Hole Crack Problems in Infinite Elastic Plate in Tension

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
Xiangqiao Yan ◽  
Baoliang Liu
Keyword(s):  
Elastic Plate ◽  
Homogeneous Problem ◽  
Crack Problem ◽  
Infinite Plate ◽  
Elliptical Hole ◽  
Numerical Approach ◽  
Displacement Discontinuity ◽  
Center Crack ◽  
Crack Problems ◽  
Hole Geometry

This paper deals with crack(s) emanating from a hole in infinite elastic plate in tension. Such a crack problem is called a hole crack problem for short. By extending Buckner’s principle suited for a crack to a hole crack problem in infinite plate in tension, here, the original problem (the hole crack problem in infinite plate in tension) is divided into a homogeneous problem (the one without hole crack) subjected to remote loads and a hole crack problem in an unloaded body with applied tractions on the surfaces of the hole and crack. 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 a hybrid displacement discontinuity (a boundary element method) proposed recently by Yan. Numerical examples are included to illustrate that the numerical approach is very simple and effective for analyzing the hole crack problem in infinite plate in tension. By using the proposed approach, three hole crack problems (i.e., a pair of cracks emanating from an elliptical hole, a pair of cracks emanating from a rhombus hole, and a crack emanating from a triangular hole in infinite plate in tension) are analyzed in detail. By changing the hole geometry form and the hole geometry parameters and by comparing the SIFs of the hole crack problem with those of the center crack problem, the effect of the hole geometry form and the hole geometry parameters on the SIFs is revealed. It is found that a hole has a shielding and an amplifying effect on the SIFs of crack(s) emanating from the hole. The shielding and amplifying effects varied with the hole geometry form and the hole geometry parameters.

Hole Crack Problems in Infinite Plate Subjected to Uniform Internal Pressure

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
Xiangqiao Yan ◽  
Baoliang Liu
Keyword(s):  
Internal Pressure ◽  
Crack Problem ◽  
Infinite Plate ◽  
Elliptical Hole ◽  
Displacement Discontinuity ◽  
Intensity Factors ◽  
Center Crack ◽  
Crack Problems ◽  
Amplifying Effect ◽  
Hole Geometry

This brief deals with crack(s) emanating from a hole in infinite plate subjected to uniform internal pressure. Such a crack problem is called a hole crack problem for short. By using a hybrid displacement discontinuity method (a boundary element method) proposed recently by Yan, three hole crack problems (an elliptical hole crack problem, a rhombus hole crack problem, and a triangle hole crack problem) in infinite plate subjected to uniform internal pressure are analyzed in detail. By changing hole geometry form and hole geometry parameters and by comparing the stress intensity factors (SIFs) of the hole crack problem with those of the center crack problem, the effect of the hole geometry form and hole geometry parameters on the SIFs is revealed. It is found that a hole has a shielding and an amplifying effect on the SIFs of crack(s) emanating from the hole. The shielding and amplifying effects are varied with hole geometry form and hole geometry parameters.

An Effective Numerical Approach for Multiple Void-Crack Interaction

2005 ◽  
Vol 73 (4) ◽  
pp. 525-535 ◽  
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.

Stress Concentration of Periodic Collinear Square Holes in an Infinite Plate in Tension

2015 ◽  
Vol 137 (5) ◽  
Author(s):  
Changqing Miao ◽  
Yintao Wei ◽  
Xiangqiao Yan
Keyword(s):  
Stress Concentration ◽  
Stress Concentration Factor ◽  
Concentration Factor ◽  
Infinite Plate ◽  
Numerical Approach ◽  
Numerical Examples ◽  
Calculated Stress ◽  
Bueckner’S Principle

A numerical approach for the stress concentration of periodic collinear holes in an infinite plate in tension is presented. It involves the fictitious stress method and a generalization of Bueckner's principle. Numerical examples are concluded to show that the numerical approach is very efficient and accurate for analyzing the stress concentration of periodic collinear holes in an infinite plate in tension. The stress concentration of periodic collinear square holes in an infinite plate in tension is studied in detail by using the numerical approach. The calculated stress concentration factor is proven to be accurate.

Theoretical Analysis and Engineering Improvement Test Verification of the Crack Problem in the Back Van of the Vehicle

2011 ◽  
Vol 121-126 ◽  
pp. 3431-3436
Author(s):  
Guo Quan Yang ◽  
You Qun Zhao ◽  
Jun Yan Li
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Theoretical Analysis ◽  
Crack Problem ◽  
Engineering Application ◽  
Reference Value ◽  
Element Analysis ◽  
Crack Problems ◽  
The Finite Element Analysis ◽  
Test Verification

This paper discussed the theoretical analysis and engineering improvement test verification of the crack problem in the back van of the vehicle. Causes that may result in the crack problem are firstly analyzed and then determined by the finite element analysis. Improvement are given and proved to be effective by the test verification of an improved vehicle. The method used in this paper will contribute to the analysis and solution of the crack problems in some parts of the vehicle and has reference value in engineering application.

Integral Equation Methods for Multiple Crack Problems and Related Topics

2007 ◽  
Vol 60 (4) ◽  
pp. 172-194 ◽  
Author(s):  
Y. Z. Chen
Keyword(s):  
Integral Equation ◽  
Integral Equations ◽  
Crack Problem ◽  
Plane Elasticity ◽  
Point Sources ◽  
Fredholm Integral Equations ◽  
Hypersingular Integral Equation ◽  
Multiple Crack ◽  
Antiplane Elasticity ◽  
Crack Problems

The content of this review consists of recent developments covering an advanced treatment of multiple crack problems in plane elasticity. Several elementary solutions are highlighted, which are the fundamentals for the formulation of the integral equations. The elementary solutions include those initiated by point sources or by a distributed traction along the crack face. Two kinds of singular integral equations, three kinds of Fredholm integral equations, and one kind of hypersingular integral equation are suggested for the multiple crack problems in plane elasticity. Regularization procedures are also investigated. For the solution of the integral equations, the relevant quadrature rules are addressed. A variety of methods for solving the multiple crack problems is introduced. Applications for the solution of the multiple crack problems are also addressed. The concept of the modified complex potential (MCP) is emphasized, which will extend the solution range, for example, from the multiple crack problem in an infinite plate to that in a circular plate. Many multiple crack problems are addressed. Those problems include: (i) multiple semi-infinite crack problem, (ii) multiple crack problem with a general loading, (iii) multiple crack problem for the bonded half-planes, (iv) multiple crack problem for a finite region, (v) multiple crack problem for a circular region, (vi) multiple crack problem in antiplane elasticity, (vii) T-stress in the multiple crack problem, and (viii) periodic crack problem and many others. This review article cites 187 references.

Sign in / Sign up

Export Citation Format

Share Document