Stabilization of computational procedures for constrained dynamical systems

Park, K. C.; Chiou, Jin-Chern

doi:10.2514/3.20320

Cited by 106 publications

(48 citation statements)

References 17 publications

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“…Because DAEs constitute a stiff set of equations, they require robust algorithms to solve. Research in the late 1980s investigated the efficiency, stability, and robustness of various methods for solving these equations [42][43][44]. Many commercial software codes used in industry, such as ADAMS [49] (Mechanical Dynamics, Inc.) and DADS [24] (Computer Aided Design Software, Inc.), use DAE solvers to perform numerical integration.…”

Section: Dae Methodsmentioning

confidence: 99%

Simulation of a Moving, Elastic Beam Using Hamilton's Weak Principle

Leigh

Kunz

2006

47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

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Hamilton's Law is derived in weak form for slender beams with closed cross sections. The result is discretized with mixed space-time finite elements to yield a system of nonlinear, algebraic equations. An algorithm is proposed for solving these equations using unconstrained optimization techniques, obtaining steady-state and time accurate solutions for problems of structural dynamics. This technique provides accurate solutions for nonlinear static and steady-state problems including the cantilevered elastica and flatwise rotation of beams. Modal analysis of beams and rods is investigated to accurately determine fundamental frequencies of vibration, and the simulation of simple maneuvers is demonstrated.iv

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Section: Dae Methodsmentioning
confidence: 99%

Simulation of a Moving, Elastic Beam Using Hamilton's Weak Principle
Leigh
¹
,
Kunz
²

2006
47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference
1
0
1
0
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“…By substituting (5) and (6) into the inertia force operator (2), one obtains 6F' = GuTM(ii + RTs":c3 + R T 5 S f o ) + 6aTMs":Rii + Jc3 + ~J w (9) where…”

Section: Inertia Operators For Rigid Bodiesmentioning
confidence: 99%

A modular multibody analysis capability for high‐precision, active control and real‐time applications
Park¹,
Downer²,
Chiou³
et al. 1991
Numerical Meth Engineering
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SUMMARYA computationally oriented formulation and its solution procedures for the analysis of rigid-flexible multibody dynamics systems are presented. The present formulation adopts a set of dual co-ordinate systems, an inertially fixed one for the measure of translational motions and a body-based one for rotational motions. The origins of these co-ordinate systems are located at the centres of rigid bodies and at the nodal points of flexible bodies for implementation ease. The flexibility is modelled by an intrinsic spatial beam theory which is approximated by transverse-shear deformable linear beam elements. The solution of the resulting equations of motion including system constraints is obtained by a partitioned procedure, which solves first for the constraint force vector, then the generalized co-ordinates for the rigid and flexible components, and finally interaction quantities such as active control forces, manoeuvring space ranges and corrections due to state measurements, with each solution stage being processed by the corresponding separate module. A central feature of the present capability is its high accuracy of the analysis results by demanding the energy conservation throughout the various stages of response analyses. Several examples are included to demonstrate the capabilities of the present analysis software both on sequential and parallel machines.

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“…Baumgarte stabilization [12], a form of position and velocity state feedback, is widely used to circumvent this problem. A more e ective stabilization method has been developed by Park et al [13].…”

Section: Introductionmentioning
confidence: 99%

Unconditionally energy stable implicit time integration: application to multibody system analysis and design
Chen
¹
,
Hansen
²
,
Tortorelli
³

2000
Int. J. Numer. Meth. Engng.
17
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SUMMARYThis paper focuses on the development of an unconditionally stable time-integration algorithm for multibody dynamics that does not artiÿcially dissipate energy. Unconditional stability is sought to alleviate any stability restrictions on the integration step size, while energy conservation is important for the accuracy of long-term simulations. In multibody system analysis, the time-integration scheme is complemented by a choice of coordinates that deÿne the kinematics of the system. As such, the current approach uses a non-dissipative implicit Newmark method to integrate the equations of motion deÿned in terms of the independent joint co-ordinates of the system. In order to extend the unconditional stability of the implicit Newmark method to non-linear dynamic systems, a discrete energy balance is enforced. This constraint, however, yields spurious oscillations in the computed accelerations and therefore, a new acceleration corrector is developed to eliminate these instabilities and hence retain unconditional stability in an energy sense. An additional beneÿt of employing the non-linearly implicit time-integration method is that it allows for an e cient design sensitivity analysis. In this paper, design sensitivities computed via the direct di erentiation method are used for mechanism performance optimization.

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Stabilization of computational procedures for constrained dynamical systems

Cited by 106 publications

References 17 publications

Simulation of a Moving, Elastic Beam Using Hamilton's Weak Principle

Simulation of a Moving, Elastic Beam Using Hamilton's Weak Principle

A modular multibody analysis capability for high‐precision, active control and real‐time applications

Unconditionally energy stable implicit time integration: application to multibody system analysis and design

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