A quaternion-based weak form quadrature element formulation for spatial geometrically exact beams

摘要

This paper deals with spatial beams undergoing large displacements and rotations. A weak form quadrature element formulation is put forward based on the geometrically exact beam model. Spatial rotations are represented by quaternion algebras to achieve a total Lagrangian formulation without singularities. Besides high computational efficiency, the present formulation retains strain objectivity and avoids locking problems that may occur in low-order finite element formulations. Several benchmark examples are studied and results are compared with those available in the literature, demonstrating the feasibility, accuracy and efficiency of the weak form quadrature element formulation.