On thickness optimization of an unilaterally supported anisotropic plate subjected to buckling - Bock, Igor; Lovisek, Jan (Computer Assisted Methods in Engineering and Science, 2002)
We shall be dealing with the eigenvalue optimization problem for an anisotropic plate. The plate is partly unilaterally supported on its boundary and subjected to longitudinal forces causing its buckling. The state problem has then the form of an eigenvalue variational inequality expressing the deflection of the plate and the maximal possible value of the acting forces keeping its stability which corresponds to the first eigenvalue. The demand of the maximal first eigenvalue with respect to variable thicknesses of the plate means to solve the optimal design problem with eigenvalue variational inequality as the state problem. The existence of a solution in the framework of the general theory will be examined. The necessary optimality conditions will be derived. The convergence of the finite elements approximation will be verified.