Research Papers

Discrete Adjoint Method for the Sensitivity Analysis of Flexible Multibody Systems

[+] Author and Article Information
Alfonso Callejo, Valentin Sonneville, Olivier A. Bauchau

Department of Aerospace Engineering,
University of Maryland,
College Park, MD 20742

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received May 17, 2018; final manuscript received August 15, 2018; published online January 7, 2019. Assoc. Editor: Radu Serban.

J. Comput. Nonlinear Dynam 14(2), 021001 (Jan 07, 2019) (11 pages) Paper No: CND-18-1217; doi: 10.1115/1.4041237 History: Received May 17, 2018; Revised August 15, 2018

The gradient-based design optimization of mechanical systems requires robust and efficient sensitivity analysis tools. The adjoint method is regarded as the most efficient semi-analytical method to evaluate sensitivity derivatives for problems involving numerous design parameters and relatively few objective functions. This paper presents a discrete version of the adjoint method based on the generalized-alpha time integration scheme, which is applied to the dynamic simulation of flexible multibody systems. Rather than using an ad hoc backward integration solver, the proposed approach leads to a straightforward algebraic procedure that provides design sensitivities evaluated to machine accuracy. The approach is based on an intrinsic representation of motion that does not require a global parameterization of rotation. Design parameters associated with rigid bodies, kinematic joints, and beam sectional properties are considered. Rigid and flexible mechanical systems are investigated to validate the proposed approach and demonstrate its accuracy, efficiency, and robustness.

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Grahic Jump Location
Fig. 1

Geometrically exact beam element

Grahic Jump Location
Fig. 2

Quarter-car suspension

Grahic Jump Location
Fig. 3

Quarter-car sensitivity derivative dψ/dk versus relative perturbation size Δk/k

Grahic Jump Location
Fig. 5

Rotating beam sensitivity derivative dψ/dD55 versus relative perturbation size ΔD55/D55



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