A new formulation for dynamics finite element

The subject of this paper is to present a new family of dynamic finite element, which has a formulation based on a simple expansion of trigonometric functions such as sine and cosine. This formulation allows to generating unconditionally stable elements and to excluding both spurious wave reflection and evanescent effect. Also, it is shown how to elevate the error order associated with the dynamic finite element.

The finite elements analyzed here are the rod and beam (according to Timoshenko beam theory) elements. These types of elements have gained even more importance in the automotive industry engineering due to its low computational cost. Today, the structural conception of a vehicle is resumed to a wireframe modeling, which accelerates considerably the optimization process by using morphing operations over the geometry. The new formulation proposed in this work, for the beam element specifically, has lower computation cost then the classic formulation, which is based on energy criteria (the minimum potential theory) leading to a consistent (full) mass matrix.

This work is a component of the author's doctor degree thesis at USP-São Carlos.