ABSTRACT

The paper deals with the problem of compliance minimization of thin transversely homogeneous shells and plates within the framework of the free material design. The elastic moduli are design variables, while the isoperimetric condition is expressed by the integral of the trace of Hooke’s tensor. The optimum design problems, in various settings, are reduced to the two mutually dual auxiliary problems similar to those known from Michell’s theory of structures of minimal weight. Like Michell’s structures, the optimal shells are cut out from the design domain by the procedure of solving the auxiliary problems. The method proposed solves simultaneously two problems: optimal material layout and optimal shape of the structure, without any restrictions on the number of holes emerging in the optimal design.