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Vasil’ev, T. A.; Shaldyrvan, V. A.

Local stress singularities in mixed axisymmetric problems of the bending of circular cylinders. (English. Russian original) Zbl 1295.74036

Int. Appl. Mech. 48, No. 2, 176-187 (2012); translation from Prikl. Mekh. Kiev 48, No. 1, 74-86 (2012).
Summary: A method of analyzing the near-edge stress state in mixed problems of the deformation of an isotropic cylindrical body is proposed. The method is based on the expansion of the solution of three-dimensional problems of elasticity into a series of Lurie-Vorovich homogeneous basis functions. An asymptotic analysis is performed to find the principal part of the solution of the infinite systems of linear algebraic systems to which the problems are reduced. The type of the stress singularity at the edge of the cylinder is the same as in the mixed problems for a quarter plane. Kummer’s convergence acceleration method is used. The obtained results are validated by testing the boundary conditions and by comparing with results obtained by other authors.

Cited in 3 Documents

MSC:

74G70 Stress concentrations, singularities in solid mechanics
74B05 Classical linear elasticity
74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics

Keywords:

isotropic cylindrical body; edge; mixed problems; plate; bending; stress singularity; Kummer convergence acceleration
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References:

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