# An analysis of compressive stability of elastic solids containing a crack parallel to the surface

Wenxue Wang, Shen Wei, Takao Yoshihiro, Shen Zhen, Chen Pu-Hui

Research output: Contribution to journalArticle

8 Citations (Scopus)

### Abstract

An analysis is presented for compressive stability of elastic solids containing a crack parallel to the free surface based on the mathematical theory of elasticity. Basic buckling equations derived from the mathematical theory of elasticity are employed and are reduced to a system of homogeneous Cauchy-type singular integral equations by means of Fourier integral transform. The integral equations are solved numerically by utilizing Gauss-Chebyshev integral formulae. Numerical results for buckling loads are presented for various geometrical parameters and are compared with those obtained from classical theory of beam-plate stability based on the Kirchhoff assumption. The comparison of both results shows that the buckling loads obtained from the classical theory of beam-plate stability are much larger than those obtained from the mathematical theory of elasticity, referring to which the limitations of the classical theory applied to the present buckling problem are discussed. A simple but accurate approximate method for estimating the buckling load is developed by the use of the elastic support coefficient obtained from the present analysis and the Euler formula derived from the classical theory for the case of elastically supported ends. Finally, the numerical results of the buckling wave shapes and the Mode I and II stress factors, which cannot be obtained from the classical theory, are presented.

Original language English 1023-1033 11 Engineering Fracture Mechanics 40 6 https://doi.org/10.1016/0013-7944(91)90167-Y Published - Jan 1 1991 Yes

### Fingerprint

Buckling
Cracks
Elasticity
Integral equations

### All Science Journal Classification (ASJC) codes

• Materials Science(all)
• Mechanics of Materials
• Mechanical Engineering

### Cite this

An analysis of compressive stability of elastic solids containing a crack parallel to the surface. / Wang, Wenxue; Wei, Shen; Yoshihiro, Takao; Zhen, Shen; Pu-Hui, Chen.

In: Engineering Fracture Mechanics, Vol. 40, No. 6, 01.01.1991, p. 1023-1033.

Research output: Contribution to journalArticle

Wang, Wenxue ; Wei, Shen ; Yoshihiro, Takao ; Zhen, Shen ; Pu-Hui, Chen. / An analysis of compressive stability of elastic solids containing a crack parallel to the surface. In: Engineering Fracture Mechanics. 1991 ; Vol. 40, No. 6. pp. 1023-1033.
title = "An analysis of compressive stability of elastic solids containing a crack parallel to the surface",
abstract = "An analysis is presented for compressive stability of elastic solids containing a crack parallel to the free surface based on the mathematical theory of elasticity. Basic buckling equations derived from the mathematical theory of elasticity are employed and are reduced to a system of homogeneous Cauchy-type singular integral equations by means of Fourier integral transform. The integral equations are solved numerically by utilizing Gauss-Chebyshev integral formulae. Numerical results for buckling loads are presented for various geometrical parameters and are compared with those obtained from classical theory of beam-plate stability based on the Kirchhoff assumption. The comparison of both results shows that the buckling loads obtained from the classical theory of beam-plate stability are much larger than those obtained from the mathematical theory of elasticity, referring to which the limitations of the classical theory applied to the present buckling problem are discussed. A simple but accurate approximate method for estimating the buckling load is developed by the use of the elastic support coefficient obtained from the present analysis and the Euler formula derived from the classical theory for the case of elastically supported ends. Finally, the numerical results of the buckling wave shapes and the Mode I and II stress factors, which cannot be obtained from the classical theory, are presented.",
author = "Wenxue Wang and Shen Wei and Takao Yoshihiro and Shen Zhen and Chen Pu-Hui",
year = "1991",
month = "1",
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language = "English",
volume = "40",
pages = "1023--1033",
journal = "Engineering Fracture Mechanics",
issn = "0013-7944",
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TY - JOUR

T1 - An analysis of compressive stability of elastic solids containing a crack parallel to the surface

AU - Wang, Wenxue

AU - Wei, Shen

AU - Yoshihiro, Takao

AU - Zhen, Shen

AU - Pu-Hui, Chen

PY - 1991/1/1

Y1 - 1991/1/1

N2 - An analysis is presented for compressive stability of elastic solids containing a crack parallel to the free surface based on the mathematical theory of elasticity. Basic buckling equations derived from the mathematical theory of elasticity are employed and are reduced to a system of homogeneous Cauchy-type singular integral equations by means of Fourier integral transform. The integral equations are solved numerically by utilizing Gauss-Chebyshev integral formulae. Numerical results for buckling loads are presented for various geometrical parameters and are compared with those obtained from classical theory of beam-plate stability based on the Kirchhoff assumption. The comparison of both results shows that the buckling loads obtained from the classical theory of beam-plate stability are much larger than those obtained from the mathematical theory of elasticity, referring to which the limitations of the classical theory applied to the present buckling problem are discussed. A simple but accurate approximate method for estimating the buckling load is developed by the use of the elastic support coefficient obtained from the present analysis and the Euler formula derived from the classical theory for the case of elastically supported ends. Finally, the numerical results of the buckling wave shapes and the Mode I and II stress factors, which cannot be obtained from the classical theory, are presented.

AB - An analysis is presented for compressive stability of elastic solids containing a crack parallel to the free surface based on the mathematical theory of elasticity. Basic buckling equations derived from the mathematical theory of elasticity are employed and are reduced to a system of homogeneous Cauchy-type singular integral equations by means of Fourier integral transform. The integral equations are solved numerically by utilizing Gauss-Chebyshev integral formulae. Numerical results for buckling loads are presented for various geometrical parameters and are compared with those obtained from classical theory of beam-plate stability based on the Kirchhoff assumption. The comparison of both results shows that the buckling loads obtained from the classical theory of beam-plate stability are much larger than those obtained from the mathematical theory of elasticity, referring to which the limitations of the classical theory applied to the present buckling problem are discussed. A simple but accurate approximate method for estimating the buckling load is developed by the use of the elastic support coefficient obtained from the present analysis and the Euler formula derived from the classical theory for the case of elastically supported ends. Finally, the numerical results of the buckling wave shapes and the Mode I and II stress factors, which cannot be obtained from the classical theory, are presented.

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