Studies of 4-node Membrane Element with Analytical Stiffness Matrix based on the Quadrilateral Area Coordinates (QAC)

摘要

The new Quadrilateral Area Coordinate (QAC) method is a powerful tool to construct 2D finite element models. Compared with the traditional models using isoparametric coordinates, these new models are less sensitive to mesh distortion. Theoretically, by using the area integral formulae the analytical stiffness matrix could be obtained, which may greatly benefit the computation procedure. However, as the derivation of the analytical expression is relatively complicated, all the current papers still adopt the numerical integration method for computer coding, which indeed impedes the advantages of the QAC method. So in this paper, by introducing the basic QAC formulae into software Maple, the analytical expression of the stiffness matrix of the 4-node membrane QAC element AGQ6-I is obtained for the first time. Then a corresponding FORTRAN subroutine is compiled. Numerical examples show that the present scheme exhibits excellent performances in both computation efficiency and accuracy when compared with the traditional isoparametric models using numerical integration scheme.