Applied Mathematics and Mechanics

, Volume 25, Issue 1, pp 47–58

# Non-interior smoothing algorithm for frictional contact problems

• Zhang Hong-wu
• He Su-yan
• Li Xing-si
Article

## Abstract

A new algorithm for solving the three-dimensional elastic contact problem with friction is presented. The algorithm is a non-interior smoothing algorithm based on an NCP-function. The parametric variational principle and parametric quadratic programming method were applied to the analysis of three-dimensional frictional contact problem. The solution of the contact problem was finally reduced to a linear complementarity problem, which was reformulated as a system of nonsmooth equations via an NCP-function. A smoothing approximation to the nonsmooth equations was given by the aggregate function. A Newton method was used to solve the resulting smoothing nonlinear equations. The algorithm presented is easy to understand and implement. The reliability and efficiency of this algorithm are demonstrated both by the numerical experiments of LCP in mathematical way and the examples of contact problems in mechanics.

## Key words

three-dimensional frictional contact problem parametic quadratic programming method linear complementarity problem NCP-function aggregate function non-interior smoothing algorithm

O221 O242.21

## 2000 Mathematics Subject Classification

65K05 90C90 74M10 74M15

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© Editorial Committee of Applied Mathematics and Mechanics 2004

## Authors and Affiliations

• Zhang Hong-wu
• 1
• He Su-yan
• 1
• Li Xing-si
• 1
1. 1.State Key Laboratory of Structural Analysis of Industrial EquipmentDalian University of TechnologyDalianP. R. China