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• W111287795 abstract "Problems involving material anisotropy are in general more difficult to solve than the isotropic ones. The problem of an anisotropic composite material can be examined on the assumption that the matrix is only slightly anisotropic (Lekhnitskii, 1963, 1968; Sachenkov and Daragan, 1972). On the other hand, as it has been shown by Kosmodamianskii for an anisotropic plane with two identical elliptic holes (Kosmodamianskii, 1966, 1976), strong anisotropy leads to the possibility of sufficient simplifications of the governing boundary value problems. Independently Manevitch, Pavlenko and Shamrovskii (1970, 1971) and Everstine and Pipkin (1971, 1973) (see also Spencer, 1974; Sanchez and Pipkin, 1978; Pipkin, 1979, 1984; Christensen, 1979), beginning with elasticity theory and treating the extensibility of the material in a preferred direction as a small parameter, used the singular perturbation method to obtain approximate boundary value problems. The governing plane problem is reduced to that of solving two Laplace equations and, if higher-order approximations are wanted, a number of Poisson’s equations. The comparison of approximate solutions with the exact anisotropic elastic solutions showed satisfactory agreement (Kosmodamianskii, 1976; Manevitch, Pavlenko and Shamrovskii, 1970, 1971; Everstine and Pipkin, 1971, 1973; Spencer, 1974; Pipkin, 1979, 1984; Sanchez and Pipkin, 1978; Christensen, 1979). In the paper by Everstine and Pipkin (1971) a cantilever beam with end load was analysed. Spencer (1974) studied the problem of a crack parallel to the fibres in shear, as well as a crack normal to the fibre direction opened by internal pressure. Bogan (1981, 1994) considered the stress distribution within the elliptic region, and the contact problem for the half-plane. Sanchez and Pipkin (1978) showed how to compute the elastic stress factor at a crack tip from the force in the singular fiber passing throw the tip. The efficiency of the asymptotic approach for solving of plane anisotropic contact problems was shown in the papers (Manevitch and Pavlenko, 1975, 1982; Manevitch, Pavlenko and Koblik, 1979; Manevitch, 2001; Pavlenko, 1981; Andrianov, Awrejcewicz and Manevitch, 2004). A generalization for the axially symmetric case with a cylindrically orthotropic matrix was proposed in the papers by Pavlenko (1980), Manevitch and Pavlenko (1991). The papers by Kagadii and Pavlenko (1989, 1992) are devoted to the fibre reinforced composites with a viscoelastic orthotropic matrix." @default.
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• W111287795 date "2008-01-01" @default.
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• W111287795 title "Asymptotic Analysis of Strongly Anisotropic Solids" @default.
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