Simple degenerate formulation for large displacement analysis of beams

A finite-element formulation for the large displacement analysis of beams i s proposed. It is based on the degeneration approach: The governing equatio ns for a general solid are directly discretized. The assumptions of the Tim oshenko beam theory are implemented in the discretization process by devisi ng beam elements and utilizing the penalty method. The formulation for 2D b eam analysis is first presented and the 3D formulation follows. Characteris tically, the proposed beam elements possess relative nodes and rotations ar e excluded from nodal variables. The beam formulations thus developed are q uite simple and straightforward. It is noteworthy that unlike conventional formulations, the present formulation for 3D beam analysis is just a simple extension of the 2D case, which can be attributed mainly to the avoidance of rotations in nodal variables. In numerical examples, the approximate pen alty number is investigated first by analyzing a cantilever beam, and it tu rns out to be 10(3) times Young's modulus. With this value, example problem s are solved and excellent agreement with the existing solutions is observe d, confirming the validity of the present formulation.