An Improved Biharmonic Model—incorporating Higher Order Responses of the Plate Bending Phenomena

Abstract. We modify the usual biharmonic model, still frequently used in the engineering community to model linearly elastic plates. In its traditional form, the biharmonic model diverges in general, since it does not incorporate shear effects. Our changes make it convergent for all loads, under a usual assumption on how the loads depend on the thickness. The idea is to add “higher order” terms that appear in the asymptotic expansion of the exact solution. The changes can be readily incorporated to engineering codes, without degrading the computational performance.