Nonsmooth/Nonconvex Mechanics: Modeling, Analysis and Numerical Methods / Edition 1

by David Yang Gao, Raymond W. Ogden, Georgios E. Stavroulakis

Overview

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.
Audience: Faculty, graduate students, and researchers in applied mathematics, optimization, control and engineering.

Product Details

ISBN-13:	9780792367864
Publisher:	Springer US
Publication date:	03/31/2001
Series:	Nonconvex Optimization and Its Applications , #50
Edition description:	2001
Pages:	476
Product dimensions:	6.14(w) x 9.21(h) x 0.05(d)

Table of Contents

Contributing Authors. Preface. In Memoriam, Professor P.D. Panagiotopoulos. 1. Stability of a quasi-static evolution; F. Abed-Meraim, Q.S. Nguyen. 2. Variational principles for self-adjoint elliptic eigenproblems; G. Auchmuty. 3. A sensitivity equation method for conduction and phase change problems; J. Borggaard, D. Pelletier. 4. Rock's interface problem including adhesion; Y. Dumont, D. Goeleven, K.L. Kuttler, M. Rochdi, M. Shillor. 5. On a class of differential-hemivariational inequalities; M. Foundo. 6. Nonsmooth/nonconvex dynamics: Duality, polarity, compklementary extrema; D.Y. Gao. 7. Signorini problem with a given friction; J. Haslinger, Z. Dostál, R. Kuccera. 8. Debonding of adhesively bonded composite structures; D.N. Kaziolas, M.J. Kontoleon, C.C. Baniotopoulos. 9. Effect of nonlinearity in nonsmooth and nonconvex structural behaviour; M. Kurutz. 10. Pseudoelastic solutions for one-dimensional martensite phase transitions; K.A. Lazopoulos. 11. Inverse Coefficient Problem; S. Migórski, A. Ochal. 12. Solutions to eigenvalue problems for hemivariational inequalities; D. Motreanu. 13. Non-smooth changes in elastic material properties under finite deformation; R.W. Ogden. 14. Nonlinear Resealing in discrete minimax; R.A. Polyak, I. Griva, J. Sobieszczanski-Sobieski. 15. Multivalued problems with strong resonance; V. Radulescu. 16. Freely propagating waves in a supported nonlinear elastic beam; D.L. Russell. 17. Shape sensitivities for optimal design: A case study;L.G. Stanley. 18. Optimal design and identification problems in nonsmooth mechanics; G.E. Stavroulakis. 19. Adhesively Supported von Karman Plate; K. Tsilika. 20. Optimality conditions of semi-invex functions; V. Vetrivel, J. Dutta. 21. The chaotic behavior of a physicallynonlinear beam; Y.-H. Xu. 22. Duality principle in nonholonomic mechanical systems; H. Yoshimura, T. Kawase.

Editorial Reviews

'[...] 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)

From the Publisher