Abstract
Shape optimization problems with uncertainties are considered for a rigid punch interacting with an elastic medium. Considered loads are supposed to be given with incomplete data or described by random variables. Corresponding investigations are respectively performed in the framework of a minimax (worst case scenario) approach or a stochastic approach. As a result of the proposed approaches and applied analytical methods, the optimal designs of the punch are obtained and presented in the paper for various definitions of uncertainties.
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References
Banichuk NV (2009) Optimal forms in mechanics of contact interaction. Dokl Phys 54(7):333–337
Banichuk NV, Ivanova SYu (2009) Optimization problems of contact mechanics with uncertainties. Mech Based Des Struct Mach 37(2):143–156
Banichuk NV, Ivanova SYu (2009) Shape optimization in contact problems in the theory of elasticity with incomplete data on external actions. J Appl Math Mech 73(6):696–704
Banichuk NV, Ivanova SYu, Makeev EV, Ragnedda F (2009) Optimal stamp shape under probabilistic data concerning external loading. Probl Strength Plastic 71:52–60. In Russian
Banichuk NV, Neittaanmäki PJ (2010) Structural optimization with uncertainties. Solid mechanics and its applications, vol 162. Springer, Berlin
Banichuk NV, Ragnedda F, Serra M (2010) Some optimization problems for bodies in quasi-steady state wear. Mech Based Des Struct Mach 38(4):430–439
Haslinger J, Neittaanmäki P, Tiihonen T (1986) Shape optimization in contact problems based on penalization of the state inequality. Appl Math 31(1):54–77
Acknowledgements
The work is performed under support of RFBR (grant 11-08-00030-a), RAS Program 13, Program of Support of Leading Scientific Schools (grant 3288.2010.1).
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Banichuk, N., Ivanova, S. (2013). Uncertainties in Contact Mechanics and Shape Optimization Problems. In: Repin, S., Tiihonen, T., Tuovinen, T. (eds) Numerical Methods for Differential Equations, Optimization, and Technological Problems. Computational Methods in Applied Sciences, vol 27. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5288-7_19
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DOI: https://doi.org/10.1007/978-94-007-5288-7_19
Publisher Name: Springer, Dordrecht
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