Nonsmooth/Nonconvex Mechanics: Modeling, Analysis and Numerical Methods

ISBN-13: 9781461379737 / Angielski / Miękka / 2011 / 476 str.

David Yang Gao; Raymond W. Ogden; Georgios E. Stavroulakis

Opis

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."

Recenzje

'[...] 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)

Spis treści

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 physically nonlinear beam; Y.-H. Xu. 22. Duality principle in nonholonomic mechanical systems; H. Yoshimura, T. Kawase.