Fracture Calculation of Bending Plates by Boundary Collocation Method

WANG Yuan-han; WU You-lun; YU Fei

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2003 > 24(6): 605-610

WANG Yuan-han, WU You-lun, YU Fei. Fracture Calculation of Bending Plates by Boundary Collocation Method[J]. Applied Mathematics and Mechanics, 2003, 24(6): 605-610.

Citation:

WANG Yuan-han, WU You-lun, YU Fei. Fracture Calculation of Bending Plates by Boundary Collocation Method[J]. Applied Mathematics and Mechanics, 2003, 24(6): 605-610.

Citation:

WANG Yuan-han, WU You-lun, YU Fei. Fracture Calculation of Bending Plates by Boundary Collocation Method[J]. Applied Mathematics and Mechanics, 2003, 24(6): 605-610.

PDF( 263 KB)

Fracture Calculation of Bending Plates by Boundary Collocation Method

School of Civil Engineering, Huazhong University of Science and Technology, Wuhan 430074, P. R. China

Received Date: 2001-09-25
Rev Recd Date: 2003-02-19
Publish Date: 2003-06-15

Abstract

Abstract

Fracture of Kirchhoff plates is analyzed by the theory of complex variables and boundary collocation method. The deflections, moments and shearing forces of the plates are assumed to be the functions of complex variables. The functions can satisfy a series of basic equations and governing conditions, such as the equilibrium equations in the domain, the boundary conditions on the crack surfaces and stress singularity at the crack tips. Thus, it is only necessary to consider the boundary conditions on the external boundaries of the plate, which can be approximately satisfied by the collocation method and least square technique. Different boundary conditions and loading cases of the cracked plates are analyzed and calculated. Compared to other methods, the numerical examples show that the present method has many advantages such as good accuracy and less computer time. This is an effective semi-analytical and semi-numerical method.
- Kirchhoff plate,
- fracture,
- boundary collocation method,
- complex variables function,
- stress intensity factors

FullText(HTML)

References(12)

References

[1]	柳春图,李英治.平板弯曲断裂问题的研究进展[J].力学进展,1982,12(4):346-359.
[2]	柳春图,蒋持平. 板壳断裂力学[M].北京:国防工业出版社,2000,1-111.
[3]	中国航空研究院. 应力强度因子手册(增订版)[M].北京:科学出版社,2000, 858-913.
[4]	Murakami Y.Stress Intensity Factor Handbook[M].Vol 2.New York: Pergamon Press, 1987, 1249-1341.
[5]	Sih G C,Paris P C,Erdogan F.Crack-tip stress-intensity factors for plane extension and plate bending problems[J].Journal of Applied Mechanics,1962,29(2):306-312.
[6]	Barsoum R S.A degenerate solid element for linear fracture analysis of plate bending and general shells[J].International Journal for Numerical Methods in Engineering,1976,10(3):551-564.
[7]	Rhee H C, Atluri S N.Hybrid stress finite element analysis of bending of a plate with a through flaw[J].International Journal for Numerical Methods in Engineering,1982,18(2):259-271.
[8]	Jiang C P,Cheung Y K.A special bending crack tip finite element[J].International Journal of Fracture,1995,71(1):57-69.
[9]	WANG Yuan-han. The elastic and elasto-plastic fracture analysis by method of weighted residuals and elasto-viscoplasticity[D].Ph D Thesis.Hong Kong:The University of Hong Kong,1988,13-200.
[10]	Muskhelishvili NI.Some Basic Problems of Mathematical Theory of Elasticity[M].The Netherlands, Leyden:Noordhoff,1975.
[11]	Savin G N.Stress Concentration Around Holes[M].Oxford: Pergamon Press, 1961.
[12]	曲庆璋, 章权,季求和,等,弹性板理论[M].北京:人民交通出版社,2000,167-190.