Some optimal and inverse problems for orthotropic noncircular cylindrical shells

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In this paper, we consider problems of optimal control involving stressed or strained states of orthotropic, noncircular cylindrical shells. It is assumed that the thickness of the shell is variable. The thickness and the radius of curvature of the directrix of the shell are assumed to be the controls. Existence of solutions for the optimal control problems considered is shown. In particular, existence of solutions for the problem of the minimal weight shell and the problem of nearest-to-equal-strength shell is shown. We present results on the approximation of the optimal control problems by a sequence of finite-dimensional problems, which may be reduced to nonlinear programming problems.