End effects in plane anisotropic elasticity



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n the application of the theory of elasticity to problems of practical interest, an essential simplification is made by ignoring "end effects" and considering resultant boundary- conditions instead of mathematically exact conditions. This procedure is justified by invoking the classical "Saint-Venant1s Principle", the validity of which has rarely been questioned in practical applications. This "principle" justifies the neglect of local stress effects due to statically equivalent load conditions. The modern emphasis and interest in the technological applications of high strength composite materials has motivated the present study. We are concerned with investigation of the basic issues underlying the use of Saint-Venant1s principle for highly anisotropic and sandwich type materials. There is evidence both theoretical [1-3] and experimental [4-7] that the classic application of Saint-Venant1s principle is not valid in the cases mentioned. This raises some basic questions, particularly concerning current testing practice in the measurement of elastic constants for anisotropic materials. To clarify these issues, we analyze the traction problem of plane elasticity for a rectangular anisotropic elastic strip and for a sandwich strip. We use eigenfunctions analogous to the well-known Fadle-Papkovich eigenfunctions of isotropic elasticity. Particular attention is directed to the case of a highly anisotropic material. Numerical solutions are presented for a graphite/epoxy material illustrating extremely slow decay of end effects compared with the isotropic case. For the sandwich strip, when the core material is much less rigid than the face material, a similar slow decay of end effects is demonstrated.