Minimization of the discretization error in mass and stiffness formulations by an inverse method

This paper is concerned with the formulation of mass and sti¤ness matrices. In the direct approach one uses assumed shape functions to develop the mass and sti¤ness terms. Alternatively, we may construct the matrices by using an inverse approach; the terms are assigned so that the di¤erence between an analytical model and a numerical (discrete) one is minimized. Here we show that more accurate models can be obtained by the latter approach. The accuracy of rod, beam and plate elements that have been developed by both of the approaches are discussed, and an accurate model of a rectangular plate is obtained by using the inverse method. The superior performance of the new element compared to other established models is demonstrated for the cases of static and dynamic response of a clamped plate