Wpływ wstępnych ugięć na pracę tarczy prostokątnej poddanej nieliniowemu rozkładowi obciążeń

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 the non-linear load – after the stability loss. These Airy stress functions are then determined by means 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. Thc 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.