(untitled) (International Journal of Engineering and Computer Science, 2016)
This paper presents an explicit finite element integration scheme to compute the stiffness matrices for linear convex quadrilaterals. Finite element formulationals express stiffness matrices as double integrals of the products of global derivatives. These integrals can be shown to depend on triple products of the geometric properties matrix and the matrix of integrals containing the rational functions with polynomial numerators and linear denominator in bivariates as integrands over a 2-square. These integrals are computed explicitely by using symbolic mathematics capabilities of MATLAB. The proposed explicit finite element integration scheme can be applied solve boundary value problems in continuum mechanics over convex polygonal domains.We have also developed an automatic all quadrilateral mesh generation technique for convex polygonal domain which provides the nodal coordinates and element connectivity. We have used the explicit integration scheme and the novel mesh generation technique to solve the Poisson equation with given Dirichlet boundary conditions over convex polygonal domains.