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- W251048310 abstract "We consider the problem of determining the stresses in a thin, homogeneous disc, weakened by N like holes situated at the same distance from the center and acted upon by a constant normal load applied along its periphery. Such a cyclically symmetric problem was solved by Buivol in [1], who reduced the Sherman integral equation [2, 3] along the boundary L of the region in question, to an equation along the part of L designated by / and lying within the angle θ 0 ⩽ θ ⩽ θ 0 + τ where τ = 2π / N and θ is the angular coordinate of the points of l in the polar coordinate system chosen in the plane of the annulus in the usual manner, and θ 0 is arbitrary. Such an approach utilizes the symmetry of the problem when the resulting equations are solved numerically and, unlike other methods [4–6], it does not impose any restrictions on the size and distribution of the holes, while a suitable choice of the norm in the method of least squares ensures uniform convergence of the complex potentials Φ (z) and ψ (z) and their derivatives right up to their boundaries. Unfortunately, the paper [1] contains an error. The transformation of the function ω ( t ) under a rotation by the angle τ is determined with the accuracy of only up to its principal term, i.e. up to the limiting value of the function holomorphic outside the region in question (see [7] for a representation of holomorphic functions in terms of the Cauchy integrals). Such a limiting value affects the form of ψ (z) and hence the result. In the present paper this value is determined with help of the condition of transformation of ψ (z) under rotation, used in [1], It is proved that ω ( t ) belongs to some subspace W 2 3 ( L , τ ) of the space W 2 3 ( L ), constructed by taking into account the symmetry of the problem. The application of the method of least squares in W 2 3 ( L , τ ) leads to an economic computational scheme. We give numerical results for N = 4 in the case of different disk-geometries. The method of solution can be easily extended to the case of an arbitrary static load which does not violate the symmetry of the problem." @default.
- W251048310 created "2016-06-24" @default.
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- W251048310 date "1974-01-01" @default.
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- W251048310 title "On the plane problem of the theory op elasticity for multiply-connected domains with cyclic symmetry" @default.
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- W251048310 doi "https://doi.org/10.1016/0021-8928(74)90135-x" @default.
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