Self-Similar Solutions of Fracture Dynamics Problems on Axially Symmetry

LÜ Nian-chun; CHENG Jin; CHENG Yun-hong; QU De-zhi

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2001 > 22(12): 1285-1290

LÜ Nian-chun, CHENG Jin, CHENG Yun-hong, QU De-zhi. Self-Similar Solutions of Fracture Dynamics Problems on Axially Symmetry[J]. Applied Mathematics and Mechanics, 2001, 22(12): 1285-1290.

Citation:

LÜ Nian-chun, CHENG Jin, CHENG Yun-hong, QU De-zhi. Self-Similar Solutions of Fracture Dynamics Problems on Axially Symmetry[J]. Applied Mathematics and Mechanics, 2001, 22(12): 1285-1290.

Citation:

LÜ Nian-chun, CHENG Jin, CHENG Yun-hong, QU De-zhi. Self-Similar Solutions of Fracture Dynamics Problems on Axially Symmetry[J]. Applied Mathematics and Mechanics, 2001, 22(12): 1285-1290.

PDF( 254 KB)

Self-Similar Solutions of Fracture Dynamics Problems on Axially Symmetry

1.
Department of Astronautics and Mechanics, Harbin Institute of Technology, Harbin 150001, P. R. China;
2.
Department of Civil Engineering, Northeastern University, Shenyang 110006, P. R. China;
3.
Compressive Vessel Manufacturer of Constructive Installation Group Company of Daqing, Daqing 163711, P. R. China

Received Date: 1999-10-08
Rev Recd Date: 2001-06-29
Publish Date: 2001-12-15

Abstract

Abstract

By the theory of complex functions, a penny-shaped crack on axially symmetric propagating problems for composite materials was studied. The general representations of the analytical solutions with arbitrary index of self-similarity were presented for fracture elastodynamics problems on axially symmetry by the ways of self-similarity under the ladder-shaped loads. The problems dealt with can be transformed into Riemann-Hilbert problems and their closed analytical solutions are obtained rather simple by this method. After those analytical solutions are utilized by using the method of rotational superposition theorem in conjunction with that of Smirnov-Sobolev, the solutions of arbitrary complicated problems can be obtained.
- penny-shaped crack,
- axially symmetric,
- composite materials,
- analytical solutions

FullText(HTML)

References(9)

References

[1]	Charepanov G P.Mechanics of Brittle Fracture [M].New York:McGraw-Hill International Book Company,1979.
[2]	Kostrov B V.The axisymmetric problem of propagation of a tension crack[J].J Appl Math Mech,1964,28(4):793-803.
[3]	Kostrov B V.Self-similar problems of propagation of shear cracks [J].J Appl Math Mech,1964,28(5):1077-1087.
[4]	Muskhelishvili N I.Singular Integral Equations[M].Moscow:Nauka,1968.
[5]	Charepanov G P,Afanasov E F.Some dynamic problems of the theory of elasticity-Areview[J].Int J Engng Sci,1970,12(5):66 5-690.
[6]	Erigen A C,Suhubi E S.Elastodynamics,Vol 2,Linear Theory[M].New York,San Francisco,London:Academic Press,1975.
[7]	Hoskins R F.Generalized Functions[M].New York:Ellis Horwo od,1979.
[8]	Sih G C.Mechanics of Fracture 4.Elastodynamics Crack Problems [M].Leyden:Noordhoff International Publishing,1977,213-247.
[9]	Kanwal R P,Sharma D L.Singularity methods for elastostatics[J].J Elasticity,1976,6(4):405-418.