Boundary-type Ritz method for the analysis of arbitrarily shaped polygonal plates

This study presents an upgraded Ritz method capable of providing solutions to thin polygonal plates of regular and irregular shapes with various boundary conditions. The method presented herein is called the Boundary-Type Ritz (BTR) Method and it circumvents the complexity of the involved domains by transforming the encountered integrals to other forms that need to be evaluated only at corners. This leads to very fast computations with full preservation of the accuracy. The divergence theorem is implemented for this purpose. Following this method, the coordinates of the corners are solely needed to perform the integrations. The applicability of this method is proved in this paper by presenting various examples involving plates of different polygonal shapes with different boundary conditions. The results are compared to the counterpart FEM solutions and a very good agreement is observed.