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论文类型：期刊论文

发表时间：2009-01-01

发表刊物：JOURNAL OF MECHANICS OF MATERIALS AND STRUCTURES

收录刊物：SCIE、Scopus

卷号：4

期号：10

页面范围：1741-1754

ISSN号：1559-3959

关键字：Saint-Venant problem; elastic foundation; symplectic; Hamilton principle; Legendre transformation

摘要：Analytic solutions describing the stresses and displacements of beams on a Pasternak elastic foundation are presented using a symplectic method based on classical two-dimensional elasticity theory. Hamilton's principle with a Legendre transformation is employed to derive the Hamiltonian dual equation, and separation of variables reduces the dual equation to an eigenequation that differs from the conventional eigenvalue problems involved in vibration and buckling analysis. Using adjoint symplectic orthonormality, a group of eigensolutions of zero eigenvalue, corresponding to the Saint-Venant problem, are derived. This approach differs from the traditional semi-inverse analysis, which requires stress or deformation trial functions in the Lagrangian system. The final solutions, which account for the effects of an elastic foundation and applied lateral loads, are approximated by an eigenfunction expansion. Comparisons with existing numerical solutions are conducted to validate the efficiency of this new approach.