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Complementarity, duality, and symmetry are closely related concepts, and have always been a rich source of inspiration in human understanding through the centuries, particularly in mathematics and science. The Proceedings of IUTAM Symposium on Complementarity, Duality, and Symmetry in Nonlinear Mechanics brings together some of world's leading researchers in both mathematics and mechanics to provide an interdisciplinary but engineering flavoured exploration of the field's foundation and state of the art developments. Topics addressed in this book deal with fundamental theory, methods, and applications of complementarity, duality and symmetry in multidisciplinary fields of nonlinear mechanics, including nonconvex and nonsmooth elasticity, dynamics, phase transitions, plastic limit and shakedown analysis of hardening materials and structures, bifurcation analysis, entropy optimization, free boundary value problems, minimax theory, fluid mechanics, periodic soliton resonance, constrained mechanical systems, finite element methods and computational mechanics. A special invited paper presented important research opportunities and challenges of the theoretical and applied mechanics as well as engineering materials in the exciting information age. Audience: This book is addressed to all scientists, physicists, engineers and mathematicians, as well as advanced students (doctoral and post-doctoral level) at universities and in industry.
Content Level »Research
Keywords »Boundary value problem - Finite - Fundament - calculus - mathematics - optimization - structure - theorem
List of Figures
1. Mechanics and Materials: Research and Challenges in the Twenty-First Century; Ken P. Chong
2. Non-Convex Duality; Ivar Ekeland
3. Duality, Complementarity, and Polarity in Nonsmooth/Nonconvex Dynamics; David Y. Gao
4. Tri-Duality Theory in Phase Transformations of Ferroelectric Crystals with Random Defects; David Y. Gao, Jie-Fang Li, D. Viehland
5. Mathematical Modeling of the Three-Dimensional Delamination Processes of Laminated Composites; Thomas C. Gasser, Gerhard A. Holzapfel
6. Newton’s and Poisson’s Impact Law for the Non-Convex Case of Re-Entrant Corners; Christoph Glocker
7. Duality in Kinematic Approaches of Limit and Shakedown Analysis of Structures; Nguyen-Dang Hung, Aimin Yan, Vu Duc Khoi
8. Bifurcation Analysis of Shallow Spherical Shells with Meridionally Nonuniform Loading; Charles G. Lange, Frederic Y.M. Wan
9. Duality for Entropy Optimization and Its Applications; Xingsi Li, Shaohua Pan
10. Dual Variational Principles for the Free-Boundary Problem of Cavitated Bearing Lubrication; Gao-Lian Liu
11. Finite Dimensional Frictional Contact Quasi-Static Rate and Evolution Problems Revisited; J.A.C. Martins, A. Pinto da Costa
12. Minimax Theory, Duality and Applications; D. Motreanu
13. Min-Max Duality and Shakedown Theorems in Hardening Plasticity; Quoc Son Nguyen
14. A Fluid Problem with Navier-Slip Boundary Conditions; Adriana Valentina Busuioc, T. S. Ratiu
15. An Extension of Limit Analysis Theorems to Incompressible Material with a Non-Associated Flow Rule; J. Joachim Telega, Mohammed Hjiaj, Scott W. Sloan
16. Periodic Soliton Resonances; Masayoshi Tajiri
17. Generalized Legendre-Fenchel Transformation; Claude Vallée, Mohammed Hjiaj, Danièle Fortune Géry de Saxcé
18. A Robust Variational Formulation for a Rod Subject to Inequality Constraints; G.H.M. van der Heijden
19. Computing FEM Solutions of PlasticityProblems via NonLinear Mixed Variational Inequalities; Paolo Venini, Roberto Nascimbene
20. Finite Element Dual Analysis in Piezoelectric Crack Estimation; Chang-Chun Wu, Zi-Ran Li, Lei Li, G. Yagawa
21. Duality and Complementarity in Constrained Mechanical Systems; Hiroaki Yoshimura
22. Mixed Energy Method for Solution of Quadratic Programming Problems; Zhong Wanxie Zhang Hongwu