scholarly journals Analytical Method to Interpret Displacement in Elastic Anisotropic Soil due to a Tunnel Cavity with an Arbitrary Cross Section

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Qiongfang Zhang ◽  
Kang Cheng ◽  
Yadong Lou ◽  
Tangdai Xia ◽  
Panpan Guo ◽  
...  
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Surface Displacement ◽  
Horizontal Displacement ◽  
Distribution Patterns ◽  
Mapping Method ◽  
Arbitrary Cross Section ◽  
Image Method ◽  
Variable Theory ◽  
Anisotropic Soil

Based on complex variable theory and conformal mapping method, the paper presents full plane elastic solutions around an unlined tunnel with arbitrary cross section in anisotropic soil. The solutions describe soil elastic solutions for assuming that the displacement vectors along the tunnel boundary are directed towards the center of the tunnel. Tunnels with different cross sections are used to illustrate the method and its correctness. An elliptical unlined tunnel case is discussed in detail in the paper. Using the image method, an approximate solution for predicting surface displacement and subsurface horizontal displacement around an unlined tunnel in anisotropic soil can be obtained. The results show anisotropic stiffness properties n n = E h / E v and m m = G v h / E v have a great effect on the displacement distribution patterns around an elliptical tunnel with certain shape.

Numerical Simulating Open-Channel Flows with Regular and Irregular Cross-Section Shapes Based on Finite Volume Godunov-Type Scheme

2020 ◽  
pp. 2050047
Author(s):  
Xiaokang Xin ◽  
Fengpeng Bai ◽  
Kefeng Li
Keyword(s):  
Finite Volume ◽  
Cross Section ◽  
Cross Sections ◽  
Open Channel ◽  
Arbitrary Cross Section ◽  
Second Order ◽  
Cross Sectional ◽  
Shallow Flows ◽  
Natural Streams ◽  
Saint Venant Equations

A numerical model based on the Saint-Venant equations (one-dimensional shallow water equations) is proposed to simulate shallow flows in an open channel with regular and irregular cross-section shapes. The Saint-Venant equations are solved by the finite-volume method based on Godunov-type framework with a modified Harten, Lax, and van Leer (HLL) approximate Riemann solver. Cross-sectional area is replaced by water surface level as one of primitive variables. Two numerical integral algorithms, compound trapezoidal and Gauss–Legendre integrations, are used to compute the hydrostatic pressure thrust term for natural streams with arbitrary and irregular cross-sections. The Monotonic Upstream-Centered Scheme for Conservation Laws (MUSCL) and second-order Runge–Kutta methods is adopted to achieve second-order accuracy in space and time, respectively. The performance of the resulting scheme is evaluated by application in rectangular channels, trapezoidal channels, and a natural mountain river. The results are compared with analytical solutions and experimental or measured data. It is demonstrated that the numerical scheme can simulate shallow flows with arbitrary cross-section shapes in practical conditions.

Estimation of Nusselt Number in Microchannels of Arbitrary Cross-Section With Constant Axial Heat Flux

2008 ◽  
Author(s):  
Ehsan Sadeghi ◽  
Majid Bahrami ◽  
Ned Djilali
Keyword(s):  
Heat Flux ◽  
Nusselt Number ◽  
Cross Section ◽  
Cross Sections ◽  
Numerical Solutions ◽  
Arbitrary Cross Section ◽  
Geometrical Parameters ◽  
Thermal Systems ◽  
Cross Sectional ◽  
Axial Heat

In many practical instances such as basic design, parametric study, and optimization analysis of thermal systems, it is often very convenient to have closed form relations to obtain the trends and a reasonable estimate of the Nusselt number. However, finding exact solutions for many practical singly-connected cross-sections, such as trapezoidal microchannels, is complex. In the present study, the square root of cross-sectional area is proposed as the characteristic length scale for Nusselt number. Using analytical solutions of rectangular, elliptical, and triangular ducts, a compact model for estimation of Nusselt number of fully-developed, laminar flow in microchannels of arbitrary cross-sections with “H1” boundary condition (constant axial wall heat flux with constant peripheral wall temperature) is developed. The proposed model is only a function of geometrical parameters of the cross-section, i.e., area, perimeter, and polar moment of inertia. The present model is verified against analytical and numerical solutions for a wide variety of cross-sections with a maximum difference on the order of 9%.

