Abstract
Boundary value problems for the Lamé operator with piecewise constant material coefficients are investigated on polyhedral domains. Because of geometric peculiarities and non-smooth material constants, the displacement fields and especially the stress fields have a singular behavior in the neighborhood of corners, edges and those points where the material constants jump. For 3D problems it is not clear if the displacement fields are bounded. In this article we describe sufficient conditions on the distribution of the material parameters and the geometry which guarantee that weak solutions of the BVP are bounded and piecewise continuous.
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Knees, D. (2003). Regularity results for transmission problems of linear elasticity on polyhedral domains. In: Wendland, W., Efendiev, M. (eds) Analysis and Simulation of Multifield Problems. Lecture Notes in Applied and Computational Mechanics, vol 12. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-36527-3_25
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DOI: https://doi.org/10.1007/978-3-540-36527-3_25
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