The radially nonhomogeneous elastic axisymmentric problem

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES

卷:45

Article

Theotokoglou, E. E.¹  Stampouloglou, I. H.¹ 

[1] Natl Tech Univ Athens, Fac Sci Appl, Mat Lab, Dept Mech, GR-015773 Athens, Greece

关键词: Linear elasticity;    Axisymmetric problem;    Stress function;    Homogeneous differential equation;    Radially nonhomageneous;    Hollow cylinder;   

DOI  :  10.1016/j.ijsolstr.2008.08.011

来源: Elsevier

【 摘 要 】

The plane axisymmetric problem with axisymmetric geometry and loading is analyzed for a radially nonhomogeneous circular cylinder, in linear elasticity. Considering the radial dependence of the stress, the displacements fields and of the stiffness matrix, after a series of admissible functional manipulations, the general differential system solving the problem is developed. The isotopic radially inhomogeneous elastic axisymmetric problem is also analyzed. The exact elasticity solution is developed for a radially nonhomogeneous hollow circular cylinder of exponential Young's modulus and constant Poisson's ratio and of power law Young's modulus and constant Poisson's ratio. For the isotropic elastic axisymmetric problem, a general expression of the stress function is derived. After the satisfaction of the biharmonic equation and making compatible the stress field's expressions, the stress function and the stress and displacements fields of the axisymmetric problem are also deduced. Applications have been made for a radially nonhomogeneous hollow cylinder where the stress and displacements fields are determined. (C) 2008 Elsevier Ltd. All rights reserved.

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