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Dynamic Stress Analysis Around a Circular Cavity in Two-Dimensional Inhomogeneous Medium with Density Variation

Published online by Cambridge University Press:  04 April 2016

B.-P. Hei ,
Z.-L. Yang ,
B.-T. Sun  and
D.-K. Liu
B.-P. Hei
Affiliation:
College of Aerospace and Civil Engineering Harbin Engineering University Harbin, China
Z.-L. Yang*
Affiliation:
College of Aerospace and Civil Engineering Harbin Engineering University Harbin, China
B.-T. Sun
Affiliation:
Institute of Engineering Mechanics China Earthquake Administration Harbin, China
D.-K. Liu
Affiliation:
College of Aerospace and Civil Engineering Harbin Engineering University Harbin, China
*
*Corresponding author ([email protected])
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Abstract

Based on the complex function theory and the homogenization principle, an universal approach of solving the dynamic stress concentration around a circular cavity in two-dimensional (2D) inhomogeneous medium is developed. The Helmholtz equation with variable coefficient is converted to the standard Helmholtz equation by means of the general conformal transformation method (GCTM) analytically. As an example, the inhomogeneous medium with density varying as a function of two spatial coordinates and the constant elastic modulus is studied. The dynamic stress concentration factors (DSCF) are calculated numerically. It shows that medium inhomogeneous parameters and wave numbers have significant influence on the dynamic stress concentration by the circular cavity in two-dimensional inhomogeneous medium.

Keywords

Complex function theory2D inhomogeneous mediumVariable coefficient Helmholtz equationDynamic stress concentration
Type
Research Article
Information
Journal of Mechanics , Volume 32 , Issue 5 , October 2016 , pp. 519 - 526
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2016 

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