On symbolic manipulation and code generation of a hybrid three-dimensional solid element

A symbolic procedure is utilized to derive the analytical expressions of the component matrices resulting to the closed-form integration of a stiffness matrix of a hybrid finite element. In order to alleviate the expression growth problem, we employ special techniques, including the use of symmetry conditions, pattern search, and introduction of intermediate variables, so that the final form of the derived stiffness matrix is suitable for coding implementation. Application of the symbolic procedure is made on a hybrid three-dimensional 8-node solid element. The same procedure is equally applicable to other types of hybrid elements.