scholarly journals An augmented Lagrangian formulation for the equations of motion of multibody systems subject to equality constraints

2017 ◽  
Vol 199 ◽  
pp. 747-752 ◽  
Author(s):  
Elias Paraskevopoulos ◽  
Nikolaos Potosakis ◽  
Sotirios Natsiavas
Keyword(s):  
Multibody Systems ◽  
Augmented Lagrangian ◽  
Equations Of Motion ◽  
Equality Constraints ◽  
Lagrangian Formulation ◽  
Augmented Lagrangian Formulation

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

Comparison of Selected Methods of Handling Redundant Constraints in Multibody Systems Simulations

2012 ◽  
Vol 8 (2) ◽  
Author(s):  
Marek Wojtyra ◽  
Janusz Frączek
Keyword(s):  
Numerical Methods ◽  
Rigid Body ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Point Of View ◽  
Redundant Constraints ◽  
Reaction Solution ◽  
Constraints Handling ◽  
Mathematical Operations ◽  
Augmented Lagrangian Formulation

When redundant constraints are present in a rigid body mechanism, only selected (if any at all) joint reactions can be determined uniquely, whereas others cannot. Analytic criteria and numerical methods of finding joints with uniquely solvable reactions are available. In this paper, the problem of joint reactions solvability is examined from the point of view of selected numerical methods frequently used for handling redundant constraints in practical simulations. Three different approaches are investigated in the paper: elimination of redundant constraints; pseudoinverse-based calculations; and the augmented Lagrangian formulation. Each method is briefly summarized; the discussion is focused on techniques of handling redundant constraints and on joint reactions calculation. In the case of multibody systems with redundant constraints, the rigid body equations of motion are insufficient to calculate some or all joint reactions. Thus, purely mathematical operations are performed in order to find the reaction solution. In each investigated method, the redundant constraints are treated differently, which—in the case of joints with nonunique reactions—leads to different reaction solutions. As a consequence, reactions reflecting the redundancy handling method rather than physics of the system are calculated. A simple example of each method usage is presented, and calculated joint reactions are examined. The paper points out the origins of nonuniqueness of constraint reactions in each examined approach. Moreover, it is shown that one and the same method may lead to different reaction solutions, provided that input data are prepared differently. Finally, it is demonstrated that—in case of joints with solvable reactions—the obtained solutions are unique, regardless of the method used for redundant constraints handling.

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