Abstract
AbstractNew problem statements for the optimal design of thin‐wall structural elements are considered by means of optimal control theory. The distribution of initial curvature of shallow curvilinear structural elements in a non‐strain state is taken as the control function.1–3 Integral stiffness is considered as the optimized performance index. The necessary optimality condition and the partial differential equations for the adjoint variables are derived. An analysis of these relations is carried out, and the initial optimal control problem is reduced to a boundary problem of the bending of an uncurved element. Problems of optimal design of plates under transverse loads, as well as under tensile or compression forces acting in the middle surface, are studied. Analogous problems of optimal design for shallow curvilinear plates on an elastic foundation are also investigated. Some two‐dimensional analytical solutions for optimal plates under loads of different types are obtained.
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