Non-linear analysis of arbitrary quadrilateral plates by use of Kirchhoff-Love theory

Abstract

Very large displacement but small strain of a very thin quadrilateral plate is studied using Kirchhoff-Love theory. The numerical investigation is based on the mapping of the quadrilateral plate onto the computational coordinates of a standard square and interpolation of the displacement field over the whole domain with no director assignment. The present investigation, which is basically a limiting analysis of the Cosserat’s theory, enforces the well known Kirchhoff’s hypothesis which denies the existence of shear strain in the direction of the plate’s thickness. After forming the decoupled nonlinear equations, the material and geometric tangential stiffness matrices are derived through a linearization process and different stages of the problem solution are presented. Finally through certain numerical examples and comparison of the results with some existing researches the validity and the accuracy of the present method are verified.