Applied Mathematics and Mechanics

, Volume 24, Issue 6, pp 684–690 | Cite as

Fracture calculation of bending plates by boundary collocation method

  • Wang Yuan-han
  • Wu You-lun
  • Yu Fei


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.

Key words

Kirchhoff plate fracture boundary collocation method complex variables function stress intensity factors 

Chinese Library Classification


2000 MR Subject Classification

74R10 74K20 


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Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 2003

Authors and Affiliations

  • Wang Yuan-han
    • 1
  • Wu You-lun
    • 1
  • Yu Fei
    • 1
  1. 1.School of Civil EngineeringHuazhong University of Science and TechnologyWuhanP. R. China

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