Augmented Lagrangian index-3 semi-recursive formulations with projections

Dopico, Domingo Calvo; Varela, Álvaro López; Luaces, Alberto

doi:10.1007/s11044-020-09771-9

Cited by 9 publications

(18 citation statements)

References 15 publications

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“…In this paper, the direct differentiation method has been successfully applied to the semirecursive augmented Lagrangian index-3 formulation with velocity and acceleration projections (ALI3-P) recently reviewed in [13]. As a result, a semi-recursive ALI3-P forward sensitivity formulation has been developed for an arbitrary selection of reference points.…”

Section: Discussionmentioning

confidence: 99%

“…As it was presented in [13], a rotation matrix of a body can be computed as A i = A i−1 A i−1 i , being A i−1 the rotation matrix of body i − 1 and A i−1 i a relative rotation matrix between bodies i − 1 and i. Taking derivatives of this expression, (A i ) z becomes:…”

Section: Evaluation Of (A I ) Zmentioning

confidence: 99%

“…One efficient, accurate and robust constraint enforcement scheme is the augmented Lagrangian index-3 formulation with velocity and acceleration projections (ALI3-P). The combination of the semi-recursive method with the ALI3-P formulation, studied in [13], combines the reduced number of coordinates and constraints of the semi-recursive process with the advantages of the ALI3-P constraint enforcement scheme.…”

Section: Introductionmentioning

confidence: 99%

“…This paper is regarded as a continuation of the former paper [13] in which the semirecursive ALI3-P formulation is thoroughly described. Here, a brief description of the formulation is presented, while the reader is referred to [13] for further details.…”

Section: Introductionmentioning

confidence: 99%

“…The semi-recursive ALI3-P formulation is briefly outlined in this section, and the reader is referred to[13] to gain insight into the composition of the EoM, recursive relations and assembly procedures.…”

mentioning

confidence: 99%

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Augmented Lagrangian index-3 semi-recursive formulations with projections. Direct sensitivity analysis.

Varela

Dopico

Luaces

2023

Preprint

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Sensitivity analysis represents a powerful tool for the optimization of multibody system dynamics. The performance of a gradient-based optimization algorithm is strongly tied to the dynamic and the sensitivity formulations considered. Accuracy and efficiency are critical to any optimization problem, thus they are key factors in the selection of the dynamic and sensitivity analysis approaches used to compute an objective function gradient. Semi-recursive methods usually outperform global methods in terms of computational time, even though they involve sometimes demanding recursive procedures. Semi-recursive methods are well suited to be combined with different constraints enforcement schemes as the augmented Lagrangian index-3 formulation with velocity and acceleration projections (ALI3-P), taking advantage of the robustness, accurate fulfillment of constraint equations and the low computational burden. The sensitivity analysis of the semi-recursive ALI3-P formulation is studied in this document by means of the direct differentiation method. As a result, a semi-recursive ALI3-P sensitivity formulation is developed for an arbitrary reference point selection, and then two particular versions are unfolded and implemented in the general purpose multibody library MBSLIM, using as reference point the center of mass (RTdyn0) or the global origin of coordinates (RTdyn1). Besides, the detailed derivatives of the recursive terms are provided, which will be useful not only for the direct sensitivity formulation presented herein, but also for other sensitivity formulations relying on the same recursive expressions. The implementation has been tested in two numerical experiments, a five-bar benchmark problem and a buggy vehicle.

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Section: Discussionmentioning

confidence: 99%

Section: Evaluation Of (A I ) Zmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Augmented Lagrangian index-3 semi-recursive formulations with projections. Direct sensitivity analysis.

Varela

Dopico

Luaces

2023

Preprint

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Nonlinear response of a multidirectional negative‐stiffness isolation system via semirecursive multibody dynamic approach

Dai,

Carboni,

Quaranta

et al. 2024

Int Journal of Mech Sys Dyn

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This paper investigates an innovative negative‐stiffness device (NSD) that modifies the apparent stiffness of the supported structure for seismic isolation. The NSD comprises a lower base on the bottom and a cap on the top, together with a connecting rod, vertical movable wall, and compressed elastic spring, as well as circumferentially arranged, pretensioned external ropes, and inclined shape memory wires. This configuration can deliver negative stiffness and energy dissipation in any direction within the horizontal plane. A numerical model of the device is developed through a two‐step semirecursive method to obtain the force–displacement characteristic relationship. Such a model is first validated through comparison with the results obtained via the commercial software ADAMS. Finally, a large parametric study is performed to assess the role and the influence of each design variable on the overall response of the proposed device. Useful guidelines are drawn from this analysis to guide the system design and optimization.

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Discrete adjoint variable method for the sensitivity analysis of ALI3-P formulations

Varela

Sandu

et al. 2023

Multibody Syst Dyn

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Augmented Lagrangian index-3 semi-recursive formulations with projections

Cited by 9 publications

References 15 publications

Augmented Lagrangian index-3 semi-recursive formulations with projections. Direct sensitivity analysis.

Augmented Lagrangian index-3 semi-recursive formulations with projections. Direct sensitivity analysis.

Nonlinear response of a multidirectional negative‐stiffness isolation system via semirecursive multibody dynamic approach

Discrete adjoint variable method for the sensitivity analysis of ALI3-P formulations

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