Semi-analytical sensitivity analysis approach for fully coupled optimization of flexible multibody systems

Zhang, Mengru; Peng, Haijun; Song, Ningning

doi:10.1016/j.mechmachtheory.2021.104256

Cited by 18 publications

(7 citation statements)

References 36 publications

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“…Here, part of the chain rule is calculated via finite differencing e.g. for the direct method: [38,44,62,138] direct differentiation [24,111,132,[137][138][139]159] adjoint variable method [6, 20, 21, 26, 44, 60, 72-74, 81, 84, 100, 101, 105, 106, 123, 149, 159] complex step method [20,21,26] automatic differentiation [4,25,63] The complex-step method of sensitivity analysis in which the perturbation is carried out with the imaginary value j x i originates in [95,96,130],…”

Section: General Sensitivity Analysismentioning

confidence: 99%

“…In other cases, cumbersome and error-prone coding effort involved in analytic differentiation can be avoided by using other methods including automatic differentiation [4] and numerical differentiation. Examples of the semi-analytical approach for the computation of the partial derivatives with a numerical differentiation method in order to limit the implementation effort are given in [64,152,159]. This combines the advantage of high computational efficiency due to the analytical direct differentiation of the equation of motion including the application of the chain rule to system parameter sensitivities and the advantage of limited implementation effort due to the numerical differentiation of partial derivatives of the system parameters, leading to a semi-analytic approach.…”

Section: Sensitivity Analysis For Governing Equationsmentioning

confidence: 99%

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A review of flexible multibody dynamics for gradient-based design optimization

2021

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Design optimization of flexible multibody dynamics is critical to reducing weight and therefore increasing efficiency and lowering costs of mechanical systems. Simulation of flexible multibody systems, though, typically requires high computational effort which limits the usage of design optimization, especially when gradient-free methods are used and thousands of system evaluations are required. Efficient design optimization of flexible multibody dynamics is enabled by gradient-based optimization methods in concert with analytical sensitivity analysis. The present study summarizes different formulations of the equations of motion of flexible multibody dynamics. Design optimization techniques are introduced, and applications to flexible multibody dynamics are categorized. Efficient sensitivity analysis is the centerpiece of gradient-based design optimization, and sensitivity methods are introduced. The increased implementation effort of analytical sensitivity analysis is rewarded with high computational efficiency. An exemplary solution strategy for system and sensitivity evaluations is shown with the analytical direct differentiation method. Extensive literature sources are shown related to recent research activities.

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Section: General Sensitivity Analysismentioning

confidence: 99%

Section: Sensitivity Analysis For Governing Equationsmentioning

confidence: 99%

A review of flexible multibody dynamics for gradient-based design optimization

2021

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“…Furthermore, the deformations of the structural components in this work are assumed to be small such that multibody formulations relying on the small-deformation assumption can be used. Nevertheless, interesting works on structural optimization that are described using the Absolute Nodal Coordinates Formulation (ANCF) have been published [6,7,8,9,10].…”

Section: Introductionmentioning

confidence: 99%

Topology Optimization for Dynamic Flexible Multibody Systems Using the Flexible Natural Coordinates Formulation

Vanpaemel

Asrih

Vermaut

et al. 2023

Preprint

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“…Alternatively, it is recommended in [8] to apply automatic differentiation [10] to obtain the derivatives of the system equations with respect to the state and design variables, in particular, for complex multibody systems. A third way is presented in [22], where the state sensitivities are computed analytically and the design sensitivities by numerical differentiation.…”

Section: Introductionmentioning

confidence: 99%

On design sensitivities in the structural analysis and optimization of flexible multibody systems

Held

2021

Multibody Syst Dyn

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The structural analysis and optimization of flexible multibody systems become more and more popular due to the ability to efficiently compute gradients using sophisticated approaches such as the adjoint variable method and the adoption of powerful methods from static structural optimization. To drive the improvement of the optimization process, this work addresses the computation of design sensitivities for multibody systems with arbitrarily parameterized rigid and flexible bodies that are modeled using the floating frame of reference formulation. It is shown that it is useful to augment the body describing standard input data files by their design derivatives. In this way, a clear separation can be achieved between the body modeling and parameterization and the system simulation and analysis.

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Semi-analytical sensitivity analysis approach for fully coupled optimization of flexible multibody systems

Cited by 18 publications

References 36 publications

A review of flexible multibody dynamics for gradient-based design optimization

A review of flexible multibody dynamics for gradient-based design optimization

Topology Optimization for Dynamic Flexible Multibody Systems Using the Flexible Natural Coordinates Formulation

On design sensitivities in the structural analysis and optimization of flexible multibody systems

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