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On optimal shape design of systems governed by mixed Dirichlet‐Signorini boundary value problems
Author(s) -
Haslinger J.,
Neittaanmäki P.,
Meister E.
Publication year - 1986
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670080111
Subject(s) - mathematics , discretization , variational inequality , boundary value problem , finite element method , dirichlet boundary condition , convergence (economics) , dirichlet problem , dirichlet distribution , mathematical optimization , mathematical analysis , physics , economics , thermodynamics , economic growth
A problem for finding optimal shape for systems governed by the mixed unilateral boundary value problem of Dirichlet‐Signorini‐type is considered. Conditions for the solvability of the problem are stated when a variational inequality formulation and when a penalty method is used for solving the state problem in question. The asymptotic relation of design problems based on these two formulations is presented. The optimal shape design problem is discretized by means of finite element method. The convergence results for the approximation are proved. The discretized versions are then formulated as a non‐linear programming problem. Results of practical computations of the problem in question are reported.