Unconditionally Energy Stable Implicit Time Integration: Application to Multibody System Analysis and Design

Advances in computer hardware and improved algorithms for multibody dynamics over the past decade have generated widespread interest in real-time simulations of multibody mechanics systems. At the heart of the widely used algorithms for multibody dynamics are a choice of coordinates which define the kinmatics of the system, and a choice of time integrations algorithms. The current approach uses a non-dissipative implict Newmark method to integrate the equations of motion defined in terms of the independent joint coordinates of the system. The reduction of the equations of motion to a minimal set of ordinary diffferential equations is employed to avoid the instabilities associated with the direct integrations of differential-algebraic equations. To extend the unconditional stability of the implicit Newmark method to nonlinear dynamic systems, a discrete energy balance is enforced. This constraint however yields spurious oscillations in the computed accelerations. Therefore, a new acceleration correction is applied to eliminate these instabilities and hence retain unconditional stability in an energy sense. In addition sensitivity analyisis and optimizations are applied to create a mechanism design tool. To exemplify the methodology, a wheel loader mechanism is designed to minimize energy consumption subject to trajectory constraints.