The Performance of an Hexahedron C* Element in Finite Element Analysis

The performance of an 8-noded hexahedron C1* element in elasticity is investigated. Three translational displacements and their derivatives as strain in each direction are considered as degrees of freedom (d.o.f.’s) at each node. The geometric mapping is enforced using a C0 element with no derivative as nodal d.o.f.’s . The stiffness matrix of the element is also computed using a transformation matrix obtained from an equivalent C0 element. The results obtained from elastic stress analysis of a cantilever show that: (i) the convergence rate of 8-noded C1* element is nearly equal to its equivalent C0 element, while it consumes less CPU time with respect to the C0 element; (ii) the element has successfully passed the patch and distortion tests; (iii) the condition number of the stiffness matrix for C1* element is less than the C0 element; (iv) the directly computation of strains  as derivative degrees of freedom at the nodes along with excellent convergence makes the C1* element superior compared with its equivalent  C0 element.