Equivalent Systems for Variable Thickness Plates

Abstract

The research work in this paper consists of a rigorous closed form solution regarding the deflection of thin rectangular plates with variable thickness in one dimension. The rigorous closed form solution is given in the form of an equivalent system of flat plates that replaces the original variable thickness plate. The sum of the deflections of the flat plates is equal to the deflection of the original variable thickness plate. A simplified equivalent system is also obtained in order to reduce the mathematical complexity of the problem. Various variable thickness rectangular plates have been solved by using the method stated above, and the results are compared with those obtained by using the finite difference method.