Theory of cuspidal defects with different types of angular cuspidal points

Berezhnitskii, L. T.; Mazurak, L. P.; Delyavskii, M. V.

doi:10.1007/bf00715263

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“…Even for a sharp concentrator with turning points on the contour, it is necessary to have additional parameters of its tip, because the gradient of opening of lips of a cracklike defect can be different for various problems [17,20,21]. For example, according to the classification given in [21], the tip of a crack is a tuning point with zero opening measure and the tip of a hypocycloidal hole is a tuning point with the first opening measure.…”

Section: Expansion Of the Radius Of Curvature Of The Contour Of A Holmentioning

confidence: 99%

Method of perturbations of the shape of the boundary in fracture mechanics. Part 3: Cracklinke defects in thin sloping shells

Berezhnyts'kyi¹

1998

Mater Sci

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We consider thin sloping shells of a positive or zero Gaussian curvature satisfying the Kirchhoff-Love hypotheses with through cracklike holes. By using a method of perturbation of the shape of the boundary, we obtained numerical and analytic results in the case of"small" cracklike defects with a negligible but finite radius of curvature at the tips. By using new formulas of the Irwin type, we calculated the corresponding generalized stress intensity factors (factors of 1/~/p + 2z I in the stress distribution). As an example, we consider the elastic equilibrium of a spherical shell with a square rounded hole or an absolutely rigid inclusion.Presently, shells are a basic structure in different fields of industry because, not being heavy, they can carry considerable tensile and bending loadings.We consider only thin elastic isotropic homogeneous sloping shells of constant thickness with cracklike holes.I By calculating bending stresses, we use theories based on the Kirchhoff-Love hypotheses. By using the method of perturbation of the shape of the boundary, we obtained particular results in the case of "small" and, sometimes, "middle" cracklike holes and absolutely rigid inclusions with a small but nonzero radius of curvature at the tips. We calculate the stress intensity factors for cracks with the same accuracy as for the solved problem of an elliptic hole in sloping shells. We consider so-called convex shells with positive or zero Gaussian curvature RIR2 R12where R i are the radii of curvature of the shell.The problem is to determine the elastic equilibrium of thin sloping shells with lateral through nonreinforced holes, in particular, cracks or absolutely rigid inclusions, i.e., to calculate the corresponding stress intensity factors with regard for the radius of curvature at the tips of defect. The external admissible loading is assumed to be selfbalanced when the principal vector and the principal moment of forces applied to the edge of the shell L 0 or hole L l are equal to zero. In the case of a simply connected infinite region (an infinite shell with a through lateral hole), the uniqueness conditions of small complex elastic displacements are satisfied automatically.

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Section: Expansion Of the Radius Of Curvature Of The Contour Of A Holmentioning

confidence: 99%

Method of perturbations of the shape of the boundary in fracture mechanics. Part 3: Cracklinke defects in thin sloping shells

Berezhnyts'kyi¹

1998

Mater Sci

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Theory of cuspidal defects with different types of angular cuspidal points

Cited by 1 publication

References 1 publication

Method of perturbations of the shape of the boundary in fracture mechanics. Part 3: Cracklinke defects in thin sloping shells

Method of perturbations of the shape of the boundary in fracture mechanics. Part 3: Cracklinke defects in thin sloping shells

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