Analytical solution for functionally graded anisotropic cantilever beam subjected to linearly distributed load

The bending problem of a functionally graded anisotropic cantilever beam subjected to a linearly distributed load is investigated. The analysis is based on the exact elasticity equations for the plane stress problem. The stress function is introduced and assumed in the form of a polynomial of the lo...

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Bibliographic Details
Published in:Applied mathematics and mechanics 2007-07, Vol.28 (7), p.855-860
Main Authors: Huang, De-jin, Ding, Hao-jiang, Chen, Wei-qiu
Format: Article
Language:English
Subjects:
Anisotropy
Bending
Cantilever beams
Finite element method
Functionally gradient materials
Mathematical analysis
Mathematical models
Stress functions
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Summary:The bending problem of a functionally graded anisotropic cantilever beam subjected to a linearly distributed load is investigated. The analysis is based on the exact elasticity equations for the plane stress problem. The stress function is introduced and assumed in the form of a polynomial of the longitudinal coordinate. The expressions for stress components are then educed from the stress function by simple differentiation. The stress function is determined from the compatibility equation as well as the boundary conditions by a skilful deduction. The analytical solution is compared with FEM calculation, indicating a good agreement.
ISSN:0253-4827
1573-2754
DOI:10.1007/s10483-007-0702-1