Bending of Thin Plate with Three‐Point Support

Abstract

A series solution for stresses and displacements in a rectangular plate that is simply supported at three corners has been developed. Surprisingly simple and rigorous formulae for maximum displacement under arbitrary load are given. This is due to the fact that only one term in the series contributes to the displacement of the unsupported corner. This term is orthogonal in energy to all the other terms, and therefore can be immediately found without solving the system of equations. The system of equations to find the coefficients in the series is obtained by applying the conditions of minimum potential energy. A table with maximum displacements and maximum absolute values for principal moments for different ratios of sides has been given. Results are used for an aluminum auto part design optimization.