An Analytical Method for Plane Elasticity Problems Involving Circular Boundaries

Jiang, Zhizhen; Zhang, Rui; Gong, Shuxi; Hou, Jiahui; Jin, Xiaoqing

doi:10.1088/1742-6596/2002/1/012028

Cited by 2 publications

(2 citation statements)

References 9 publications

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“…According to the linear elasticity theory, after removing multivalued terms of displacement and the terms leading to stress dispersion at infinity [10], we take the following form of the closely spaced Fourier series as the Michell stress function in polar coordinates,…”

Section: Stress Function and Stress Componentmentioning

confidence: 99%

General Series Solutions for Stresses around an Arbitrarily Loaded Hole in the Infinite Plate

Qi,

Yuan,

Jiao

et al. 2023

J. Phys.: Conf. Ser.

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Based on the linear elasticity theory and the Michell-Fourier series technique, a general series solution for stresses around an arbitrarily loaded hole in the infinite plate is presented. An Airy stress function in the form of Michell-Fourier series is chosen. The stresses are expressed by polar coordinates and two sets of stress coefficients. Arbitrarily distributed normal and tangential tractions on the edge of the hole are expanded into Fourier series. Then the loads are expressed by two sets of loading coefficients. The stress boundary is utilized for conditions on the edge of the hole. The stress coefficients are related to the loading coefficients. The general series solution for stresses around an arbitrarily loaded hole in the infinite plate is obtained. The verification solution of stresses around a uniformly pressured hole, and the stresses around a hole loaded by uniform tangential force are presented. The stresses around a circular hole partially loaded by varying traction are also calculated. The results show that the presented analytical solution is in great consistence with that from ANSYS.

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Section: Stress Function and Stress Componentmentioning

confidence: 99%

General Series Solutions for Stresses around an Arbitrarily Loaded Hole in the Infinite Plate

Qi,

Yuan,

Jiao

et al. 2023

J. Phys.: Conf. Ser.

View full text Add to dashboard Cite

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“…Consider a rectangular isotropic thin plate with a circular central hole of diameter (d) and thickness (t), subjected to pure tensile stress in the direction of the plate's axis x (Figure 1); the plate's dimensions are assumed to be sufficiently large in comparison to the radius r, and volume forces are ignored in-plane stress. According to literature the analytical solution of the plane elasticity distribution of the stress field in polar coordinates (r, θ) [16][17][18][19]:…”

Section: Theoretical Formulationmentioning

confidence: 99%

A Three-Node Triangular Constant Strain Element for Evaluation of Stress Concentration Factor of a Rectangular Thin Plate Under Tension Load

Fethallah¹,

Deghboudj²

2022

RCMA

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In many engineering fields such as aerospace, marine, automotive and mechanical, the design of planar structures consisting of rectangular plates commonly requires the use of holes as a technological solution in fastening assemblies. The major goal of this research is to examine the impact of stress concentration factors (SCF) in the specific case of planar structures, highlight their relevance as a potential source of structural failure, and compare the various techniques employed to gauge their magnitude. Particular emphasis will be placed on rectangular plates with holes since these plates' shape discontinuities alter the stress field, leading to a local increase in the stress field that, if not accurately predicted and analyzed at the design stage, could endanger the entire structure. For the studied case (rectangular plate with central hole subjected to uniform tensile field), a new finite element formulation based on 3-noded triangular element has been suggested to estimate the field variables (stress). MATLAB programming has been developed by considering this element. Analysis has been carried out for the same structure (rectangular plate) with analysis software Abaqus. Finding was compared to several analytical solutions published in the literature, based on Heywood, Howland, and Flynn formulations. Obtained results were in good agreement.

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An Analytical Method for Plane Elasticity Problems Involving Circular Boundaries

Cited by 2 publications

References 9 publications

General Series Solutions for Stresses around an Arbitrarily Loaded Hole in the Infinite Plate

General Series Solutions for Stresses around an Arbitrarily Loaded Hole in the Infinite Plate

A Three-Node Triangular Constant Strain Element for Evaluation of Stress Concentration Factor of a Rectangular Thin Plate Under Tension Load

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