Lower Order Tetrahedral Finite Elements With Rotational Degrees of Freedom for Solid Modelling

The investigation reported in this paper is concerned with the development of efficient, conceptually simpler, mathematically rigorous and physically meaningful three-dimensional (3D) finite elements for solid modelling. A mixed variational principle based on the hybrid strain formulation has been adopted for the derivation of element stiffness matrices of two lower order tetrahedral finite elements. Explicit expressions for element matrices have been derived with a combination of hand manipulation and computer algebraic package, MAPLE. Each of the two finite elements has four nodes. Every one of the latter has six degrees of freedom (DOF). These include three translational and three rotational DOF. Element performance is evaluated with benchmark problems. For brevity, only two benchmark problems are included in this paper. It is shown numerically that the results converge to the true solution and have superior accuracy compared with those previously published in the literature. Mathematically, the elements being proposed are simple and frame invariant. Computationally, they are very efficient compared with higher order tetrahedral finite elements and other lower order tetrahedral finite elements.