A fast nonlinear conjugate gradient based method for 3D concentrated frictional contact problems

被引：20

作者：

Zhao, Jing ^{[1
]}

Vollebregt, Edwin A. H. ^{[1
,2
]}

Oosterlee, Cornelis W. ^{[1
,3
]}

机构：

[1] Delft Univ Technol, Delft Inst Appl Math, NL-2628 CD Delft, Netherlands

[2] VORtech BV, NL-2600 AG Delft, Netherlands

[3] CWI Ctr Math & Comp Sci, NL-1090 GB Amsterdam, Netherlands

来源：

JOURNAL OF COMPUTATIONAL PHYSICS | 2015年 / 288卷

关键词：

Frictional contact problem; Azimuth angle variables; Active set strategy; Nonlinear conjugate gradient; Preconditioner; Fast Fourier transform; ALGORITHM; SOLVER; 2D;

D O I：

10.1016/j.jcp.2015.02.016

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

This paper presents a fast numerical solver for a nonlinear constrained optimization problem, arising from 3D concentrated frictional shift and rolling contact problems with dry Coulomb friction. The solver combines an active set strategy with a nonlinear conjugate gradient method. One novelty is to consider the tractions of each slip element in a polar coordinate system, using azimuth angles as variables instead of conventional traction variables. The new variables are scaled by the diagonal of the underlying Jacobian. The fast Fourier transform (FFT) technique accelerates all matrix-vector products encountered, exploiting the matrix' Toeplitz structure. Numerical tests demonstrate a significant reduction of the computational time compared to existing solvers for concentrated contact problems. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：86 / 100

页数：15

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