Similarity transformations for the axisymmetric Boussinesque’s problem. (Similarity transformations for the axisymmetric Boussinesq’s problem.) (English) Zbl 0621.73002
Lie’s infinitesimal transformation groups, which leave the basic equations of axially symmetric problems of classical elasticity invariant, are constructed. For the case of the axisymmetric Boussinesq’s problem of an elastic semi-space subjected to a point force applied normal to its surface, the invariance of boundary and boundary conditions leads to the explicit form of similarity transformations which are used to solve the problem. Expressions for the displacements and stresses derived by this approach, which is believed to be new, are found to agree with the known results.
MSC:
| 74B05 | Classical linear elasticity |
| 22E70 | Applications of Lie groups to the sciences; explicit representations |
| 35A30 | Geometric theory, characteristics, transformations in context of PDEs |
| 35A22 | Transform methods (e.g., integral transforms) applied to PDEs |
Keywords:
reduction to pair of coupled ordinary differential equations; explicit closed form solutions; Lie’s infinitesimal transformation groups; axisymmetric Boussinesq’s problem; elastic semi-space; point force; invariance of boundary and boundary conditions; similarity transformationsReferences:
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