TY - RPRT

T1 - Unconditionally Energy Stable Implicit Time Integration:
Application to Multibody System Analysis and Design

AU - Chen, Shanshin

AU - Tortorelli, Daniel A.

AU - Hansen, John Michael

PY - 1999

Y1 - 1999

N2 - 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.

AB - 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.

M3 - Report

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

ER -