Summary
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 Boussinesque'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.
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Chowdhury, K.L. Similarity transformations for the axisymmetric Boussinesque's problem. Acta Mechanica 68, 171–183 (1987). https://doi.org/10.1007/BF01190881
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DOI: https://doi.org/10.1007/BF01190881