Abstract: The spring element method (SEM) is a numerical method that uses a spring system to describe an element. Different elements can be described as different spring systems; and the definition of the spring stiffness expressions in the systems is the key point of the spring element method. The four-node rectangular element is described by 6 basic springs, each of which contains two derived springs: normal spring and tangential spring. Poisson spring and pure shear spring are used to describe Poisson and shear effects of the element. Thus a four-node rectangular spring element is presented. Compared with the element stiffness matrix of finite element method, the stiffness expression of each spring is obtained. Springs of the same kind have the same expressions. The stiffness expressions of the normal and tangential springs have corresponding coefficients to be decided. By varying the coefficients in the stiffness expressions of springs, expressions of constant strain, bilinear or Wilson incompatible finite element are achieved by this element. The accuracy of the SEM is verified by theoretical derivation; and this method is applied to the continuum-based discrete element method (CDEM) for case verification. The features of the four-node rectangular spring element are as follows. Different accuracies can be found in different elements. This element can significantly improve the accuracy of the bending problem of beam. Elements with different accuracies can be achieved by using different coefficients.

Key words: four-node rectangular element, spring element method (SEM), finite element method (FEM), spring stiffness