Hamel's field variational integrator for simulating dynamics of thin-walled geometrically exact beams with warping effects

Abstract

Using discrete variational principle, a Hamel's field variational integrator (HFVI) for simulating dynamics of thin-walled geometrically exact beams with warping effects is originally proposed. Firstly, a spacetime independent interpolation way for thin-walled beam elements is established on SE(3) × R space by using Hamel's formalism. Then, a new discretization formulation of convective velocity and convective strains on Lie algebra is proposed by using frame operators, which helps to reduce the system's nonlinearity. After that, the variations of discrete convective velocity and discrete convective strain are decoupled from the cross-section configuration variables. This way can avoid the computation of nonlinear exponential map's tangent map and reduce the computation complexity significantly. According the Hamiltonian form of proposed HFVI, the warping variables and discrete convective strains can be independently solved by using discrete compatibility equations on Lie algebra. Finally, the efficiency and accuracy of HFVI is validated by six static and dynamic examples.