Efficient and robust implementation of the TLISMNI method

Aboubakr, Ahmed K.; Shabana, Ahmed A.

doi:10.1016/j.jsv.2015.05.008

Cited by 17 publications

(11 citation statements)

References 23 publications

(53 reference statements)

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“…For numerically solving the equations of motion, the two-loop implicit sparse matrix numerical integration (TLISMNI) method that utilises the concept of coordinate partitioning and the second-order backward difference formula for time integration is used in this work (Aboubakr and Shabana, 2015). An important feature of TLISMNI is that it satisfies the constraint equations at the position, velocity, and acceleration levels.…”

Section: Mbs Equations Of Motionmentioning

confidence: 99%

Integration of geometry and small and large deformation analysis for vehicle modelling: chassis, and airless and pneumatic tyre flexibility

Patel

Pappalardo

Wang

et al. 2019

IJVP

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The goal of this study is to propose an approach for developing new and detailed vehicle models that include flexible components with complex geometries, including chassis, and airless and pneumatic tyres with distributed inertia and elasticity. The methodology used is based on integration of geometry, and small and large deformation analysis using a mechanics-based approach. The floating frame of reference (FFR) formulation is used to model the small deformations, whereas the absolute nodal coordinate formulation (ANCF) is used for the large deformation analysis. Both formulations are designed to correctly capture complex geometries including structural discontinuities. To this end, a new ANCF-preprocessing approach based on linear constraints that allows for systematically eliminating dependent variables and reducing the component model dimension is proposed. One of the main contributions of this paper is the development of the first ANCF airless tyre model which is integrated in a three-dimensional multibody system (MBS) algorithm designed for solving the differential/algebraic equations of detailed

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Section: Mbs Equations Of Motionmentioning

confidence: 99%

Integration of geometry and small and large deformation analysis for vehicle modelling: chassis, and airless and pneumatic tyre flexibility

Patel

Pappalardo

Wang

et al. 2019

IJVP

Self Cite

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“…Therefore after each integration step relying on acceleration, it is necessary to move positions and velocities back to their manifolds. This corrections process is called poststabilization procedure and can be implemented using Newton-Raphson method [17]. The poststabilization of rotational multibody system subjected to nonholonomic constraints has been presented recently in [18].…”

Section: Position and Velocity Stabilizationmentioning

confidence: 99%

Computational Design Scheme for Wind Turbine Drive-Train Based on Lagrange Multipliers

et al. 2017

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The design optimization of wind turbines and their subsystems will make them competitive as an ideal alternative for energy. This paper proposed a design procedure for one of these subsystems, which is the Wind Turbine Drive-Train (WTDT). The design of the WTDT is based on the load assumptions and considered as the most significant parameter for increasing the efficiency of energy generation. In industry, these loads are supplemented by expert assumptions and manipulated to design the transmission elements. In contrary, in this work, the multibody system approach is used to estimate the static as well as dynamic loads based on the Lagrange multipliers. Lagrange multipliers are numerical parameters associated with the holonomic and nonholonomic constraints assigned in the drive-train model. The proposed scheme includes computational manipulations of kinematic constraints, mapping the generalized forces into Cartesian respective, and enactment of velocity-based constrains. Based on the dynamic model and the obtained forces, the design process of a planetary stage of WTDT is implemented with trade-off’s optimization in terms of gearing parameters. A wind turbine of 1.4 megawatts is introduced as an evaluation study of the proposed procedure, in which the main advantage is the systematic nature of designing complex systems in motion.

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“…The initial time step in the case of the trapezoidal method is evaluated as hi=6ɛ/|D3y|, where D3y=|y·n+1-2y·n+y·n-1|/(h2/4). 13 The trapezoidal method is implemented in the TLISMNI framework 10 in order to allow comparison with the new TLISMNI/Adams algorithm. The results of the new algorithm are also compared with the explicit predictor-corrector Adams method with variable-order and variable time step.…”

Section: Error and Time Step Selection Criteriamentioning

confidence: 99%

“…In order to address these concerns regarding the use of implicit integrators in MBS simulations, the two-loop implicit sparse matrix numerical integration (TLISMNI) method was proposed. 10–12 Unlike other implicit numerical integration algorithms, the TLISMNI method does not require the numerical differentiation of the forces, ensures that the constraint equations are satisfied at all levels, and allows for effectively using sparse matrix techniques at all stages of the function evaluation. The TLISMNI method is designed to have two iterative loops; the outer and inner loops.…”

Section: Introductionmentioning

confidence: 99%

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TLISMNI/Adams algorithm for the solution of the differential/algebraic equations of constrained dynamical systems

Shabana

Zhang

Wang

2017

Proceedings of the Institution of Mechanical Engineers, Part K:

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This paper examines the performance of the 3rd and 4th order implicit Adams methods in the framework of the two-loop implicit sparse matrix numerical integration method in solving the differential/algebraic equations of heavily constrained dynamical systems. The variable-step size two-loop implicit sparse matrix numerical integration/Adams method proposed in this investigation avoids numerical force differentiation, ensures satisfying the nonlinear algebraic constraint equations at the position, velocity, and acceleration levels, and allows using sparse matrix techniques for efficiently solving the dynamical equations. The iterative outer loop of the two-loop implicit sparse matrix numerical integration/Adams method is aimed at achieving the convergence of the implicit integration formulae used to solve the independent differential equations of motion, while the inner loop is used to ensure the convergence of the iterative procedure used to satisfy the algebraic constraint equations. To solve the independent differential equations, two different implicit Adams integration formulae are examined in this investigation; a 3rd order implicit Adams-Moulton formula with a 2nd order explicit predictor Adams Bashforth formula, and a 4th order implicit Adams-Moulton formula with a 3rd order explicit predictor Adams Bashforth formula. A standard Newton-Raphson algorithm is used to satisfy the nonlinear algebraic constraint equations at the position level. The constraint equations at the velocity and acceleration levels are linear, and therefore, there is no need for an iterative procedure to solve for the dependent velocities and accelerations. The algorithm used for the error check and step-size change is described. The performance of the two-loop implicit sparse matrix numerical integration/Adams algorithm developed in this investigation is evaluated by comparison with the explicit predictor-corrector Adams method which has a variable-order and variable-step size. Simple and heavily constrained dynamical systems are used to evaluate the accuracy, robustness, damping characteristics, and effect of the outer-loop iterations of the proposed implicit schemes. The results obtained in this investigation show that the two-loop implicit sparse matrix numerical integration methods proposed in this study can be more efficient for stiff systems because of their ability to damp out high-frequency oscillations. Explicit integration methods, on the other hand, can be more efficient in the case of non-stiff systems.

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Efficient and robust implementation of the TLISMNI method

Cited by 17 publications

References 23 publications

Integration of geometry and small and large deformation analysis for vehicle modelling: chassis, and airless and pneumatic tyre flexibility

Integration of geometry and small and large deformation analysis for vehicle modelling: chassis, and airless and pneumatic tyre flexibility

Computational Design Scheme for Wind Turbine Drive-Train Based on Lagrange Multipliers

TLISMNI/Adams algorithm for the solution of the differential/algebraic equations of constrained dynamical systems

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