Closed form stiffness matrix solutions for some commonly used hybrid finite elements

Abstract

Closed form solutions for the element stiffness matrices for four commonly used hybrid finite elements, namely, the 5-β-I, 5-β-II, RGH4 and RGH8 elements are given in detail. By using the closed forms, the computational effort needed for the formation of the element stiffness matrices is greatly reduced and the danger of matrix rank deficiency due to the use of insufficient integration points is eliminated. Numerical experiment shows that the CPU time needed for the element stiffness matrix formation procedure for hybrid elements is much less than that for conventional high order displacement finite elements while the quality of the solutions obtained is of similar, and in many cases of better, accuracy.