On cyclically symmetric crack problems

In this paper, a new kind of finite element method (FEM) is proposed, which use the two-dimensional Hermite interpolation scaling function constructed by tensor product as the basis interpolation function of field function, and then combine with the energy functional with related mechanics and variational principle, the wavelet finite element equations for solving elastic thin plate unit that constructed in this paper are derived. Then the bending problem of thin plate is solved very quickly and availably through the matlab program. The numerical example in this paper indicates the correctness and validity of this method, and has high calculation precision and convergence speed. Moreover, it also provides a reliable method to solve the free vibration problem of thin plate and the pipe crack problems.

Download Full-text

Application of boundary element method with singular and isoparametric elements in three dimensional crack problems

Engineering Fracture Mechanics ◽

10.1016/0013-7944(88)90010-0 ◽

1988 ◽

Vol 29 (1) ◽

pp. 97-106 ◽

Cited By ~ 13

Author(s):

Gangming Luo ◽

Yongyuan Zhang

Keyword(s):

Boundary Element Method ◽

Boundary Element ◽

Three Dimensional ◽

Crack Problems ◽

Element Method ◽

Isoparametric Elements

Download Full-text

An Effective Numerical Approach for Multiple Void-Crack Interaction

Journal of Applied Mechanics ◽

10.1115/1.2127955 ◽

2005 ◽

Vol 73 (4) ◽

pp. 525-535 ◽

Cited By ~ 18

Author(s):

Xiangqiao Yan

Keyword(s):

Boundary Element Method ◽

Boundary Element ◽

Elastic Plate ◽

Homogeneous Problem ◽

Crack Problem ◽

General System ◽

Numerical Approach ◽

Displacement Discontinuity ◽

Crack Problems ◽

Element Method

This paper presents a numerical approach to modeling a general system containing multiple interacting cracks and voids in an infinite elastic plate under remote uniform stresses. By extending Bueckner’s principle suited for a crack to a general system containing multiple interacting cracks and voids, the original problem is divided into a homogeneous problem (the one without cracks and voids) subjected to remote loads and a multiple void-crack problem in an unloaded body with applied tractions on the surfaces of cracks and voids. Thus the results in terms of the stress intensity factors (SIFs) can be obtained by considering the latter problem, which is analyzed easily by means of the displacement discontinuity method with crack-tip elements (a boundary element method) proposed recently by the author. Test examples are included to illustrate that the numerical approach is very simple and effective for analyzing multiple crack/void problems in an infinite elastic plate. Specifically, the numerical approach is used to study the microdefect-finite main crack linear elastic interaction. In addition, complex crack problems in infinite/finite plate are examined to test further the accuracy and robustness of the boundary element method.

Download Full-text