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Optimal size of a rigid thin stiffener reinforcing an elastic plate on the outer edge
Author(s) -
Lazarev N. P.,
Rudoy E. M.
Publication year - 2017
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201600291
Subject(s) - enhanced data rates for gsm evolution , boundary (topology) , boundary value problem , penalty method , function (biology) , mathematics , mathematical analysis , materials science , mathematical optimization , computer science , telecommunications , evolutionary biology , biology
The mathematical models describing equilibrium of cracked elastic plates with rigid thin stiffeners on the outer boundary are studied. On the crack faces the boundary conditions are specified in the form of inequalities which describe the mutual nonpenetration of the crack faces. We analyze the dependence of solutions on the length of the thin rigid stiffener reinforcing the cracked Kirchhoff‐Love plate on the outer edge. The existence is proved of the solution to the optimal control problem. For this problem the cost functional is defined by an arbitrary continuous functional, while the length parameter of the thin rigid stiffener is chosen as a control function.