Geometrical shape of in-plane inclusion characterized by polynomial internal stress field under uniform eigenstrains

doi:10.1007/s10483-016-2130-6

Applied Mathematics and Mechanics (English Edition) ›› 2016, Vol. 37 ›› Issue (9): 1113-1130.doi: https://doi.org/10.1007/s10483-016-2130-6

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Geometrical shape of in-plane inclusion characterized by polynomial internal stress field under uniform eigenstrains

Jian WU¹, C. Q. RU², Liang ZHANG^1,3, Ling WAN¹

1. College of Aerospace Engineering, Chongqing University, Chongqing 400044, China;
2. Department of Mechanical Engineering, University of Alberta, Alberta T6G 2G8, Canada;
3. State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, China

Received:2016-02-17 Revised:2016-05-13 Online:2016-09-01 Published:2016-09-01
Contact: Jian WU E-mail:jwu@cqu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (No. 11372363), the Fundamental Research Funds for the Central Universities of China (No. 0241005202006), the Natural Science & Engineering Research Council of Canada, and the Open Research Foundation of the State Key Laboratory of Structural Analysis for Industrial Equipment (No. GZ1404)

Abstract

Abstract:

The internal stress field of an inhomogeneous or homogeneous inclusion in an infinite elastic plane under uniform stress-free eigenstrains is studied. The study is restricted to the inclusion shapes defined by the polynomial mapping functions mapping the exterior of the inclusion onto the exterior of a unit circle. The inclusion shapes, giving a polynomial internal stress field, are determined for three types of inclusions, i.e., an inhomogeneous inclusion with an elastic modulus different from the surrounding matrix, an inhomogeneous inclusion with the same shear modulus but a different Poisson's ratio from the surrounding matrix, and a homogeneous inclusion with the same elastic modulus as the surrounding matrix. Examples are presented, and several specific conclusions are achieved for the relation between the degree of the polynomial internal stress field and the degree of the mapping function defining the inclusion shape.

Key words: inclusion shape, polynomial, internal stress field, eigenstrain

2010 MSC Number:

74A40
74A60

Jian WU, C. Q. RU, Liang ZHANG, Ling WAN. Geometrical shape of in-plane inclusion characterized by polynomial internal stress field under uniform eigenstrains. Applied Mathematics and Mechanics (English Edition), 2016, 37(9): 1113-1130.

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References

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Geometrical shape of in-plane inclusion characterized by polynomial internal stress field under uniform eigenstrains

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