A numerical procedure for the determination of certain quantities related to the stress intensity factors in two-dimensional elasticity. (English) Zbl 0851.73004
Summary: This work is devoted to the investigation of corner and interface singularities in linear elasticity and to the development of a numerical code that computes certain quantities associated with those singularities. We compute several terms of the asymptotic expansion of the solution of the elasticity system near the corner or interface, which is of the form \(k_n r^{\alpha_n} f_n (\theta)\). We treat our problem as a nonlinear eigenvalue problem and we use an approach based on the shooting method for boundary value problems to create an analytic function whose zeros are the \(\alpha_n\) above. The zeros of this function are then found using an iteration method and a global method to make sure that no zero was overlooked. The program works for the general case of anisotropic non-homogeneous wedge with general boundary conditions as well as in the case of crossing interfaces in an internal point. We test the convergence, accuracy, robustness, efficiency and reliability of the code.
MSC:
| 74B10 | Linear elasticity with initial stresses |
| 74B05 | Classical linear elasticity |
| 74G70 | Stress concentrations, singularities in solid mechanics |
| 74H35 | Singularities, blow-up, stress concentrations for dynamical problems in solid mechanics |
Keywords:
corner and interface singularities; asymptotic expansion; nonlinear eigenvalue problem; shooting method; iteration method; global method; anisotropic non-homogeneous wedge; convergenceReferences:
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