An alternate stable midpoint quadrature to improve the element stiffness matrix of quadrilaterals for application of functionally graded materials (FGM). (1st January 2017) - Jeyakarthikeyan, P.V.; Subramanian, G.; Yogeshwaran, R.
Highlights: A weighted integration route with robust stable one-point integration is recommended. It's an alternative to Gauss quadrature to obtain stiffness matrix of quadrilaterals. A weighted addition of the two approximations produces a far better stiffness matrix. Due to many simple sampling points, the method is most suited for FGM applications. Abstract: An efficient, stable and accurate quadrilateral element and its improved stiffness matrix on the midpoint quadrature concept is proposed in this research study. As a first approximation, the integrating point is considered as midpoint of the element of the mapped 2-square in the (ξ, η) plane (same as one-point Gauss-Quadrature). As a second approximation or stabilizing function, integrating points are assumed to be either at the midpoint of the four quadrants or four element edges of the mapped 2-square element in the (ξ, η) plane and these interpolated data are assembled. An appropriate weighted addition of the two approximations is found to result in a better and stable stiffness matrix than equivalent time delayed value of Gauss Quadrature.