(untitled) (International Journal of Engineering and Computer Science, 2014)
This paper presents an explicit finite element integration scheme to compute the stiffness matrices for plane problems using symbolic mathematics. Stiffness matrices are expressed as double integrals of the products of global derivatives over the all quadrilateral plane region. These matrices can be shown to depend on material and geometric properties matrix and the rational functions with polynomial numerators and linear denominator in bivariates over a 2-square. We have computed the integrals of these rational functions over a 2-square by explicit integration using the symbolic mathematics capabilities of MATLAB. The proposed explicit finite element integration scheme is illustrated by computing the Prandtl stress function values and the torisonal constant for the square cross section by using the four node linear convex quadrilateral finite elements.An automatic all quadrilateral mesh generation techniques which is recently proposed by the authours is also integrated in the appended application programs written in MATLAB.