A family of triangular and tetrahedral elements with rotational degrees of freedom

A purely kinematic approach to the formulation of plane stress/strain triangular elements with three nodes as well as tetrahedral elements with four nodes including rotational degrees of freedom is presented. The class of elements is shown to perform comparably well in several well-established test cases. Essentially, the displacement interpolation functions are cubic allowing for more flexibility in the displacement-based formulation. The in-plane triangle can be augmented by a plate bending element to form an efficient triangular shell element.