GE Ren-yu, CHENG Chang-zheng, YANG Zhi-yong, NIU Zhong-rong. Singularity Analysis for Notches in Orthotropic Composite Plates With the Interpolating Matrix Method[J]. Applied Mathematics and Mechanics, 2014, 35(4): 459-470. doi: 10.3879/j.issn.1000-0887.2014.04.011
 Citation: GE Ren-yu, CHENG Chang-zheng, YANG Zhi-yong, NIU Zhong-rong. Singularity Analysis for Notches in Orthotropic Composite Plates With the Interpolating Matrix Method[J]. Applied Mathematics and Mechanics, 2014, 35(4): 459-470.

# Singularity Analysis for Notches in Orthotropic Composite Plates With the Interpolating Matrix Method

##### doi: 10.3879/j.issn.1000-0887.2014.04.011
Funds:  The National Natural Science Foundation of China(11272111；11372049)
• Received Date: 2013-08-08
• Rev Recd Date: 2013-09-24
• Publish Date: 2014-04-15
• Based on asymptotic expansion of generalized displacement field at the V-notch tip, a new method for analyzing the stress singularity exponents of the notches in orthotropic composite plates was proposed. Through introduction of the typical terms in asymptotic expansion of the generalized displacement functions into the basic elastic equations of the plate, the eigenvalue problem of a set of nonlinear ordinary differential equations(ODEs) about the stress singularity exponents of the notch was obtained, then the nonlinear eigenvalue problem was transformed into a linear one by means of variable substitution, and the interpolating matrix method was employed to solve the problem to determine the stress singularity exponents and associated characteristic functions at the notch tip in the orthotropic bi-material plate. With the present method, both the stress singularity exponents and the associated characteristic angle functions can be acquired simultaneously, and the stress singularity exponents can be easily distinguished between plane and anti-plane singularities according to the corresponding characteristic angle functions. Validity of the present method is confirmed in comparison with the existing results through numerical calculation.
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沈阳化工大学材料科学与工程学院 沈阳 110142

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