Application of an augmented Lagrangian approach to multibody systems with equality motion constraints

Potosakis, Nikolaos; Paraskevopoulos, Elias; Natsiavas, S.

doi:10.1007/s11071-019-05059-6

Cited by 19 publications

(15 citation statements)

References 25 publications

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“…On the contrary, the results obtained by the DAE solvers exhibit a gradual and noticeable change in the mechanical energy. Similar behavior has also been observed and reported in other applications [8,9,15].…”

Section: Sphere Rolling Inside a Cylindersupporting

confidence: 90%

“…A similar path was followed in a recent work of the authors [15]. In that work, the emphasis was placed on mechanical systems with holonomic constraints.…”

Section: Introductionmentioning

confidence: 84%

“…In this work, these curves are selected to be the autoparallels, corresponding to the "straightest" curves on the configuration space [19,22]. Moreover, following earlier approaches [23,15], all the variations in Eqs. ( 20)-( 25 in Eq.…”

Section: Temporal Discretization Of the Equations Of Motionmentioning

confidence: 99%

“…In addition, the set of unknowns arising in each time step of the present treatment includes both the generalized velocities and the time derivatives of the Lagrange multipliers. In contrast, the method applied in [15] was based on an augmented Lagrangian approach and treated the generalized velocities and the time derivatives of the Lagrange multipliers at different solution levels. Finally, all the numerical examples investigated in that work involved holonomic constraints, while the examples examined in this study involve nonholonomic constraints.…”

Section: Introductionmentioning

confidence: 99%

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Numerical integration of multibody dynamic systems involving nonholonomic equality constraints

2021

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This work considers a class of multibody dynamic systems involving bilateral nonholonomic constraints. An appropriate set of equations of motion is employed first. This set is derived by application of Newton's second law and appears as a coupled system of strongly nonlinear second order ordinary differential equations in both the generalized coordinates and the Lagrange multipliers associated to the motion constraints. Next, these equations are manipulated properly and converted to a weak form. Furthermore, the position, velocity and momentum type quantities are subsequently treated as independent. This yields a three-field set of equations of motion, which is then used as a basis for performing a suitable temporal discretization, leading to a complete time integration scheme. In order to test and validate its accuracy and numerical efficiency, this scheme is applied next to challenging mechanical examples, exhibiting rich dynamics. In all cases, the emphasis is put on highlighting the advantages of the new method by direct comparison with existing analytical solutions as well as with results of current state of the art numerical methods. Finally, a comparison is also performed with results available for a benchmark problem.

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Section: Sphere Rolling Inside a Cylindersupporting

confidence: 90%

“…A similar path was followed in a recent work of the authors [15]. In that work, the emphasis was placed on mechanical systems with holonomic constraints.…”

Section: Introductionmentioning

confidence: 84%

Section: Temporal Discretization Of the Equations Of Motionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Numerical integration of multibody dynamic systems involving nonholonomic equality constraints

2021

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“…In the framework of multibody system dynamics [35,46], a large number of studies have been presented that demonstrate coupling of multibody systems and hydraulic actuators [22,40]. Coupling has been carried out using either monolithic [48,49] or cosimulation approaches [44,47].…”

Section: Introductionmentioning

confidence: 99%

Efficiency comparison of various friction models of a hydraulic cylinder in the framework of multibody system dynamics

2021

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Dynamic simulation of mechanical systems can be performed using a multibody system dynamics approach. The approach allows to account systems of other physical nature, such as hydraulic actuators. In such systems, the nonlinearity and numerical stiffness introduced by the friction model of the hydraulic cylinders can be an important aspect to consider in the modeling because it can lead to poor computational efficiency. This paper couples various friction models of a hydraulic cylinder with the equations of motion of a hydraulically actuated multibody system in a monolithic framework. To this end, two static friction models, the Bengisu–Akay model and Brown–McPhee model, and two dynamic friction models, the LuGre model and modified LuGre model, are considered in this work. A hydraulically actuated four-bar mechanism is exemplified as a case study. The four modeling approaches are compared based on the work cycle, friction force, energy balance, and numerical efficiency. It is concluded that the Brown–McPhee approach is numerically the most efficient approach and it is well able to describe usual friction characteristics in dynamic simulation of hydraulically actuated multibody systems.

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A Novel Time-Stepping Method for Multibody Systems with Frictional Impacts

Natsiavas

Passas

Paraskevopoulos

2022

NODYCON Conference Proceedings Series

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Application of an augmented Lagrangian approach to multibody systems with equality motion constraints

Cited by 19 publications

References 25 publications

Numerical integration of multibody dynamic systems involving nonholonomic equality constraints

Numerical integration of multibody dynamic systems involving nonholonomic equality constraints

Efficiency comparison of various friction models of a hydraulic cylinder in the framework of multibody system dynamics

A Novel Time-Stepping Method for Multibody Systems with Frictional Impacts

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