. A large number of mathematical and engineering colleagues supported our efforts by presenting lectures at the Minisymposium in which the available mathematical methods were described and many problems of nonsmooth and nonconvex mechanics were discussed. The interest of the many participants encourages us all to continue our research efforts.

About this title

Review

'[...] in my opinion it is interesting and useful to all researchers in theoretical and applied mechanics, since it represents a rich source of information on recent developments concerning mathematical models which at present arise more and more frequently in various technological and engineering sectors.'
Meccanica, 36 (2001)

Synopsis

Nonsmooth and nonconvex models arise in several important applications of mechanics and engineering. The interest in this field is growing from both mathematicians and engineers. The study of numerous industrial applications, including contact phenomena in statics and dynamics or delamination effects in composites, require the consideration of nonsmoothness and nonconvexity. The mathematical topics discussed in this book include variational and hemivariational inequalities, duality, complementarity, variational principles, sensitivity analysis, eigenvalue and resonance problems, and minimax problems. Applications are considered in the following areas among others: nonsmooth statics and dynamics, stability of quasi- static evolution processes, friction problems, adhesive contact and debonding, inverse problems, pseudoelastic modeling of phase transitions, chaotic behavior in nonlinear beams, and nonholonomic mechanical systems.This volume contains 22 chapters written by various leading researchers and presents a cohesive and authoritative overview of recent results and applications in the area of nonsmooth and nonconvex mechanics.

This book is useful for faculty, graduate students, and researchers in applied mathematics, optimization, control and engineering.

Edition details

• Publisher: Springer
• Publication date: 2001
• Language: English
• ISBN 10: 0792367863
• ISBN 13: 9780792367864
• Binding: Hardcover
• Number of pages: 520
• Editor: Yang Gao David, Ogden Raymond W., Stavroulakis Georgios E.