DUAN Shujin, FUJII Koju, NAKAGAWA Kenji. Construction of General Analytic Functions With Finite Stress Concentration for Mono-Material Cracks and Bi-Material Interface Cracks[J]. Applied Mathematics and Mechanics, 2018, 39(12): 1364-1376. doi: 10.21656/1000-0887.390030
Citation: DUAN Shujin, FUJII Koju, NAKAGAWA Kenji. Construction of General Analytic Functions With Finite Stress Concentration for Mono-Material Cracks and Bi-Material Interface Cracks[J]. Applied Mathematics and Mechanics, 2018, 39(12): 1364-1376. doi: 10.21656/1000-0887.390030

Construction of General Analytic Functions With Finite Stress Concentration for Mono-Material Cracks and Bi-Material Interface Cracks

doi: 10.21656/1000-0887.390030
  • Received Date: 2018-01-22
  • Rev Recd Date: 2018-02-03
  • Publish Date: 2018-12-01
  • The constructing methods for finite stress concentration analysis near the crack tip were summarized. The stress functions for plane problems with cracks were expressed with irrational or exponential functions. For the mono-material crack, with the crack length as the parameter, the direct weighted integration of the irrational-function-type analytic function was conducted to avoid stress singularity at the crack tip, and construct the finite stress concentration functions and the wedge-type opening displacement functions. The indirect integration of the exponential-function-type analytic function was suitable for the interface crack problem, but put the stress distribution within the integral interval into positive-negative inversion and irrational opening displacement shape, which can be improved through combining selection and superposition of different weight functions. The basic solutions for the central cracks and the symmetrical edge cracks were given in 6 stress states of plane stretching, shearing and bending, etc. The reason why the analytic function can avoid the stress singularity at the crack tip was given.
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