Topology optimization of quasistatic contact problems

Allaire, G. (2002). Shape Optimization by the Homogenization Method, Springer, New York, NY.10.1007/978-1-4684-9286-6Search in Google Scholar

Allaire G., Jouve, F. and Toader, A., (2004). Structural optimization using sensitivity analysis and a level let method, Journal of Computational Physics 194(1): 363-393.10.1016/j.jcp.2003.09.032Search in Google Scholar

Ammari, H., Kang, H. and Lee, H. (2009). Layer Potential Techniques in Spectral Analysis, Mathematical Surveys and Monographs, Vol. 153, AMS, Providence, RI.Search in Google Scholar

Amstuz, S., Takahashi T., Vexler, B. (2008). Topological sensitivity analysis for time-dependent problems, ESAIM: Control, Optimisation, and Calculus of Variations 14(3): 427-455.10.1051/cocv:2007059Search in Google Scholar

Ayyad, Y. and Sofonea, M. (2007). Analysis of two dynamic frictionless contact problems for elastic-visco-plastic materials, Electronic Journal of Differential Equations (55): 1-17.Search in Google Scholar

Bendsoe, M.P and Sigmund, O. (2003). Topology Optimization: Theory, Methods, and Applications, Springer, Berlin.Search in Google Scholar

Chambolle, A. (2003). A density result in two-dimensional linearized elasticity and applications, Archive for Rational Mechanics and Analysis 167(3): 211-233.10.1007/s00205-002-0240-7Search in Google Scholar

Chudzikiewicz, A. and Myśliński, A. (2009). Thermoelastic wheel-rail contact problem with elastic graded materials, 8th International Conference on Contact Mechanics and Wear of Rail/Wheel Systems, Firenze, Italy, pp. 795-801.Search in Google Scholar

Duvaut, G. and Lions, J. L. (1972). Les inequations en mecanique et en physique, Dunod, Paris.Search in Google Scholar

Denkowski, Z. and Migórski, S. (1998). Optimal shape design problems for a class of systems described by hemivariational inequalities, Journal of Global Optimization 12(1): 37-59.10.1023/A:1008299801203Search in Google Scholar

Eck, C., Jarušek, J. and Krbeč, M. (2005). Unilateral Contact Problems: Variational Methods and Existence Theorems, Pure and Applied Mathematics, Vol. 270, CRC Press, New York, NY.Search in Google Scholar

Eschenauer, H. A., Kobolev V. V. and Schumacher, A. (1994). Bubble method for topology and shape optimization of structures, Structural Optimization 8(1): 42-51.10.1007/BF01742933Search in Google Scholar

Fulmański, P., Laurain, A., Scheid, J. F. and Sokołowski, J. (2007). A level set method in shape and topology optimization for variational inequalities, International Journal of Applied Mathematics and Computer Science 17(3): 413-430, DOI: 10.2478/v10006-007-0034-z.10.2478/v10006-007-0034-zSearch in Google Scholar

Garreau, S., Guillaume, Ph. and Masmoudi, M. (2001). The topological asymptotic for PDE systems: The elasticity case, SIAM Journal on Control Optimization 39(6): 1756-1778.10.1137/S0363012900369538Search in Google Scholar

Han, W. and Sofonea, M. (2002). Quasistatic Contact Problems in Viscoelasticity and Viscoplasticity, AMS/IP Studies in Advanced Mathematics, Vol. 30, AMS/IP, Providence, RI.Search in Google Scholar

Haslinger, J. and Mäkinen, R. (2003). Introduction to Shape Optimization. Theory, Approximation, and Computation, SIAM Publications, Philadelphia, PA.10.1137/1.9780898718690Search in Google Scholar

Hüber, S., Stadler, G. and Wohlmuth, B. (2008). A primal-dual active set algorithm for three-dimensional contact problems with Coulomb friction, SIAM Journal on Scientific Computation 30(2): 572-596.10.1137/060671061Search in Google Scholar

Jarušek, J., Krbec, M., Rao, M. and Sokołowski, J. (2003). Conical differentiability for evolution variational inequalities, Journal of Differential Equations 193(1): 131-146.10.1016/S0022-0396(03)00136-0Search in Google Scholar

Kowalewski, A., Lasiecka, I. and Sokołowski, J. (2010). Sensitivity analysis of hyperbolic optimal control problems, Computational Optimization and Applications, DOI: 10.1007/s10589-010-9375-x.10.1007/s10589-010-9375-xSearch in Google Scholar

Myśliński, A. (2006). Shape Optimization of Nonlinear Distributed Parameter Systems, Academic Publishing House EXIT, Warsaw.Search in Google Scholar

Myśliński, A. (2008). Level set method for optimization of contact problems, Engineering Analysis with Boundary Elements 32(11): 986-994.10.1016/j.enganabound.2007.12.008Search in Google Scholar

Myśliński, A. (2010). Topology optimization of systems governed by variational inequalities, Discussiones Mathematicae: Differential Inclusions, Control and Optimization 30(2): 237-252.10.7151/dmdico.1122Search in Google Scholar

Nazarov, S. A. and Sokołowski, J. (2003). Asymptotic Analysis of Shape Functionals, Journal de Mathématiques Pures et Appliquées 82(2): 125-196.10.1016/S0021-7824(03)00004-7Search in Google Scholar

Novotny, A. A., Feijóo, R. A., Padra, C. and Tarocco, E. (2005). Topological derivative for linear elastic plate bending problems, Control and Cybernetics 34(1): 339-361.Search in Google Scholar

Rocca, R. and Cocu, M. (2001). Existence and approximation of a solution to quasistatic Signorini problem with local friction, International Journal of Engineering Science 39(11): 1233-1255.10.1016/S0020-7225(00)00089-6Search in Google Scholar

Sokołowski, J. and Zolesio, J. P. (1992). Introduction to Shape Optimization. Shape Sensitivity Analysis, Springer, Berlin.Search in Google Scholar

Sokołowski, J. and Żochowski, A. (1999). On the topological derivative in shape optimization, SIAM Journal on Control and Optimization 37(4): 1251-1272.10.1137/S0363012997323230Search in Google Scholar

Sokołowski, J. and Żochowski, A. (2004). On topological derivative in shape optimization, in T. Lewiński, O. Sigmund, J. Sokołowski and A. Żochowski (Eds.), Optimal Shape Design and Modelling, Academic Publishing House EXIT, Warsaw, pp. 55-143.Search in Google Scholar

Sokołowski, J. and Żochowski, A. (2005). Modelling of topological derivatives for contact problems, Numerische Mathematik 102(1): 145-179.10.1007/s00211-005-0635-0Search in Google Scholar

Sokołowski, J. and Żochowski, A. (2008). Topological derivatives for optimization of plane elasticity contact problems, Engineering Analysis with Boundary Elements 32(11): 900-908.10.1016/j.enganabound.2007.08.013Search in Google Scholar

Strömberg, N. and Klabring, A. (2010). Topology optimization of structures in unilateral contact, Structural Multidisciplinary Optimization 41(1): 57-64.10.1007/s00158-009-0407-zSearch in Google Scholar