Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6748671 | International Journal of Solids and Structures | 2015 | 16 Pages |
Abstract
This paper develops a Hamiltonian formalism for the solution of Almansi-Michell's problem that generalizes the corresponding solution of Saint-Venant's problem. Saint-Venant's and Almansi-Michell's problems can be represented as homogenous and non-homogenous Hamiltonian systems, respectively. The solution of Almansi-Michell's problem is determined by the coefficients of the Hamiltonian matrix but also by the distribution pattern of the applied loading. The solution proceeds in two steps: first, for the homogenous problem, a projective transformation is constructed based on a symplectic matrix and second, the effects of the external loading are taken into account by augmenting this projection. With the help of this projection, the three-dimensional governing equations of Almansi-Michell's problem are reduced to a set of one-dimensional beam-like equations, leading to a recursive solution process. Furthermore, the three-dimensional displacement, strain, and stress fields can be recovered from the one-dimensional solution. Numerical examples show that the predictions of the proposed approach are in excellent agreement with exact solutions of two-dimensional elasticity and three-dimensional FEM analysis.
Keywords
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Physical Sciences and Engineering
Engineering
Civil and Structural Engineering
Authors
Shilei Han, Olivier A. Bauchau,