Journal of Theoretical
and Applied Mechanics

11, 3, pp. 211-227, Warsaw 1973

Wpływ wstępnych ugięć na pracę płyty prostokątnej, zginanej w swej płaszczyźnie

Władysław Walczak
This paper presents a theoretical analysis of the influence of initial deflections on the state of stress and strain in an isotropic, rectangular plate simply supported along the edges and subject to bending in its plane – after the stability loss. The Airy stress function is introduced, and the form of initial deflection and final deflection is assumed to satisfy the boundary conditions. These functions are then determined with the aid of the Karman equations of the non-linear plate theory, the unknown parameters appearing in the function of deflection being found by means of the Galerkin method. The final formulas determining the stresses and strains in the post-critical state of the plate are written in terms of dimensionless coefficients. Numerical calculations are performed for two different forms of the initial deflection of the middle surface of the plate; conditions are also derived under which the influence of initial deflections may be disregarded.