An Analytical Solution to Isotropic Rectangular Cantilever Kirchhoff Plates Using Two Single Series and the Boundary Collocation Method

An analytical solution to arbitrarily loaded isotropic rectangular cantilever Kirchhoff plates was presented. In this study the deflection surface was approximated with the sum of a particular solution to the governing differential equation (GDE) and two single series. The terms of the single series were the product of an unknown function of an independent variable and a trigonometric function of the other independent variable, whereby the trigonometric functions were consistent with the deflection-related boundary conditions (zero deflection or not along an edge). On the one hand the terms of the series were required to satisfy the homogeneous GDE, leading to two uncoupled differential equations, one for each unknown function, and so the approximate solution satisfied exactly the GDE. On the other hand the boundary conditions were satisfied only at selected collocation points along the boundary, the number of collocation points in each direction corresponding to the number of terms of the associated series. Numerical results will be presented in a future version of this paper.