scholarly journals Analytical solution and numerical verification for the pressure-relief method of a circular tunnel

2018 ◽  
Vol 38 (3) ◽  
pp. 338-351
Author(s):  
Shunchuan Wu ◽  
Miaofei Xu ◽  
Yongtao Gao ◽  
Shihuai Zhang ◽  
Fan Chen
Keyword(s):  
Stress Distribution ◽  
Analytical Solution ◽  
High Stress ◽  
Mapping Function ◽  
Mapping Method ◽  
Numerical Verification ◽  
Fast Method ◽  
Circular Tunnel ◽  
Variable Theory ◽  
Releasing Effect

This paper presents an elastic analytical solution to a circular tunnel with releasing slots at high stress areas near the hole by using a conformal mapping method and the complex variable theory. Compared to the original stress distribution around the circular hole, the releasing effect on elastic stresses is evaluated. After grooving slots, low stress area is generated where the high stress concentration is located. This is agreeable with what was predicted by the finite difference FLAC2D. Besides, displacements are obtained along the periphery of the released hole and are in accordance with those of FLAC2D. In addition to the intersection of the mapping contour, the influences of the sampling points distribution, series number in mapping function, and slot shape are discussed. It is inevitable that the mapping accuracies for the slot and the circle cannot be satisfied at the same time The mapping effect on the circle has to be considered primarily since the stress distribution around the circle is much more significant than the tunnel stability. The analytical solution can be available and fast method of estimating the releasing effect of the application on the tunnel without rock parameters.

Evaluation of Seismic Simplified Methods for Deep Circular Tunnel

2011 ◽  
Vol 261-263 ◽  
pp. 1862-1866
Author(s):  
Zheng Fang Dong ◽  
Yi Chao Yao ◽  
Jun Jie Wang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Analytical Solution ◽  
Displacement Method ◽  
Circular Tunnel ◽  
Variable Theory ◽  
Soil Response ◽  
Complex Variable Theory ◽  
Spring Coefficient ◽  
Deep Circular Tunnel

Firstly several seismic simplified methods commonly used for deep circular tunnel are evaluated and the difficulties in response displacement method are pointed out. Then the analytical solution of soil spring coefficient and soil response of deep circular tunnel is derived from using complex variable theory of planar elastic theory based on pseudo-static hypothesis. The analytical solution has been verified by comparing its predictions with results from an analysis in finite element method. It is concluded that the analytical solution can be regarded as one feasible reference for the simplification of response displacement method.

scholarly journals Research on Stress Analysis and Control of Surrounding Rock of Trapezoidal Roadways Based on Complex Variable Theory

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Zhiqiang Wang ◽  
Chao Wu ◽  
Jianqiao Luo ◽  
Wenyu Lv ◽  
Lei Shi ◽  
...  
Keyword(s):  
Stress Concentration ◽  
Stress Distribution ◽  
Control Method ◽  
Mapping Function ◽  
Confining Pressure ◽  
Field Application ◽  
Surrounding Rock ◽  
Wire Mesh ◽  
Variable Theory ◽  
Anchor Cable

Aiming at the problem of the serious deformation of the mining roadways in the trapezoidal section of the coal mine, the method of combining theoretical analysis and field application is used to study the surrounding rock control method of the trapezoidal roadways. The conformal mapping function of the trapezoidal roadways is calculated by the theory of complex change, and then from the analytical solution of the tangential stress distributed in the surrounding rock of trapezoidal roadways which is under the influence of the bidirectional unequal pressure, homogeneous, isotropic, and elastic rock mass is obtained. Research studies show that the roof-stress distribution of the trapezoidal roadways is uniform and the confining pressure is small, while the two sidewalls and the floor are opposite. The stress distribution of the two sidewalls and the floor varies greatly, and the stress concentration factor is large. The top corner of the trapezoidal roadways is basically not affected by stress concentration, but the stress concentration coefficient at the bottom corner is relatively large, and reinforcement measures are required in the roadway support. Based on the aforementioned research results, the multisupport scheme of “bolting with wire mesh and anchor cable + W-type steel belt + joist steel shed support + anchor cable grouting” was proposed to the surrounding rock of trapezoidal roadways with large stress caused by mining influence, thus solving the actual mining problem.

The Stresses Around Square Holes with Rounded Corners

1958 ◽  
Vol 2 (03) ◽  
pp. 37-41
Author(s):  
Joseph S. Brock
Keyword(s):  
Stress Distribution ◽  
Analytical Solution ◽  
Infinite Plate ◽  
Mapping Function ◽  
Mapping Technique ◽  
Radius Of Curvature ◽  
Stress Concentrations ◽  
Method Of Solution ◽  
Christoffel Transformation ◽  
Square Hole

This paper presents an analytical solution for the stress distribution around a square hole with rounded corners in an infinite plate subjected to pure tension. The method of solution is a combination of a conformal mapping technique and the complexvariable method of Muskhelishvili. The form of the mapping function is obtained from the Schwarz-Christoffel transformation. The mapping function is general and gives a good approximation to square holes with rounded corners of arbitrary radius of curvature. The ratios of the corner radius to the width of the opening considered cover the range from 0.03 to 0.5. This is considered 1o be the interesting range for ship structures. The results are given in terms of stress concentrations around the boundary of the opening.

