On the solution of Almansi-Michell's problem

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES

卷:75-76

Article

Han, Shilei¹  Bauchau, Olivier A.² 

[1] Univ Michigan Shanghai Jiao Tong Univ Joint Inst, Shanghai, Peoples R China

[2] Hong Kong Univ Sci & Technol, Hong Kong, Hong Kong, Peoples R China

关键词: Almansi-Michell's problem;    Saint-Venant's problem;    Hamiltonian formalism;    Symplectic transformation;    Beam;   

DOI  :  10.1016/j.ijsolstr.2015.08.010

来源: Elsevier

【 摘 要 】

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. (C) 2015 Elsevier Ltd. All rights reserved.

【 授权许可】

Free