Analysis of shear lag in cylindrical tubes of arbitrary cross section

1983 ◽  
Vol 389 (1797) ◽  
pp. 259-277
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Bending Moment ◽  
General Purpose ◽  
Simple Eigenvalue ◽  
Arbitrary Cross Section ◽  
Longitudinal Distribution ◽  
Shear Lag ◽  
Cylindrical Tubes ◽  
Polynomial Distribution

A very general analysis is given of the phenomenon of shear lag in thin-walled cylindrical tubes, with single-cell cross sections of arbitrary shape, containing any number of concentrated longitudinal booms that carry direct stress only, and subjected to any longitudinal distribution of bending moment and torque. Two equations relating the distributions of direct and shearing stresses on the cross section are derived for the most general case where the tube is non-uniform because of an arbitrary longitudinal variation of wall thicknesses and boom areas. These equa­tions, which are remarkably simple in view of their generality, incor­porate all the requirements of equilibrium and compatibility and provide corrections to the stresses, curvature and twist calculated from the engineers’ theory of bending and torsion. They also govern the distri­bution of stresses arising from the application of self-equilibrating systems of tractions to the end cross sections. Exact solutions are ob­tained for the case of a uniform, but otherwise arbitrary, cross section under any polynomial distribution of bending moment and torque, and it is shown how conditions at the end cross sections can be satisfied with the aid of solutions of a simple eigenvalue problem. The equations are in a particularly ideal form for incorporating into a general purpose com­puter program for the automatic numerical solution of any problem of this type.

Pressure Distributions in Porous Ducts of Arbitrary Cross Section

1973 ◽  
Vol 95 (3) ◽  
pp. 342-348 ◽  
Author(s):  
J. C. P. Huang ◽  
H. S. Yu
Keyword(s):  
Pressure Gradient ◽  
Cross Section ◽  
Cross Sections ◽  
Porous Plate ◽  
Porous Wall ◽  
Design Criterion ◽  
Arbitrary Cross Section ◽  
Solid Particles ◽  
Equivalent Diameter ◽  
Pressure Distributions

A general analytical method has been developed to approximate the pressure distribution along a porous duct of an arbitrary cross section with uniform fluid extraction or addition through the wall. Application of this method is made to a variety of cross sections including circular tubes, parallel plate channels, elliptical ducts, rectangular ducts, annular ducts, and isosceles triangular ducts. Comparisons have been made with results from existing literature on cases of the circular porous tube and the parallel porous plate channel in which exact solutions are available. A numerical solution for the case of a parallel channel consisting of an impermeable wall on one side and a porous wall on the other side is also presented. One important filter duct design criterion has been found for each of the above cases. At a critical wall Reynolds number, defined by flow velocity normal to the wall and the equivalent diameter of the duct, the pressure gradient along the filter duct approaches zero. The zero pressure gradient in a filter duct ensures uniform filtration of solid particles.

Vibration of Stress-Free Hollow Cylinders of Arbitrary Cross Section

1995 ◽  
Vol 62 (3) ◽  
pp. 718-724 ◽  
Author(s):  
K. M. Liew ◽  
K. C. Hung ◽  
M. K. Lim
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Three Dimensional ◽  
Arbitrary Cross Section ◽  
Mode Shapes ◽  
Width Ratio ◽  
Cross Sectional ◽  
Hollow Cylinders ◽  
Displacement Based ◽  
Bending Modes

A three-dimensional elasticity solution to the vibrations of stress-free hollow cylinders of arbitrary cross section is presented. The natural frequencies and deformed mode shapes of these cylinders are obtained via a three-dimensional displacement-based energy formulation. The technique is applied specifically to the parametric investigation of hollow cylinders of different cross sections and sizes. It is found that the cross-sectional property of the cylinder has significant effects on the normal mode responses, particularly, on the transverse bending modes. By varying the length-to-width ratio of these elastic cylinders, interesting results demonstrating the dependence of frequencies on the length of the cylinder have been concluded.

Theoretical and experimental study of braid pattern in mandrels with arbitrary cross-sections

2018 ◽  
Vol 52 (29) ◽  
pp. 4009-4022 ◽  
Author(s):  
Jalil Hajrasouliha ◽  
Reza Jafari Nedoushan ◽  
Mohammad Sheikhzadeh ◽  
Wonjin Na ◽  
Woong-Ryeol Yu
Keyword(s):  
Theoretical Model ◽  
Cross Section ◽  
Cross Sections ◽  
Arbitrary Cross Section ◽  
Continuous Change ◽  
Accurate Design ◽  
Key Factor ◽  
Point To Point ◽  
Two Parameters ◽  
Design And Manufacture

Braid angle is a key factor associated with the mechanical properties of braided composites, so accurate prediction of this angle is of vital importance for the design and manufacture of braided preforms. This paper presents a theoretical model for the prediction of braid angle at any point of a mandrel with constant arbitrary cross-section by taking into account the kinematic parameters of circular braiding machine. The proposed theoretical model pays particular attention to two parameters that strongly affect the braid angle, namely the position of fell point on the mandrel’s surface and the yarn length between this point and the carrier. Both of these parameters undergo continuous change during braiding and thus should be calculated on a point-to-point basis. The model was validated by a series of braiding experiments conducted, using a circular braiding machine, on mandrels with circular, elliptical, and oval cross-sections and then determining the resulting braid angles over the mandrel’s surface by an image processing method. The experimental results showed the high accuracy of the proposed theoretical model in predicting the braid angle for mandrels with constant arbitrary cross-section. Thus, the proposed model can contribute to faster and more accurate design and manufacture of braided composite preforms.

