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Evaluation of \(J\) integrals and stress intensity factors in a 2D quadratic boundary contour method. (English) Zbl 0921.73260

Summary: A quadratic polynomial expression is used as the displacement shape function to develop the boundary contour method. In particular, we prove the divergence-free property of the \(J\) integral; the evaluation of the \(J\) integral is transformed, through an application of Stokes’ theorem, into a linear combination of the displacement and traction at the boundary point that have been calculated by the quadratic boundary contour method such that numerical integrals are not needed at all. Numerical results are presented for two-dimensional problems, and these are compared against conventional solutions.

MSC:

74S30 Other numerical methods in solid mechanics (MSC2010)
74G70 Stress concentrations, singularities in solid mechanics
74H35 Singularities, blow-up, stress concentrations for dynamical problems in solid mechanics
74R99 Fracture and damage
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References:

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