Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
800975 | Mechanics Research Communications | 2012 | 6 Pages |
Abstract
A symplectic approach is proposed to investigate the Saint-Venant problem of functionally graded beams with Young's modulus varying exponentially in the axial direction and constant Poisson radio. A matrix state equation is derived with a shift-Hamiltonian operator matrix whose particular eigenvalues are proved to compose the basic solutions of the Saint-Venant problem. The present analyses demonstrate that the Saint-Venant solutions under simple extension and pure bending can be derived using either the direct expansion method or the rigid motion removing method.
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Authors
L. Zhao, W.Q. Chen, C.F. Lü,