Dynamic analysis of rigid and deformable multibody systems with penalty methods and energy–momentum schemes

Ruigómez, José María Goicolea; Orden, Juan Carlos García

doi:10.1016/s0045-7825(99)00362-x

Cited by 41 publications

(19 citation statements)

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“…A combination of the rigid body, nonlinear elastodynamic and joint constraint methodologies is presented in Puso (2002) and in Ibrahimbegović, Taylor and Lim (2003). Joint constraints were also modeled using penalty approaches in Goicolea and García Orden (2000) and García Orden and .…”

Section: Energy-preserving and Momentumpreserving Algorithmsmentioning

confidence: 99%

Computational Structural Dynamics

Hulbert

2004

Encyclopedia of Computational Mechanics

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This chapter presents an overview and a state‐of‐the art compilation of time integration methods for solving problems of dynamics, with a particular focus on developments that have occurred during the past 25 years. Various classifications of time integration algorithms are provided that assist the reader in understanding the many different types of numerical methods available for solving time‐dependent problems. Time integration algorithms for linear structural dynamics are reviewed thoroughly, from classical Newmark‐type schemes, to recent developments in time finite element‐based approaches. The distinction between linear and nonlinear dynamics is articulated and numerical methods developed for direct application towards solving nonlinear dynamics probems are presented. The chapter concludes with guidelines towards selecting an appropriate time integration method, along with guidelines towards choosing appropriate time step sizes.

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Section: Energy-preserving and Momentumpreserving Algorithmsmentioning

confidence: 99%

Computational Structural Dynamics

Hulbert

2004

Encyclopedia of Computational Mechanics

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“…Exact discrete energy conservation does not guarantee unconditional stability for the non linear case, but definitely enhance it, as it has been widely reported in the literature (Stuart and Humphries, 1996;García Orden and Dopico Dopico, 2006). This is the main motivation behind this work, that aims to extend a previously developed conserving penalty formulation Goicolea and García Orden, 2000;García Orden and Goicolea, 2001), which showed excellent stability properties, to the augmented Lagrangian formulation, which is the main contribution of this paper and it is developed in Section 3.2.…”

Section: Introductionmentioning

confidence: 97%

A Conservative Augmented Lagrangian Algorithm for the Dynamics of Constrained Mechanical Systems

Orden

Ortega

2006

Mechanics Based Design of Structures and Machines

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The motion of many practical mechanical systems is often constrained. An important example is the dynamics of multibody systems, where the numerical solution of this type of systems faces several difficulties. A strategy for to solve this type of problems is the augmented Lagrange formulation, which allows the use of numerical integrators for ODEs, combined with an update scheme for the algebraic variables, accomplishing exact fulfillment of the constraints. This work focuses on the design of a conservative version of this augmented Lagrangian formulation for holonomic constraints, proposing a numerical procedure that exhibits excellent stability.

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“…More recently, Laursen and Love (2002) extended these methods for frictionless contact, with the use of a contact velocity correction that imposes the geometric admissibility and leads to a conserving algorithm. The use of a contact potential was also proposed by Goicolea and Garcia Orden (2000) to simulate the frictional contact. Finally, these contact methods were used in the context of quasi-rigid bodies (small deformations added to a rigid transformation), such as gear trains, by Demkowicz and Bajer (2001) and Bajer and Demkowicz (2002).…”

Section: Introductionmentioning

confidence: 99%