A mathematical analogy and a unified asymptotic formulation for singular elastic and electromagnetic fields at multimaterial wedges. (English) Zbl 1304.74026
Summary: In the present contribution, the mathematical analogy existing between the singular stress field in elasticity due to antiplane loading and the singular electromagnetic fields in electromagnetism is derived with reference to the problem of isotropic multimaterial wedges. These configurations, where dissimilar sectors converge to the same vertex, are commonly observed in composite materials and may lead to singularities. The proposed analogy permits to extend several elastic solutions for the power of the stress-singularity already available in the elasticity literature to the analogous electromagnetic problems and viceversa. Finally, electromagnetic structures that cannot be treated according to the proposed analogy, such as those related to bi-isotropic multimaterial wedges, are discussed.
MSC:
| 74F15 | Electromagnetic effects in solid mechanics |
| 74B05 | Classical linear elasticity |
| 74G70 | Stress concentrations, singularities in solid mechanics |
| 74G10 | Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics |
Keywords:
singularities; re-entrant corners; antiplane loading; linear Elasticity; electromagnetic fieldsReferences:
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