Article
MSC:
49A27,
49A29,
49A34,
49J27,
49J40,
49J99,
73k40,
74G30,
74H25,
74K15,
74P99 | MR 0982340 | Zbl 0678.73059 | DOI: 10.21136/AM.1989.104331
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Keywords:
optimal control problem; elliptic, linear symmetric operator; unique solution of stationary variational inequalities; convex set; principle of virtual power; unilateral constraints; bending; cylindrical shell; thickness function; obstacle
optimal control problem; elliptic, linear symmetric operator; unique solution of stationary variational inequalities; convex set; principle of virtual power; unilateral constraints; bending; cylindrical shell; thickness function; obstacle
Summary:
The aim of the present paper is to study problems of optimal design in mechanics, whose variational form are inequalities expressing the principle of virtual power in its inequality form. We consider an optimal control problem in whixh the state of the system (involving an elliptic, linear symmetric operator, the coefficients of which are chosen as the design - control variables) is defined as the (unique) solution of stationary variational inequalities. The existence result proved in Section 1 is applied in Section 2 to the optimal design of an elastic cylindrical shell subject to unilateral constraints. We assume that the bending of the shell is limited by a rigid obstacle. The role of the design variable is played by the thickness of the shell.
References:
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