Plates on two-parameter elastic foundations with nonlinear boundary conditions by the boundary element method

A boundary element method is developed for the bending analysis of plates having nonlinear boundary conditions and resting on two-parameter elastic foundations. The nonlinearity of the problem arises from the normal bending moment of plates which is assumed to be nonlinear function of the boundary slope recognized as a support model with nonlinear rotational restraint. Thus, the solution can be treated all cases of the boundary conditions ranging from simple support to completely fixed support. The kernels of the boundary integral equations are conveniently established which the fundamental solution for the linear plate theory is used. The surface integration of the kernels for the foundation pressure is evaluated by using the property of Dirac delta function. The system of nonlinear equations is established and solved by the Newton–Raphson iterative process. The application of high-order elements, i.e. cubic elements, for improving the solution is adopted. Numerical results of several problems are given to demonstrate the accuracy and applicability of the proposed method.