Finite displacement static analysis of thin plate with an opening-a variational approach

A generalized work–energy method for the linear and geometrically nonlinear static analysis of thin isotropic plate with a cutout is presented. The plate geometry is divided into few quadrilateral segments. Each segment is defined by four curved edges and the natural coordinates in conjunction with the Cartesian coordinates are used in formulating the stiffness matrix and the load vector. Two different sets of interpolating functions are used for the geometric and displacement representations respectively. The matrix equation of equilibrium is derived from the variational principle. By exploiting the geometric symmetry, numerical results are obtained for the following examples: (a) square plate with circular opening at the centre and (b) circular plate with circular or square inner boundary. The plates are subjected to uniformly distributed load and both the pinned and fixed outside boundary conditions are considered. Very good comparison is observed between the present results and those published in the literature for the fixed square plate without an opening. Effects of the opening size on the displacement are examined in detail.