Line field analysis and complex variable method for solving elastic-plastic fields around an anti-plane elliptic hole

Guo, Junhong; Lu, Zixing

doi:10.1007/s11433-011-4397-7

Cited by 6 publications

(2 citation statements)

References 21 publications

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“…Akinola [6] emphasized the alternate formulation of the Cauchy-Riemann criteria for the analyticity of a complex variable function. Using the complex variable method, Guo and Lu [7] proposed a new approach to solving the elastic-plastic fields close to the elliptical hole's major-axis line. Ioakimidis and Theocaris [8] suggested a numerical approach for the solution of Cauchy-type singular integral equations along contours in the complex plane.…”

Section: Introductionmentioning

confidence: 99%

New Approach of Normal and Shear Stress Components for Multiple Curvilinear Holes Which Weakened a Flexible Plate

Alharbi,

Alhendi

2024

Symmetry

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In this article, a thin infinite flexible plate weakened by multiple curvilinear holes is considered. The strength shapes are mapped outside a unit circle with the assistance of particular conformal mapping under certain conditions. The mathematical model that governs the rounded forces of the current physical problem is the boundary value problem of elastic media. This study is applicable to many phenomena throughout nature, like tunnels, caves, and excavations in soil or rock. The Cauchy method for complex variables is used to get the closed forms of Gaursat functions and change the problem to a second-type integrodifferential equation with a Cauchy kernel, which is used for a large area of the contact problems. Then, the normal and shear stress components that act on the model are derived. Afterward, some of the physical applications are studied, and different stress components at specific values in each application are calculated and plotted using Maple 2023.

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Section: Introductionmentioning

confidence: 99%

New Approach of Normal and Shear Stress Components for Multiple Curvilinear Holes Which Weakened a Flexible Plate

Alharbi,

Alhendi

2024

Symmetry

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“…It abandons the small-scale yielding assumption, and thus, the related parameters such as the length of the plastic zone and the unit normal vector of the elastic-plastic boundary can be obtained. A series of problems have been solved by using the crack line analysis method [33][34][35][36][37]. Moreover, such a method can be extended for elastic-plastic analysis near the crack surface [38,39].…”

Section: Introductionmentioning

confidence: 99%

Near Crack Line Elastic‐Plastic Field for Mode I Cracks under Plane Stress Condition in Rectangular Coordinates

Feng

Wang

et al. 2020

Advances in Materials Science and Engineering

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By using the crack line analysis method, this paper carries out an elastic-plastic analysis for mode I cracks under plane stress condition in an elastic perfectly plastic solid and obtains the general form of matching equations of the elastic stress field and the plastic stress field near the crack line in rectangular coordinate form. The analysis in rectangular coordinates in this paper avoids the conversion from rectangular coordinates into polar coordinates in the existing analysis and greatly simplifies the power series forms of the elastic stress field and plastic stress field near the crack line during the solving process. Furthermore, by focusing on a new problem, i.e., the center-cracked plate with finite width under unidirectional uniform tension, this paper obtains the elastic stress field, plastic stress field, and the length of the elastic-plastic boundary near the crack line by using the general form of the solution. When the dimensions of the plate tend to be infinite, the results of this paper are consistent with those obtained for an infinite plate with a mode I crack. Furthermore, the variation curves of the length of the elastic-plastic boundary are also delineated in different sized center-cracked plates, and the results are compared with those obtained under the small-scale yielding conditions. The solving process and the results in this paper abandon the small-scale yielding conditions completely. The method used in this paper not only makes the solving process simpler during the elastic-plastic analysis near the crack line but also enriches the crack line analysis method.

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Complex variable solution for boundary value problem with X-shaped cavity in plane elasticity and its application

Zhou

2017

Appl. Math. Mech.-Engl. Ed.

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Line field analysis and complex variable method for solving elastic-plastic fields around an anti-plane elliptic hole

Cited by 6 publications

References 21 publications

New Approach of Normal and Shear Stress Components for Multiple Curvilinear Holes Which Weakened a Flexible Plate

New Approach of Normal and Shear Stress Components for Multiple Curvilinear Holes Which Weakened a Flexible Plate

Near Crack Line Elastic‐Plastic Field for Mode I Cracks under Plane Stress Condition in Rectangular Coordinates

Complex variable solution for boundary value problem with X-shaped cavity in plane elasticity and its application

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