The problem of deflection shapes of a simply supported plate under a longitudinal strain

In this paper the approximate study the problem of the bifurcation behavior of an elastic plate with the change of the longitudinal compressive strain is carried out. A new scheme which allows to determine the critical values of the strain at which the plate takes a stable curvilinear equilibrium. The scheme also leads to an asymptotic formula which describes the nonlinear deflections of the plate when passing through the critical strain.