Derivation OF STIFFNESS Matrix for A general Two Dimensional Curved Element in General Global Coordinates System

الملخص

In present paper, the derivation of stiffness matrix for a general two dimensional curved element in the global coordinates system is presented. The derivation depends on the assumption that any curved in-plane element can be approximated by a specified curve in polar coordinates. The polar curve assumed in this polar depends on some variables that enable it to represent any two dimensional curved element. The derivation process accompanied by complex integrals which are evaluated by using (Gaussian Quadrature) method of numerical integration. One numerical example is presented to verify the accuracy and efficiency of the derived stiffness matrix. Very good agreement is obtained between the results of the derived stiffness matrix and the results of the exact model.