Stability on a kind of welding problems under perturbations

Abstract

In this paper, we discuss stability of a kind of welding problems when there exist perturbations for the boundary of an elastic body and displacement differences of the boundary. Using the complex variable methods in plane elasticity, error estimates of complex stress functions are given. The stability of stresses and displacements is also obtained based on those estimates.

Keywords:

• welding problem
• complex stress functions
• Cauchy integral
• Riemann boundary value problem
• singular integral equation
• perturbations

AMS Subject Classifications:

• 30E20
• 45E05

Acknowledgements

The authors would like to extend their thankfulness to Professor Qian Tao for his support to the authors during their stay in University of Macau while the article was discussed.

Notes

This article is dedicated to Professor Wei Lin on the occasion his 80th birthday.

This work is supported by Macao Science and Technology Development Fund [grant number 041/2012/A], the Science and Technology Fund of Education Department of Fujian Province [grant number JA11341], the National Natural Science Foundation of China [grant number 11171260] and the Specialized Research Fund for the Doctoral Program of Higher Education of China [grant number 20100141110054].