CLOSED-FORM EXPRESSIONS FOR THE LINEAR AND QUADRATIC STRAIN TETRAHEDRAL FINITE-ELEMENTS

The use of closed-form expressions in a finite element code significan tly reduces the time required to evaluate the element stiffness matrix as compared to Gaussian quadrature. The development of closed-form ex pressions for the element stiffness matrices for the plane-faced linea r strain and quadratic strain tetrahedral finite elements has been pre viously presented elsewhere. In this paper, a reformulation of the pro cess is given which significantly reduces the size of the element stif fness expressions. Expression growth is prevented by decomposing the s train-displacement matrix and utilizing a new matrix which is geometry and material dependent.