On computer‐aided analytic element analysis and the similarities of tetrahedron elements

A complete analytical analysis of three‐dimensional, quadratic displacement tetrahedron elements is presented. The results show that the element stiffness can readily be obtained from the much simpler stiffness matrix of the linear displacement element. Thus, the task of obtaining the matrix of the quadratic displacement element is, in effect, reduced to finding that of the linear displacement element. The analysis has been made possible only by using a symbolic manipulation language (PL/I–FORMAC) on a computer. A rather general program for computer‐aided basic element analysis is presented. It seems that the extremely effective tool of symbolic manipulation has hardly been used until now in mechanics.