MINIMIZATION OF THE DISCRETIZATION ERROR IN PLANE STRESS ELEMENT FORMULATION BY AN INVERSE METHOD

Common methods in determination of element mass and stiffness matrices are minimization of the energy function, the residues of the equation of motion and etc. In these methods, by using assumed shape function for element behavior and by minimization of some functions, we can determine the element formulation. Alternatively, we may construct the formulation by using an inverse approach. The purpose of inverse method is minimization of the difference between the numerical (discrete model) and the analytical (continuous model) models. In the inverse method, we obtain the optimum value of independent parameters for stiffness (and mass) matrix, so that the minimum discretization error accurse. In this paper, it is shown that more accurate models can be obtained by the inverse method, also the relation between inverse method and deformation modes of the element is developed and with the aid of this relation, an optimum model for the rectangular plane stress element is obtained.