Graphical Method for Solution of Differential Equation of Plate Bending Problems

The differential equations for indeterminate plate bending cases are complex due to presence of stresses in two-directions, especially when second order analysis is to be considered. In this case, the boundary conditions are coupled with the unknown reaction forces. Traditionally, analytical solutions are presented (Timoshenko and Krieger, 1959) in graphical manner for application to field problems. In the present paper, a graphical solution strategy is presented to avoid the total analytical solution for transcendental differential equations. Analytical solutions are adoptable for simple boundary and loading conditions, while numerical solutions strategies are more suitable and feasible for complexly-coupled boundary conditions. In the procedure presented in the paper, simple numerical integration and numerical differentiation procedures are used, that can be implemented using a computer with very basic configuration also. The method is especially useful in teaching-learning processes. The accuracy of the results from the proposed numerical procedure is presented for plate bending problems.