Analytical and Experimental Characterization of Flow in Slowly-Varying Cross-Section Microchannels

2010 ◽  
Author(s):  
M. Akbari ◽  
M. Bahrami ◽  
D. Sinton
Keyword(s):  
Pressure Drop ◽  
Cross Section ◽  
Cross Sections ◽  
Rectangular Cross Section ◽  
Arbitrary Cross Section ◽  
Geometrical Parameters ◽  
Elliptical Cross ◽  
Proposed Model ◽  
Hyperbolic Contraction ◽  
Asymmetric Microchannel

This paper outlines a novel approximate solution for determining the pressure drop of laminar, single-phase flow in slowly-varying microchannels of arbitrary cross-section. The proposed analysis is general and applicable to symmetric and asymmetric microchannel cross-sections, as examples compact relationships are reported for elliptical and rectangular shapes for three common wall profiles of linear, sinusoidal and hyperbolic. An experimental setup is designed and pressure drop measurements are conducted to validate the proposed model for streamwised periodic microchannels with rectangular cross-section and linear wall with a range of channel geometrical parameters such as aspect ratio and channel slope. The model is also compared against the numerical and experimental data of hyperbolic contraction with rectangular cross-section collected by others. It is observed that although the proposed model is based on the solution of the elliptical cross-section, it can accurately predict the pressure drop in microchannels of rectangular cross-section.

A Discussion on natural strain and geological structure - Strain patterns in the Pyrenean Chain

1976 ◽  
Vol 283 (1312) ◽  
pp. 271-280 ◽  
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Horizontal Displacement ◽  
Geological Structure ◽  
Deformation Analysis ◽  
Brittle Deformation ◽  
Deformation Axis ◽  
Narrow Zone ◽  
The North ◽  
East West

The Pyrenean Chain is a deformed part of the crust, fan-shaped in cross section, in which we can define the main characteristics of the major deformation as follows: (a) East—west folds always have their axial planes nearly vertical; the B axes of these folds have gentle plunges; (b) in the domain where schistosity is present (dominent flattening), the direction of maximum apparent elongation on cleavage planes, i.e. the X deformation axis, is nearly parallel to the geometric A axis of the folds. Inside the domain of strong flattening, a very narrow zone is present (less than 2 km wide on some cross sections) bounded by discontinuities, one of the most important is the North Pyrenean fault. This narrow zone is fundamentally different from the rest of the chain: (i) here, the deformation has the highest intensity and the rocks are metamorphosed; (ii) the B axes of the folds are curved and display steep plunges; (iii) the X deformation axis is parallel to the B geometric axis. We imagine that these anomalies have been created by sinistral horizontal displacement on the North Pyrenean fault during the folding. In addition to these facts, a brittle-deformation analysis permits the drawing of deformation trajectories in the flat northern foreland up to 400 km from the chain itself.

Flow in the Hydrodynamic Entrance Region of Ducts of Arbitrary Cross Section

1969 ◽  
Vol 91 (3) ◽  
pp. 345-354 ◽  
Author(s):  
David P. Fleming ◽  
E. M. Sparrow
Keyword(s):  
Experimental Data ◽  
Velocity Field ◽  
Pressure Drop ◽  
Cross Section ◽  
Cross Sections ◽  
Solution Method ◽  
Arbitrary Cross Section ◽  
Entrance Region ◽  
General Method ◽  
Good Agreement

A general method of analysis is presented for determining the developing velocity field and pressure drop for laminar flow in the entrance region of ducts having arbitrary cross sections. Application of the solution method is made to rectangular ducts and to triangular ducts. Available experimental data are compared with the analytical results and good agreement is found to prevail. Development characteristics for six ducts are brought together and compared, and various trends are identified.

Material tailoring in functionally graded rods under torsion

2014 ◽  
Vol 228 (18) ◽  
pp. 3283-3295 ◽  
Author(s):  
F Liaghat ◽  
MR Hematiyan ◽  
A Khosravifard
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Torsional Rigidity ◽  
Optimization Methods ◽  
Arbitrary Cross Section ◽  
Functionally Graded ◽  
Material Tailoring ◽  
Graded Material ◽  
The Cross ◽  
Torsional Analysis

Material tailoring in functionally graded isotropic hollow rods of arbitrary cross section under torsion is studied. The purposes of material tailoring pursued in this paper are divided into two categories. In the first category, we find the variation of the volume fractions of constituents of a functionally graded member under torsion to obtain an appropriate distribution of shear stress over the cross section. In the second category, the torsional rigidity of a rod with a pre-defined mass is maximized by appropriate determination of the variation of constituents of the functionally graded material. Hollow rods are studied in this paper since they have higher torsional rigidity compared to solid members with the same mass. Meshless numerical methods are used for torsional analysis of the cross sections. Moreover, numerical optimization methods are used for material tailoring of the rods. Several examples with different cross sections are presented to investigate the usefulness of the proposed technique on achieving the mentioned purposes.

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