# The Open Civil Engineering Journal

ISSN: 1874-1495 ― Volume 14, 2020
RESEARCH ARTICLE

# Studies on Static Frictional Contact Problems of Double Cantilever Beam Based on SBFEM

Zhu Chaolei1, *, Gao Qian1, Hu Zhiqiang2, Lin Gao2, Lu Jingzhou1
1 School of Civil Engineering,Yantai University,Yantai 264005, China
2 State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China

## Abstract

### Introduction:

The frictional contact problem is one of the most important and challenging topics in solids mechanics, and often encountered in the practical engineering.

### Method:

The nonlinearity and non-smooth properties result in that the convergent solutions can't be obtained by the widely used trial-error iteration method. Mathematical Programming which has good convergence properties and rigorous mathematical foundation is an effective alternative solution method, in which, the frictional contact conditions can be expressed as Non-smooth Equations, B-differential equations, Nonlinear Complementary Problem, etc.

### Result:

In this paper, static frictional contact problems of double cantilever beam are analyzed by Mathematical Programming in the framework of Scaled Boundary Finite Element Method (SBFEM), in which the contact conditions can be expressed as the B-differential Equations.

### Conclusion

The contact forces and the deformation with different friction factors are solved and compared with those obtained by ANSYS, by which the accuracy of solving contact problems by SBFEM and B-differential Equations is validated.

Keywords: Frictional contact problem, Scaled boundary finite element method, B-Differential equation, Nonlinear complementarity, Double cantilever beam, Mathematical programming.

### Article Information

#### Identifiers and Pagination:

Year: 2017
Volume: 11
Issue: Suppl-3, M10
First Page: 896
Last Page: 905
Publisher Id: TOCIEJ-11-896
DOI: 10.2174/1874149501711010896

#### Article History:

Received Date: 09/02/2017
Revision Received Date: 14/04/2017
Acceptance Date: 25/04/2017
Electronic publication date: 17/11/2017
Collection year: 2017

© 2017 Chaolei et al.

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: https://creativecommons.org/licenses/by/4.0/legalcode. This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the School of Civil Engineering,Yantai University, Yantai 264005, China; Tel:(+86)15863826315; E-mail: mengjun0000@163.com

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