| About this Abstract |
| Meeting |
2024 ASC Technical Conference, US-Japan Joint Symposium, D30 Meeting
|
| Symposium
|
2024 ASC Technical Conference, US-Japan Joint Symposium, D30 Meeting
|
| Presentation Title |
Analysis of Anisotropic Inclusion Problems Using Complex Variables |
| Author(s) |
Seiichi Nomura, Liming Chen |
| On-Site Speaker (Planned) |
Seiichi Nomura |
| Abstract Scope |
This paper presents an analytical approach to derive stress functions for an elastic medium containing a circular anisotropic inclusion embedded in an infinitely-extended isotropic matrix subjected to far-field stresses utilizing symbolic software. Complex stress functions are employed to represent the stress distribution in such composite materials.
Traditionally, the Airy stress function has been used in analyzing 2-D isotropic materials. However, for 2-D anisotropic materials, Lekhnitskii's formulation provides an alternative approach in which the stress function is expressed as the real part of the sum of two analytic functions of two independent complex numbers, determined from the roots of the characteristic equation associated with the anisotropic elastic constants.
In this study, the Airy stress function is used for the matrix phase, while Lekhnitskii's stress function is used for the inclusion phase. The stress function for the matrix phase is expressed by a Laurent series, whereas for the inclusion phase, a Taylor series is employed.
Determining the unknown complex coefficients of the series requires satisfying the continuity conditions of the displacement and the traction across the interface of the matrix and inclusion.
The derived expressions are in closed form and novel.
This methodology can be further extended to other problems such as thermal stress and heat conduction, demonstrating its applicability across various fields of study. |
| Proceedings Inclusion? |
Definite: Post-meeting proceedings |