Effects of conform, non-conform, and hybrid conformity toward stress distribution at the glenoid implant and cement: A finite element study

2021 ◽  
pp. 039139882199939
Author(s):  
Abdul Hadi Abdul Wahab ◽  
Nor Aqilah Mohamad Azmi ◽  
Mohammed Rafiq Abdul Kadir ◽  
Amir Putra Md Saad
Keyword(s):  
Stress Distribution ◽  
Daily Living ◽  
3D Model ◽  
Promising Result ◽  
High Stress ◽  
Constant Load ◽  
Posterior Region ◽  
Implant Stability ◽  
Eccentric Load ◽  
Standing Up

Glenoid conformity is one of the important aspects that could contribute to implant stability. However, the optimal conformity is still being debated among the researchers. Therefore, this study aims to analyze the stress distribution of the implant and cement in three types of conformity (conform, non-conform, and hybrid) in three load conditions (central, anterior, and posterior). Glenoid implant and cement were reconstructed using Solidwork software and a 3D model of scapula bone was done using MIMICS software. Constant load, 750 N, was applied at the central, anterior, and posterior region of the glenoid implant which represents average load for daily living activities for elder people, including, walking with a stick and standing up from a chair. The results showed that, during center load, an implant with dual conformity (hybrid) showed the best (Max Stress—3.93 MPa) and well-distributed stress as compared to other conformity (Non-conform—7.21 MPa, Conform—9.38 MPa). While, during eccentric load (anterior and posterior), high stress was located at the anterior and posterior region with respect to the load applied. Cement stress for non-conform and hybrid implant recorded less than 5 MPa, which indicates it had a very low risk to have cement microcracks, whilst, conform implant was exposed to microcrack of the cement. In conclusion, hybrid conformity showed a promising result that could compromise between conform and non-conform implant. However, further enhancement is required for hybrid implants when dealing with eccentric load (anterior and posterior).

scholarly journals Application of the Schwarz-Christoffel Transformation to the Solution of Harmonic Dirichlet Problems in Electrostatics

2020 ◽  
Vol 3 (2) ◽  
pp. 168-178
Author(s):  
ST Swem ◽  
P Ogwola ◽  
E Otene
Keyword(s):  
Electric Field ◽  
Mapping Function ◽  
Mapping Method ◽  
Infinite Strip ◽  
Dirichlet Problems ◽  
Suitable Alternative ◽  
Conformal Mapping Method ◽  
Straight Line ◽  
Christoffel Transformation ◽  
Electrostatic Problems

In this paper, a purely conformal mapping method for efficiently solving harmonic Dirichlet problems of electrostatic in domains free of charge and with charge whose boundaries have inconvenient geometries consisting of straight-line segments is presented. The method which uses the inverse of an appropriately determined Schwarz-Christoffel transformation as the mapping function, was applied to harmonic Dirichlet problems in an infinite strip and infinite sector and the solution or electrostatic potential for the problem obtained for each case. Furthermore, the equipotential lines of the electric field were also obtained in order to show the features of the solution and the field analysed accordingly. The electric field intensity was also analysed to show its variation in the field. This method could therefore be a suitable alternative method for solving Laplace's equation in two dimensional electrostatic problems.

scholarly journals A Non-Singular Analytical Technique for Reinforced Non-Circular Holes in Orthotropic Laminate

2020 ◽  
Vol 25 (1) ◽  
pp. 92-105
Author(s):  
Pradeep Mohan ◽  
R. Ramesh Kumar
Keyword(s):  
Stress Distribution ◽  
Analytical Solution ◽  
Power Series ◽  
Orthotropic Shell ◽  
Infinite Plate ◽  
Stress Singularity ◽  
Power Series Solution ◽  
Element Analysis ◽  
Full Field ◽  
Analytical Technique

AbstractThe intricacy in Lekhnitskii’s available single power series solution for stress distribution around hole edge for both circular and noncircular holes represented by a hole shape parameter ε is decoupled by introducing a new technique. Unknown coefficients in the power series in ε are solved by an iterative technique. Full field stress distribution is obtained by following an available method on Fourier solution. The present analytical solution for reinforced square hole in an orthotropic infinite plate is derived by completely eliminating stress singularity that depends on the concept of stress ratio. The region of validity of the present analytical solution on reinforcement area is arrived at based on a comparison with the finite element analysis. The present study will also be useful for deriving analytical solution for orthotropic shell with reinforced noncircular holes.

An Anisotropic Generalization of the Bridgman Analysis of Tensile Necking

1983 ◽  
Vol 105 (4) ◽  
pp. 264-267 ◽  
Author(s):  
M. A. Eisenberg ◽  
C. F. Yen
Keyword(s):  
Stress Distribution ◽  
Analytical Solution ◽  
Plastic Flow ◽  
Approximate Analytical Solution ◽  
Parameter Family ◽  
Isotropic Case ◽  
Anisotropic Plastic

Tensile necking in anisotropic bars is analyzed in the spirit of P. W. Bridgman’s treatment of the isotropic case. Anisotropic plastic flow causes an initially axisymmetric bar to develop an elliptical neck. Using physical approximations analogous to Bridgman’s, an approximate analytical solution for the stress distribution is obtained. The solution is shown to be asymptotically correct in two important limiting cases: (a) the fully developed anisotropic neck, and (b) the isotropic limit. In the latter case it is shown that the solution is a member of a one-parameter family of solutions, which includes the Bridgman and the Davidenkov and Spiridonova solutions.

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