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shape optimization; sensitivity analysis; stress-strain relations; contact
Optimal shape design problem for a deformable body in contact with a rigid foundation is studied. The body is made from material obeying a nonlinear Hooke’s law. We study the existence of an optimal shape as well as its approximation with the finite element method. Practical realization with nonlinear programming is discussed. A numerical example is included.
[1] D. Begis and R. Glowinski: Application de la méthode des éléments finis à  l’approximation d’un problème de domaine optimal. Appl. Math. & Optim. 2 (1975), 130–169. DOI 10.1007/BF01447854 | MR 0443372
[2] D. Chenais: On the existence of a solution in a domain identification problem. J. Math. Anal. Appl. 52 (1975), 189–289. DOI 10.1016/0022-247X(75)90091-8 | MR 0385666 | Zbl 0317.49005
[3] J. Haslinger and A. Klarbring: On almost constant contact stress distributions by shape optimization. Struct. Optimiz. 5 (1993), 213–216. DOI 10.1007/BF01743581
[4] J. Haslinger and R. Mäkinen: Shape optimization of elasto-plastic bodies under plane strains: sensitivity analysis and numerical implementation. Struct. Optimiz. 4 (1992), 133–141. DOI 10.1007/BF01742734
[5] J. Haslinger and P. Neittaanmäki: Finite Element Approximation for Optimal Shape, Material and Topology Design. Chichester: John Wiley & Sons, 1996. MR 1419500
[6] J. Haslinger, P. Neittaanmäki and T. Tiihonen: Shape optimization of an elastic body in contact based on penalization of the state. Apl. Mat. 31 (1986), 54–77. MR 0836802
[7] I. Hlaváček: Inequalities of Korn’s type uniform with respect to a class of domains. Apl. Mat. 34 (1989), 105–112. MR 0990298
[8] The NAG Fortran Library, Mark 16. (1993), Oxford: The Numerical Algorithms Group Limited.
[9] J. Nečas, and I. Hlaváček: Mathematical Theory of Elastic and Elasto-Plastic Bodies: an Introduction. Amsterdam: Elsevier, 1981. MR 0600655
[10] J. Nečas and I. Hlaváček: Solution of Signorini’s contact problem in the deformation theory of plasticity by secant modules method. Apl. Mat. 28 (1983), 199–214. MR 0701739
[11] I. Hlaváček, J. Haslinger, J. Nečas and J. Lovíšek: Solution of Variational Inequalities in Mechanics. Applied Mathematical Sciences 66, Springer-Verlag, 1988. MR 0952855
[12] J. Sokołowski and J.-P. Zolesio: Introduction to Shape Optimization: Shape Sensitivity Analysis. Berlin: Springer Verlag, 1992. MR 1215733
[13] K. Washizu: Variational Methods in Elasticity and Plasticity (second edition). Oxford: Pergamon Press, 1974. MR 0391680
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