Stiffness Matrices of Isoparametric Four-Node Finite Elements by Exact Analytical Integration
Gautam Dasgupta · Journal of Aerospace Engineering · 2008
Explicit algebraic expressions needed to compute element stiffness matrices using procedural (FORTRAN) and object oriented (C++) computer programs are presented. Numerical illustrations for a convex quadrilateral and a triangle with a side node are included. The wide controversy due to conventional element level approximate numerical quadrature within the computational square domain in η and ξ coordinates is completely resolved here by the closed form analytical integration within the physical element, in x and y coordinates.