Introduction

Finite element methods are today widely applied in various branches of engineering such as aeronautic and astronautic, civil and mechanical engineering. Nevertheless, improving element accuracy and developing efficient elements remain long term research topics. As well known, finite element formulas are characterized by matrix operations and large expressions for the introduction of interpolation functions and element nodal parameters. In dealing with an element, much researchers' effort and time are spent in performing and checking these algebraic manipulation. If a derivation error occurs, the researcher has to go through the tedious process once more. Even worse, if an error in derivation is not detected and the resulting element is tested poor, the idea for developing the element, which might be a right way, could be completely abandoned by the researcher.

Symbolic computer algebra, represented by symbolic computational softwares, e. g. Maple and Mathematica among others, is powerful in manipulating large symbolic expressions and has been widely applied in scientific research fields such as mathematics [1], quantum physics, fluid dynamics [2], artificial intelligence engineering and so on. Symbolic computer algebra is also being gradually applied to dealing with finite element formulations, mainly to explicitly obtain element stiffness matrix [3,4,5,6,8,7]. In this presentation, based on the authors' recent work, potential applications of symbolic computer algebra in finite element methods are explored. These applications mainly include: explicit derivation of element stiffness matrix, parametric study of finite elements based on mixed field formulations, investigation of finite element relations and development of efficient finite elements from field consistence approach.