On the use of shape functions in the cell centered finite volume formulation for plate bending analysis based on Mindlin–Reissner plate theory

This paper deals with a new formulation of the cell centered finite volume application for plate bending analysis based on Mindlin–Reissner plate theory. In this formulation shape functions are used to represent the variation of the unknown variables across the control volumes’ faces, which facilitates the calculation of stress resultants on the faces. The performance of the formulation for the computation of displacements and stress resultants for thin and thick plates is evaluated in a number of test problems. This testing reveals that the proposed approach enhances the predictive capability of the finite volume method in the analysis of thin to thick plates.