Two aggregate-function-based algorithms for analysis of 3D frictional contact by linear complementarity problem formulation

Zhang, H.W.; He, Shanying; Li, X.S.

doi:10.1016/j.cma.2005.01.002

Cited by 20 publications

(15 citation statements)

References 18 publications

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“…(40) with high efficiency. Details of this algorithm can be referred to [15] and will not be elaborated here. The edges of the explicit FDTD grid are updated using the FDTD scheme.…”

Section: Coupling Between the Nonlinear Fetd And Fdtd Methodsmentioning

confidence: 99%

“…Several highly efficient computational methods [14][15][16] from computational mathematics can be used to solve the final quadratic programming model. Therefore, the iterative process in each time step is avoided in the proposed method.…”

Section: Nonlinear Dg-fetd Formulationmentioning

confidence: 99%

“…The nonlinear FETD scheme is not based on iteration, but on the base exchanges in the solution of a standard quadratic programming problem, as the nonlinear constructive law is transformed into a set of linear complementary problems (LCP) [13] with parametric variables. These LCPs can be solved by a number of mature mathematical tools, efficiently [14][15][16]. This proposed scheme need not require updating system matrices and tedious iterative procedure at every time step, so the coupling between FDTD and nonlinear FETD is easy to be implemented based on the framework of linear case [10].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Hybrid FDTD/Fetd Technique Using Parametric Quadratic Programming for Nonlinear Maxwell's Equations

Li¹,

Zhu²,

Chen³

2017

PIER M

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Abstract-A nonlinear hybrid FDTD/FETD technique based on the parametric quadratic programming method is developed for Maxwell's equations with nonlinear media. The proposed technique allows nonconforming meshes between nonlinear FETD and linear FDTD subdomains. The coarser structured cells of FDTD are used in regular, large and linear media, whereas smaller unstructured elements of FETD based on the parametric quadratic programming method are used to simulate complicated structures with nonlinear media. This hybrid technique is particularly suitable for structures with small nonlinear regions in an otherwise linear medium. Numerical results demonstrate the validity of the proposed method.

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“…(40) with high efficiency. Details of this algorithm can be referred to [15] and will not be elaborated here. The edges of the explicit FDTD grid are updated using the FDTD scheme.…”

Section: Coupling Between the Nonlinear Fetd And Fdtd Methodsmentioning

confidence: 99%

Section: Nonlinear Dg-fetd Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Hybrid FDTD/Fetd Technique Using Parametric Quadratic Programming for Nonlinear Maxwell's Equations

Li¹,

Zhu²,

Chen³

2017

PIER M

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“…Based on the work by Zhong et al (1997), Zhong and Zhang (2002) and Zhang et al (2004Zhang et al ( , 2005a, a generalized parametric constitutive law for the simulation of van der Waals force between any two adjacent atoms and the improved quadratic programming method for numerical simulation of mechanical behaviors of nanostructures are developed. It should be emphasized that the proposed method does not depend on displacement and stress iteration, but on the base exchanges in the solution of a standard quadratic programming problem.…”

Section: Introductionmentioning

confidence: 99%

Parametric variational principle and quadratic programming method for van der Waals force simulation of parallel and cross nanotubes

Zhang

Wang

et al. 2007

International Journal of Solids and Structures

Self Cite

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A parametric variational principle for van der Waals force simulation between any two adjacent nonbonded atoms and the corresponding improved quadratic programming method for numerical simulation of mechanical behaviors of carbon nanotubes are developed. Carbon nanotubes are modeled and computed based on molecular structural mechanics model. van der Waals force is simulated by the network of bars (called bar network) with a special nonlinear mechanical constitutive law (called generalized parametric constitutive law) in the finite element analysis. Compared with conventional numerical methods, the proposed method does not depend on displacement and stress iteration, but on the base exchanges in the solution of a standard quadratic programming problem. Thus, the model and method developed present very good convergence behavior in computation and provide accurate predictions of the mechanical behaviors and displacement distributions in the nanotubes. Numerical results demonstrate the validity and the efficiency of the proposed method.

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“…Therefore, at every time step, the tension or compression state of every dropper must be determined. PVP proposed by Zhong and Zhang [27] has been proved to be advantageous for convergence for certain strong nonlinear numerical analyses, such as contact and piecewise linear analyses [29][30][31]. Therefore, in this paper, the nonlinear droppers are described by PVP, which converts the nonlinear problem to a linear complementarity problem.…”

Section: Pvp For the Nonlinear Droppermentioning

confidence: 99%

A Numerical Method Based on the Parametric Variational Principle for Simulating the Dynamic Behavior of the Pantograph‐Catenary System

Gao

Zhong

2018

Shock and Vibration

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Based on the finite element method (FEM), the parametric variational principle (PVP) is combined with a numerical time-domain integral method to simulate the dynamic behavior of the pantograph-catenary system. Based on PVP, formulations for the nonlinear droppers in the catenary and for the contact between the pantograph and the contact wire are proposed. The formulations can accurately determine the tension state or compression state of the nonlinear droppers and the contact state between the pantograph and the contact wire. Based on the periodicity of the catenary and the precise integration method (PIM), a numerical timeintegration method is developed for the dynamic responses of the catenary. For this method, the matrix exponential of only one unit cell of the catenary is computed, which greatly improves the computational efficiency. Moreover, the validation shows that the formulations can compute the contact force accurately and represent the nonlinearity of the droppers, which demonstrates the accuracy and reliability of the proposed method. Finally, the dynamic behaviors of the pantograph-catenary system with different types of catenaries are simulated.

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Two aggregate-function-based algorithms for analysis of 3D frictional contact by linear complementarity problem formulation

Cited by 20 publications

References 18 publications

Hybrid FDTD/Fetd Technique Using Parametric Quadratic Programming for Nonlinear Maxwell's Equations

Hybrid FDTD/Fetd Technique Using Parametric Quadratic Programming for Nonlinear Maxwell's Equations

Parametric variational principle and quadratic programming method for van der Waals force simulation of parallel and cross nanotubes

A Numerical Method Based on the Parametric Variational Principle for Simulating the Dynamic Behavior of the Pantograph‐Catenary System

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