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**The solution of dynamic point-ring-couple in an elastic space and its properties.**
*(English)*
Zbl 0819.73041

The solution of dynamic point-ring-couple at the origin in an elastic space is presented, and its properties are discussed. The shocking loads are uniformly distributed along the direction of circumference at a circle with radius \(a\) and centered at the origin. For obtaining the solution of the problem, the direct method is applied, with the use of Laplace transformation and inverse Laplace transformation in the limit process of integration (for \(a \to 0\)).

When the intensity of the dynamic point-ring-couple varies sinusoidally with the time, the cones in the elastic space, with apex at the origin and with symmetry axis perpendicular to the plane of the shocking point- ring-couple, become zero stressed surfaces at any time moment. The solution of the dynamic torsion problem for solids of revolution with these cones as a boundary, under the application of torque varying sinusoidally with the time, is found.

The most important property of point-ring-couple is that cones in the elastic space with apex at origin and symmetry axis perpendicular to the plane of point-ring-couple remain zero stresses at any time whatever change of the intensity of the point-ring-couple occurs.

When the intensity of the dynamic point-ring-couple varies sinusoidally with the time, the cones in the elastic space, with apex at the origin and with symmetry axis perpendicular to the plane of the shocking point- ring-couple, become zero stressed surfaces at any time moment. The solution of the dynamic torsion problem for solids of revolution with these cones as a boundary, under the application of torque varying sinusoidally with the time, is found.

The most important property of point-ring-couple is that cones in the elastic space with apex at origin and symmetry axis perpendicular to the plane of point-ring-couple remain zero stresses at any time whatever change of the intensity of the point-ring-couple occurs.

Reviewer: G.V.Vasiliev (Bucureşti)

### Keywords:

shocking loads; direct method; inverse Laplace transformation; cones; zero stressed surfaces; dynamic torsion problem
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\textit{T. Yun} and \textit{H. Gu}, Appl. Math. Mech., Engl. Ed. 14, No. 10, 891--898 (1993; Zbl 0819.73041)

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### References:

[1] | Yun Tian-quan, The solution of ”Point-Circle-Couple” in an elastic space and its applications,J. Huazhong Inst. Tech.,2, 7 (1962), 86–101. (in Chinese) |

[2] | Yun Tian-quan. An integral equation method for solving the torsion problem of rotating bodies,J. Huazhoung Inst. Tech., 3 (1979), 97–104. (in Chinese), (MR#81m: 73028). |

[3] | Yun Tian-quan, Torsion of elastic shaft of revolution embedded in an elastic half space,Applied Mathematics and Mechanics (English Ed.),11, 6 (1990), 527–536. |

[4] | Eringen A. C. and E. S. Suhubi,Elastodynamics, Academic Press, New York (1975). |

[5] | Xie Yi-quan, Lin Zhong-xiang and Ding Hao-jiang,Elasticity, Zhejiang University Publishers (1988), 47. (in Chinese) |

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