Bending problems of rectangular Reissner plate with free edges laid on tensionless Winkler foundations

In this paper, an analytical method for solving the bending problems of rectangular Reissner plate with free edges under arbitrary loads laid on tensionless Winkier foundations is proposed. By assuming proper form of Fourier series with supplementary terms, which meet derivable conditions, for deflection and shear force functions, the basic differential equations with given boundary conditions can be transformed into a set of simple infinite algebraic equations. For common Winkier foundations, this set of equations can be solved directly and for tensionless Winkler foundations, it is a set of weak nonlinear algebraic equations, the solution of which can be obtained easily by using iterative procedures.