Direct Sensitivity Analysis of Multibody Systems Modeled With Relative Coordinates Using an Augmented Lagrangian Formulation With Projections.

2021 ◽  
Author(s):  
Alvaro Lopez- Varela ◽  
Daniel Dopico ◽  
Alberto Luaces
Keyword(s):  
Sensitivity Analysis ◽  
Multibody Systems ◽  
Augmented Lagrangian ◽  
Lagrangian Formulation ◽  
Relative Coordinates ◽  
Direct Sensitivity ◽  
Augmented Lagrangian Formulation

Direct Sensitivity Analysis of Spatial Multibody Systems With Joint Friction Using Index-1 Formulation

2021 ◽  
Author(s):  
Adwait Verulkar ◽  
Corina Sandu ◽  
Daniel Dopico ◽  
Adrian Sandu
Keyword(s):  
Sensitivity Analysis ◽  
Dynamic Systems ◽  
Multibody Systems ◽  
Friction Model ◽  
Design Parameters ◽  
Adjoint Sensitivity ◽  
Joint Friction ◽  
Multibody Dynamic ◽  
Model Dynamics ◽  
Direct Sensitivity

Abstract Sensitivity analysis is one of the most prominent gradient based optimization techniques for mechanical systems. Model sensitivities are the derivatives of the generalized coordinates defining the motion of the system in time with respect to the system design parameters. These sensitivities can be calculated using finite differences, but the accuracy and computational inefficiency of this method limits its use. Hence, the methodologies of direct and adjoint sensitivity analysis have gained prominence. Recent research has presented computationally efficient methodologies for both direct and adjoint sensitivity analysis of complex multibody dynamic systems. The contribution of this article is in the development of the mathematical framework for conducting the direct sensitivity analysis of multibody dynamic systems with joint friction using the index-1 formulation. For modeling friction in multibody systems, the Brown and McPhee friction model has been used. This model incorporates the effects of both static and dynamic friction on the model dynamics. A case study has been conducted on a spatial slider-crank mechanism to illustrate the application of this methodology to real-world systems. Using computer models, with and without joint friction, effect of friction on the dynamics and model sensitivities has been demonstrated. The sensitivities of slider velocity have been computed with respect to the design parameters of crank length, rod length, and the parameters defining the friction model. Due to the highly non-linear nature of friction, the model dynamics are more sensitive during the transition phases, where the friction coefficient changes from static to dynamic and vice versa.

Anisotropic Contact and Wear Simulation Using Boundary Elements

2014 ◽  
Vol 618 ◽  
pp. 73-98 ◽  
Author(s):  
Luis Rodríguez-Tembleque ◽  
M.H. Aliabadi ◽  
R. Abascal
Keyword(s):  
Boundary Element Method ◽  
Contact Problem ◽  
Boundary Element ◽  
Tribological Properties ◽  
Augmented Lagrangian ◽  
Rolling Contact ◽  
Lagrangian Formulation ◽  
Wear Simulation ◽  
Contact Pressures ◽  
Augmented Lagrangian Formulation

Wear is present in all mechanical interface interaction problems –contact, fretting, orrolling-contact–, and it is one of the main reasons for inoperability in mechanical components. Thepresented work is a review of recent research carried out by the authors [1, 2, 3]. A boundary-element-based methodology to compute anisotropic wear on 3D contact, fretting, or rolling-contact conditionsis presented. Damage on the geometries of the solids and the contact pressures evolution under or-thotropic tribological properties can be predicted using this contact framework, where the formulationuses the Boundary Element Method to compute the elastic inuence coefcients. Contact problem isbased on an Augmented Lagrangian formulation, and restrictions fullment is established by a set ofprojection functions. The boundary element anisotropic wear formulation presented is illustrated withsome examples, in which some studies about the inuence of anisotropic wear on contact variablesevolution are shown.

Preconditioned augmented Lagrangian formulation for nearly incompressible cardiac mechanics

2017 ◽  
Vol 34 (4) ◽  
pp. e2948 ◽  
Author(s):  
Joventino Oliveira Campos ◽  
Rodrigo Weber dos Santos ◽  
Joakim Sundnes ◽  
Bernardo Martins Rocha
Keyword(s):  
Augmented Lagrangian ◽  
Cardiac Mechanics ◽  
Lagrangian Formulation ◽  
Augmented Lagrangian Formulation

Computing Sensitivity Analysis of Vehicle Dynamics Based on Multibody Models

2013 ◽  
Author(s):  
Yitao Zhu ◽  
Daniel Dopico ◽  
Corina Sandu ◽  
Adrian Sandu
Keyword(s):  
Sensitivity Analysis ◽  
Vehicle Dynamics ◽  
Multibody Systems ◽  
Dynamics Simulation ◽  
Adjoint Sensitivity ◽  
Analysis And Design ◽  
Systems Analysis And Design ◽  
Dynamics Of Multibody Systems ◽  
Direct Sensitivity ◽  
Vehicle Suspension System

Vehicle dynamics simulation based on multibody dynamics techniques has become a powerful tool for vehicle systems analysis and design. As this approach evolves, more and more details are required to increase the accuracy of the simulations, to improve their efficiency, or to provide more information that will allow various types of analyses. One very important direction is the optimization of multibody systems. Sensitivity analysis of the dynamics of multibody systems is essential for design optimization. Dynamic sensitivities, when needed, are often calculated by means of finite differences but, depending of the number of parameters involved, this procedure can be very demanding in terms of time and the accuracy obtained can be very poor in many cases if real perturbations are used. In this paper, several ways to perform the sensitivity analysis of multibody systems are explored including the direct sensitivity approaches and the adjoint sensitivity ones. Finally, the techniques proposed are applied to the dynamical optimization of a five bar mechanism and a vehicle suspension system.

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