The asymptotic form of the stress-strain state near a spatial singularity of the boundary of the ”beak tip” type.

*(English. Russian original)*Zbl 0794.73011
J. Appl. Math. Mech. 57, No. 5, 887-902 (1993); translation from Prikl. Mat. Mekh. 57, No. 5, 127-142 (1993).

Summary: The asymptotic form of the stress-strain state of a three-dimensional elastic body in the neighbourhood of a singular point of a special type is investigated. Near such a point the boundary of the body consists of four surfaces, namely, two planes forming a dihedral angle and two smooth surfaces tangent to one another at a point on the edge of the angle. (Similar singularities are present on the cutting edges of some devices.) A procedure for determining the structure of asymptotic solutions is presented.

##### MSC:

74B05 | Classical linear elasticity |

35Q72 | Other PDE from mechanics (MSC2000) |

##### Keywords:

three-dimensional elastic body
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\textit{S. A. Nazarov} and \textit{O. R. Polyakova}, J. Appl. Math. Mech. 57, No. 5, 1 (1993; Zbl 0794.73011); translation from Prikl. Mat. Mekh. 57, No. 5, 127--142 (1993)

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##### References:

[1] | Gol’denveizer, A. L.: The theory of thin elastic shells. (1976) |

[2] | GOL’DENVEIZER A. L., Construction of the approximate theory of plate bending by asymptotic integration of the equations of the theory of elasticity. Prikl. Mat. Mekh. 26, 4, 668–686. |

[3] | Zino, I. Ye.; Tropp, E. A.: Asymptotic methods in problems of the theory of heat conduction and thermoelasticity. (1978) |

[4] | Nazarov, S. A.: Introduction to asymptotic methods of the theory of elasticity. (1983) |

[5] | Maz’ya, V. G. N.; Plamenevskii, B. A.: On the asymptotic form of the solution of the Dirichlet problem near an isolated singularity of the boundary. Vestn. leningrad. GoS univ. 13, No. 3, 60-66 (1977) · Zbl 0371.35012 |

[6] | Movchan, A. B.; Nazarov, S. A.: The stress-strain state near the tip of a three-dimensional absolutely rigid spike driven into an elastic body. Prikl. mekhanika 25, No. 12, 10-19 (1989) · Zbl 0729.73016 |

[7] | Nazarov, S. A.: Asymptotics of the Stokes system solution at a surfaces contact point. C. R. Acad. sci. Paris ser. 1 312, No. 1, 207-211 (1991) · Zbl 0713.76032 |

[8] | Nazarov, S. A.: Behaviour at infinity of the solutions of the LamĂ© and Stokes systems in a layer sector. Dokl. akad. Nauk arm. SSR 87, No. 4, 156-159 (1988) · Zbl 0723.35013 |

[9] | Nazarov, S. A.: The three-dimensional effect near the tip of a crack in a thin plate. Prikl. mat. Mekh. 55, No. 3, 500-510 (1991) |

[10] | Kondrat’ev, V. A.: Boundary-value problems for elliptic equations in domains with conic or corner points. Tr. mosk. Mat. obsch. 16, 209-292 (1967) |

[11] | Maz’ya, V. G.; Plamenevskii, B. A.: On the coefficients and the asymptotic form of solutions of elliptic boundary-value problems in a domain with conic points. Math. nachr. 76, 29-60 (1977) |

[12] | Nazarov, S. A.; Plamenevskii, B. A.: Elliptic problems in domains with piecewise-smooth boundary. (1991) |

[13] | Agranovich, M. S.; Vishik, M. I.: Elliptic problems with a parameter and general parabolic problems. Usp. mat. Nauk 19, No. 3, 53-160 (1964) · Zbl 0137.29602 |

[14] | Bueckner, H. F.: A novel principle for the computation of stress intensity factor. Z. angew. Math. mech. 50, No. 9, 529-546 (1970) · Zbl 0213.26603 |

[15] | Rice, J. R.: Some remarks on elastic crack-tip stress fields. Int. J. Solids struct. 8, No. 6, 751-758 (1972) · Zbl 0245.73083 |

[16] | Zorin, I. S.; Nazarov, S. A.: Two-term asymptotic form of the solution of the problem on the longitudinal deformation of a plate fixed along an edge. Vychisl. mekh. Deform. tverd. Tela 2, 10-21 (1991) |

[17] | Zorin, I. S.; Nazarov, S. A.: Boundary effect in three-dimensional thin plate bending. Prikl. mat. Mekh. 53, No. 4, 642-650 (1989) · Zbl 0722.73037 |

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