Premium
On computer‐aided analytic element analysis and the similarities of tetrahedron elements
Author(s) -
Pedersen Pauli
Publication year - 1977
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620110402
Subject(s) - tetrahedron , element (criminal law) , displacement (psychology) , stiffness matrix , finite element method , quadratic equation , matrix (chemical analysis) , stiffness , computer science , mathematics , structural engineering , geometry , engineering , materials science , psychology , political science , law , composite material , psychotherapist
Abstract 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.