GAO Yuanyuan, LIU Guanting. Analytical Solutions to Problems of Elliptical Holes With 4 Edge Cracks in 1D Orthorhombic Quasicrystals[J]. Applied Mathematics and Mechanics, 2019, 40(2): 210-222. doi: 10.21656/1000-0887.390032
 Citation: GAO Yuanyuan, LIU Guanting. Analytical Solutions to Problems of Elliptical Holes With 4 Edge Cracks in 1D Orthorhombic Quasicrystals[J]. Applied Mathematics and Mechanics, 2019, 40(2): 210-222.

# Analytical Solutions to Problems of Elliptical Holes With 4 Edge Cracks in 1D Orthorhombic Quasicrystals

##### doi: 10.21656/1000-0887.390032
Funds:  The National Key R&D Program of China(2017YFC1405605)
• Rev Recd Date: 2018-06-24
• Publish Date: 2019-02-01
• The plane elastic problems of elliptical holes with 4 cracks in 1D orthorhombic quasicrystals were investigated through introduction of a new generalized conformal mapping with the generalized complex variable method. With the stress functions, the basic elasticity equations were reduced to 4th-order partial differential equations, the complex expression of stress components was derived in the image plane and the analytical solution of stress intensity factors (SIFs) at the crack tips was found out. With the change of parameters describing the defects, the results can not only reduce to the conclusions in previous literatures, but also give the SIFs of a variety of common defect configurations, which provides a theoretical basis for engineering mechanics analysis.
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