FINITE-ELEMENT FORMULATION OF THE FINITE ROTATION SOLID ELEMENT

The paper describes the development of an 8-node solid finite element capable of undergoing both large displacements and large rotations. The constitutive law chosen is for an elastic material. The element is developed on a sound variational basis. The incompatible modes are employed to produce a 'locking' free performance. The operator split method is employed in solving the equilibrium equations which resulted in minimal secondary storage requirements. The rotation vector is chosen as a parametrization of large rotations and, as a consequence, the stiffness matrix obtained by the consistent linearization is a symmetric one. Also, the rotation vector is expressed in a unique way so that it can be additively composed and the update procedure is the simplest one possible. In order to improve the behavior of the element for rotations exceeding 2 pi, we have somewhat modified the total Lagrangian formulation to allow for incremental rotations to appear. The correctness of the procedure is proved with a set of numerical examples.