Assumed Stress Function Finite Element Method: Towards Unification

Abstract

The assumed stress function finite element method (ASFFEM) theoretical formulation is recast as a variant of the method of weighted residuals for the solution of partial differential equations (PDEs). As such, the method is seen as a generic technique applicable in other disciplines. To reinforce this notion, an analog of the ASFFEM in the thermal conduction context is presented, along with details regarding its implementation and numerical examples. This thermal code is considered a testbed facilitating further research regarding such issues as curved and 3D element technology in the simplified scalar field problem. This formulation could be called the assumed flux function finite element method (AFFFEM), or more generally an assumed response gradient function finite element method. The accuracy of the primary and secondary quantities in the AFFFEM implementation are compared with results from a standard finite element code. Attention is also drawn to a number of past ASFFEM concerns. This study thus allows a re-characterization of ASFFEM as not restricted to structural mechanics, thus unifying it within the overall family of finite element analysis techniques.