Relations among stiffness coefficients of hexahedral 8-noded finite elements: A simple and efficient way to reduce the integration time

Computing coefficients in stiffness matrices of finite element analysis in computational mechanics is time consuming, especially in large non-linear dynamic problems involving large meshes. Thus, any improvement in computational procedures to reduce the integration CPU time is welcomed. In this work, we suggest a simple and efficient approach based on linear equations to describe the cross-relations among the element´s shape-functions derivatives to compute three coefficients of the nodal stiffness submatrix as a function of other coefficients previously computed. The coefficients can relate different degrees of freedom at a given node in the element. They are used to evaluate other coefficients inside the same nodal submatrix. Improvements ranging between 20% and 24% in CPU time are obtained when the approach is applied to three dimensional discretizations with eight-noded brick finite elements.