EXPLICIT INTEGRATION OF THE STIFFNESS MATRIX OF A 4-NODED-PLANE-ELASTICITY FINITE-ELEMENT

The paper deals with the symbolic integration of a 4-noded isoparametr ic finite element for plane elasticity. An efficient approach to gener ate explicit formulas for computing the elementary stiffness matrix is discussed. The procedure is based on the use of the Derive symbolic m anipulation code as well as in a posteriori manipulation of the expres sions obtained. The accuracy of the results is tested in extremely dis torted and geometrically ill-conditioned elements. Three practical eng ineering models are presented and the accuracy of the results is discu ssed. A computer time comparison between both numerical and symbolic i ntegration approaches is also included, showing that relevant CPU savi ngs are obtained when applying symbolic integration.