An explicit finite element integration scheme using automatic mesh generation technique for linear convex quadrilaterals over plane regions (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.