Asymptotic-based method for a plane elasticity mixed boundary eigenvalue problem

Investigation of plane plates under mixed boundary conditions is of significant practical value: a lot of problems, arisen in machine design, civil engineering etc., are reduced to similar ones. The problems mentioned are usually solved using numerical methods such as the finite element procedure. Nevertheless, numerical approach fails to meet adequately the requirements of optimal structural design methodology. The approximate analytical relation, accurate enough, will be of great practical importance for these needs. The effective analytical approach, combining boundary conditions, perturbation technique and the Pade approximates (PA) of perturbation series, are presented in this paper.

Various problems of dynamics and statics of plates, under mixed boundary conditions, may be solved effectively on the basis of the approach presented.