Geometric Interpretation of a Non-linear Beam Finite Element on the Lie Group SE(3)

VALENTIN SONNEVILLE; ALBERTO CARDONA; OLIVIER BRULS

Archive of Mechanical Engineering - The Journal of Committe of Machine Design of Polish Academy of Science

De Gruyter

Año: 2014 vol. 61 p. 305 - 329

0004-0738

Recently, the authors proposed a geometrically exact beam finite element formulation on the Lie group SE(3). Some important numerical and theoretical aspects leading to a computationally efficient strategy were obtained. For instance, the formulation leads to invariant equilibrium equations under rigid body motions and a locking free element. In this paper we discuss some important aspects of this formulation. The invariance property of the equilibrium equations under rigid body motions is discussed and brought out in simple analytical examples. The discretization method based on the exponential map is recalled and a geometric interpretation is given. Special attention is also dedicated to the consistent interpolation of the velocities.