On a spatial generalization of the Kolosov-Muskhelishvili formulae. (English) Zbl 1151.74308
Summary: The main goal of this paper is to construct a spatial analog to the Kolosov-Muskhelishvili formulae using the framework of the hypercomplex function theory. We prove a generalization of Goursat’s representation theorem for solutions of the biharmonic equation in three dimensions. On the basis of this result, we construct explicitly hypercomplex displacement and stress formulae in terms of two monogenic functions.
MSC:
| 74B05 | Classical linear elasticity |
| 30G35 | Functions of hypercomplex variables and generalized variables |
Keywords:
classical linear elasticity; functions of hypercomplex variables and generalized variables; monogenic functions; Goursat’s representation theorem; representation formulaeReferences:
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