A novel nonsmooth dynamics method for multibody systems with friction and impact based on the symplectic discrete format

Abstract

Summary As multibody systems often involve unilateral constraints, nonsmooth phenomena, such as impacts and friction, are common in engineering. Therefore, a valid nonsmooth dynamics method is highly important for multibody systems. An accuracy representation of multibody systems is an important performance indicator of numerical algorithms, and the energy balance can be used efficiently evaluate the performance of nonsmooth dynamics methods. In this article, differential algebraic equations (DAEs) of a multibody system are constructed using the D'Alembert's principle, and a novel nonsmooth dynamics method based on symplectic discrete format is proposed. The symplectic discrete format can maintain the energy conservation of a conservative system; this property is expected to extend to nonconservative systems with nonsmooth phenomena in this article. To evaluate the properties of the proposed method, several numerical examples are considered, and the results of the proposed method are compared with those of Moreau's midpoint rule. The results demonstrate that the solutions obtained using the proposed method, which is based on the symplectic discrete format, can realize a higher solution accuracy and lower numerical energy dissipation, even under a large time step.

A Symplectic Conservative Perturbation Series Expansion Method for Linear Hamiltonian Systems with Perturbations and Its Applications

“…Zhang [30] applied the symplectic Runge-Kutta method in the dynamics of spacecraft relative motion. Peng [31,32] proposed the symplectic nonsmooth dynamic method for multibody system analysis. The numerical results all illus-trated high accuracy and stability as well as good conservation properties of the symplectic algorithms above.…”