Exact Singular Solutions for an Inhomogeneous Thick Elastic Plate
The author and co-workers have developed and applied ai [1–7] a procedure for deriving a large class of exact solutions of the three-dimensional field equations of linear elasticity for plates that are isotropic but inhomogeneous in the through-thickness direction. Here the technique is applied to several problems in which the corresponding two- dimensional problem involves a singular stress field. A feature is that in every case the presence of inhomogeneity results in an increase in the order of the singularity.
KeywordsInhomogeneous elastic plates concentrated forces higher order elastic singularities Volterra dislocations semi-infinite crack
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- T.G. Rogers, Exact three-dimensional bending solutions for inhomogeneous and laminated elastic plates. In Elasticity, Mathematical methods and applications, G. Eason and R.W. Ogden, eds., Ellis Horwood, Chichester 1990, 301–313Google Scholar
- A.J.M. Spencer, Three-dimensional elasticity solutions for stretching of inhomogeneous and laminated plates. In Elasticity, Mathematical methods and applications, G. Eason and R.W. Ogden, eds., Ellis Horwood, Chichester, 1990, 347–356Google Scholar
- A.J.M. Spencer, A stress function formulation for a class of exact solutions for functionally graded elastic plates. In IUTAM Symposium on transformation problems in composite and active materials, Y.A Bahei-el-Din and G.J. Dvorak, eds., Kluwer Academic Publishers, Dordrecht, 1998, 161–172Google Scholar
- J.H. Michell, On the direct determination of stress in an elastic solid, with applications to the theory of plates. Proc. London Math. Soc. 31 (1900) 100–124Google Scholar
- P.V. Kaprielian, T.G. Rogers and A.J.M. Spencer, Theory of laminated elastic plates I. Isotropic laminae. Phil. Trans. Roy. Soc. Lond. A324 (1988) 565–594Google Scholar
- A.E.H. Love, A treatise on the mathematical theory of elasticity, 4th edition, Cambridge University Press, Cambridge, 1927.Google Scholar
- S. Timoshenko and J.N. Goodier, Theory of Elasticity, McGraw Hill, New York, 1951.Google Scholar