A nonlinear transverse shear deformable plate theory allowing a multiple choice of trial displacement and stress distributions

Abstract

This paper deals with a refined formulation of a general, geometrically nonlinear, shear deformable, static plate theory which allows a multiple choice of trial displacement and, consequently, stress distributions through the plate thickness. This is achieved with the incorporation, into a basic trial displacement approximation, of a general function of the transverse coordinate. An appropriate choice of the derivative of that function is, essentially, adequate for an a posteriori control of the transverse shear strain and stress distributions. However, a particular choice of that general function is not provided, leaving, therefore, the theory in its most general form. The development of the theory is based on the concept of small strains and moderate rotations. Its force and moment equilibrium equations are derived variationally, on the basis of the principle of the total potential energy. Under certain conditions, the present nonlinear theory becomes analogous to several linear and nonlinear plate theories available in the literature, in the sense that it can easily adopt and make use of their main characteristics.