NDLI: First order sensitivity analysis of flexible multibody systems using absolute nodal coordinate formulation

Content Provider	Springer Nature Link
Author	Pi, Ting Zhang, Yunqing Chen, Liping
Copyright Year	2011
Abstract	Design sensitivity analysis of flexible multibody systems is important in optimizing the performance of mechanical systems. The choice of coordinates to describe the motion of multibody systems has a great influence on the efficiency and accuracy of both the dynamic and sensitivity analysis. In the flexible multibody system dynamics, both the floating frame of reference formulation (FFRF) and absolute nodal coordinate formulation (ANCF) are frequently utilized to describe flexibility, however, only the former has been used in design sensitivity analysis. In this article, ANCF, which has been recently developed and focuses on modeling of beams and plates in large deformation problems, is extended into design sensitivity analysis of flexible multibody systems. The Motion equations of a constrained flexible multibody system are expressed as a set of index-3 differential algebraic equations (DAEs), in which the element elastic forces are defined using nonlinear strain-displacement relations. Both the direct differentiation method and adjoint variable method are performed to do sensitivity analysis and the related dynamic and sensitivity equations are integrated with HHT-I3 algorithm. In this paper, a new method to deduce system sensitivity equations is proposed. With this approach, the system sensitivity equations are constructed by assembling the element sensitivity equations with the help of invariant matrices, which results in the advantage that the complex symbolic differentiation of the dynamic equations is avoided when the flexible multibody system model is changed. Besides that, the dynamic and sensitivity equations formed with the proposed method can be efficiently integrated using HHT-I3 method, which makes the efficiency of the direct differentiation method comparable to that of the adjoint variable method when the number of design variables is not extremely large. All these improvements greatly enhance the application value of the direct differentiation method in the engineering optimization of the ANCF-based flexible multibody systems.
Starting Page	153
Ending Page	171
Page Count	19
File Format	PDF
ISSN	13845640
Journal	Multibody System Dynamics
Volume Number	27
Issue Number	2
e-ISSN	1573272X
Language	English
Publisher	Springer Netherlands
Publisher Date	2011-07-01
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	ANCF Direct differentiation method Adjoint variable method HHT-I3 Invariant matrices Electrical Engineering Optimization Vibration, Dynamical Systems, Control Automotive Engineering Mechanical Engineering
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Mechanical Engineering Aerospace Engineering Modeling and Simulation Computer Science Applications

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