Type of Document Master's Thesis Author Placidi, Luca Author's Email Address lplacidi@vt.edu URN etd-10212002-043618 Title SOLUTION OF ST.-VENANT'S AND ALMANSI-MICHELL'S PROBLEMS Degree Master of Science Department Engineering Science and Mechanics Advisory Committee

Advisor Name Title Bates, Robert C. Committee Chair Henneke, Edmund G. II Committee Member Morris, Don H. Committee Member Keywords

- Polynomial hypothesis
- Saint-Venant's Problem
- Linear Elasticity
- Non Linear Elasticity
- Stressed Reference Configuration
- Clebsch hypothesis
Date of Defense 2002-05-02 Availability unrestricted AbstractWe use the semi-inverse method to solve a St. Venant and an Almansi-Michell problem for a prismatic body made of a homogeneous and isotropic elastic material that is stress free in the reference configuration. In the St. Venant problem, only the end faces of the prismatic body are loaded by a set of self-equilibrated forces. In the Almansi-Michell problem self equilibrated surface tractions are also applied on the mantle of the body. The St. Venant problem is also analyzed for the following two cases: (i) the reference configuration is subjected to a hydrostatic pressure, and (ii) stress-strain relations contain terms that are quadratic in displacement gradients. The Signorini method is also used to analyze the St. Venant problem. Both for the St. Venant and the Almansi-Michell problems, the solution of the three dimensional problem is reduced to that of solving a sequence of two dimensional problems. For the St. Venant problem involving a second-order elastic material, the first order deformation is assumed to be an infinitesimal twist. In the solution of the Almansi-Michell problem, surface tractions on the mantle of the cylindrical body are expressed as a polynomial in the axial coordinate. When solving the problem by the semi-inverse method, displacements are also expressed as a polynomial in the axial coordinate. An explicit solution is obtained for a hollow circular cylindrical body with surface tractions on the mantle given by an affine function of the axial coordinateFiles

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