Stability of Plates in a Nonuniform Stressed State.

Stability of rectangular plates under the effect of contour loads is investigated. A specific feature of such problems consists in the fact that, first, it is necessary to solve the plane problem of the elasticity theory and to find the distribution of stresses in the middle surface, and then to solve the Saint-Venant stability equation with variable coefficients. In this paper, the plane problem of the elasticity theory is solved in terms of complex potentials of G. V. Kolosov using Cauchy-type integrals. The stability equation is written in terms of finite differences. The critical load is determined as the least eigenvalue of the algebraic system obtained, using the method of exponential iteration.