Formulation of a three dimensional analytical solution to evaluate stresses in backfilled vertical narrow openings

2005 ◽  
Vol 42 (6) ◽  
pp. 1705-1717 ◽  
Author(s):  
Li Li ◽  
Michel Aubertin ◽  
Tikou Belem
Keyword(s):  
Numerical Modeling ◽  
Analytical Solution ◽  
Analytical Solutions ◽  
Mechanical Response ◽  
Three Dimensional ◽  
Earth Pressure ◽  
The State ◽  
Experimental Results ◽  
State Of Stress ◽  
Earth Pressures

The mechanical response of backfill in narrow openings is significantly influenced by its interaction with the surrounding walls. Previous work conducted on backfilled trenches and mining stopes indicates that the theory of arching can be used to estimate earth pressures in narrow, vertical backfilled openings. In this paper, a 3D analytical solution is proposed to evaluate the state of stress along the boundaries of the openings. The proposed solution, based on a generalized version of the Marston approach, is compared with numerical modeling and laboratory experimental results taken from the literature. A discussion follows on some particular features and limitations of the analytical solutions.Key words: backfill, earth pressure, 3D openings, analytical solutions, trenches, mining stopes.

Application of the Conservation Element and Solution Element Method in Numerical Modeling of Three-Dimensional Heat Conduction With Melting and/or Freezing

2004 ◽  
Vol 126 (6) ◽  
pp. 937-945 ◽  
Author(s):  
Anahita Ayasoufi ◽  
Theo G. Keith ◽  
Ramin K. Rahmani
Keyword(s):  
Numerical Modeling ◽  
Heat Conduction ◽  
Fluid Mechanics ◽  
Phase Change ◽  
Numerical Method ◽  
Analytical Solutions ◽  
Three Dimensional ◽  
Solution Element ◽  
Explicit Numerical Method ◽  
Element Method

The conservation element and solution element (CE/SE) method, an accurate and efficient explicit numerical method for resolving moving discontinuities in fluid mechanics problems, is used to solve three-dimensional phase-change problems. Several isothermal phase-change cases are studied and comparisons are made to existing analytical solutions. The CE/SE method is found to be accurate, robust, and efficient for the numerical modeling of phase-change problems.

Guidelines for Design of Dividing Manifolds With Discharge Uniformly Distributed at Different Positions Along the Device Axis

2019 ◽  
Vol 142 (2) ◽  
Author(s):  
Honggang Yang ◽  
Yi Wang ◽  
Xiaojing Meng ◽  
Dong Li ◽  
Xiaofan Cai
Keyword(s):  
Experimental Data ◽  
Analytical Solution ◽  
Governing Equation ◽  
Analytical Solutions ◽  
Dimensionless Parameter ◽  
Operating Conditions ◽  
Experimental Results ◽  
Practical Operation ◽  
Discharge Distribution

Abstract For practical operation of dividing manifolds, the discharge uniformity is a property generally required. To investigate the dependence of discharge uniformity on the manifold geometry and operating conditions, analytical solution to the governing equation, Bajura's equation, was secured. Furthermore, examples were derived by substituting experimental data into the analytical solutions; the resultant curves of discharge distribution indicated essential agreement between the theoretical and experimental results. For evaluating the property of discharge distribution, a uniformity index, U, was introduced. The calculated results of U showed a well-defined dependence of uniformity on the dimensionless parameter, γ, and a maximum of U presented around 1.44 of γ.

Application of the Conservation Element and Solution Element Method in Numerical Modeling of Three-Dimensional Heat Conduction With Melting and/or Freezing

2003 ◽  
Author(s):  
Anahita Ayasoufi ◽  
Theo G. Keith
Keyword(s):  
Numerical Modeling ◽  
Heat Conduction ◽  
Fluid Mechanics ◽  
Phase Change ◽  
Numerical Method ◽  
Analytical Solutions ◽  
Three Dimensional ◽  
Solution Element ◽  
Explicit Numerical Method ◽  
Element Method

The conservation element and solution element (CE/SE) method, an accurate and efficient explicit numerical method for resolving moving discontinuities in fluid mechanics problems, is used to solve three-dimensional phase change problems. Several isothermal phase change cases are studied and comparisons are made to existing analytical solutions. The CE/SE method is found to be accurate, robust and efficient for the numerical modeling of phase change problems.

scholarly journals Solutions without Space-Time Separation for ADS Experiments: Overview on Developments and Applications

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
B. Merk ◽  
V. Glivici-Cotruţă
Keyword(s):  
Analytical Solution ◽  
Analytical Solutions ◽  
Space Time ◽  
Experimental Results ◽  
Time Dependent ◽  
Special Configuration ◽  
Time Separation ◽  
Function Solution ◽  
Boundary Source ◽  
Good Agreement

The different analytical solutions without space-time separation foreseen for the analysis of ADS experiments are described. The SC3A experiment in the YALINA-Booster facility is described and investigated. For this investigation the very special configuration of YALINA-Booster is analyzed based on HELIOS calculations. The results for the time dependent diffusion and the time dependentP1equation are compared with the experimental results for the SC3A configuration. A comparison is given for the deviation between the analytical solution and the experimental results versus the different transport approximations. To improve the representation to the special configuration of YALINA- Booster, a new analytical solution for two energy groups with two sources (central external and boundary source) has been developed starting form the Green's function solution. Very good agreement has been found for these improved analytical solutions.

scholarly journals Discrete Greenwood–Williamson Modeling of Rough Surface Contact Accounting for Three-Dimensional Sinusoidal Asperities and Asperity Interaction

2019 ◽  
Vol 141 (12) ◽  
Author(s):  
S. Zhang ◽  
H. Song ◽  
S. Sandfeld ◽  
X. Liu ◽  
Y. G. Wei
Keyword(s):  
Analytical Solution ◽  
Rough Surface ◽  
Mechanical Response ◽  
Three Dimensional ◽  
Fem Simulation ◽  
Contact Problems ◽  
Discrete Version ◽  
Successful Model ◽  
Surface Contact ◽  
Rough Surface Contact

Abstract The Greenwood–Williamson (GW) model has been one of the commonly used contact models to study rough surface contact problems during the past decades. While this has been a successful model, it still has a number of restrictions: (i) surface asperities are spheres; (ii) the overall deformation must be assumed to be small enough, such that there is no interaction between asperities, i.e., they are independent of each other; and (iii) asperity deformation remains elastic. This renders the GW model unrealistic in many situations. In the present work, we resolve above restrictions in a discrete version of the GW model: instead of spherical asperities, we assumed that the surface consists of three-dimensional sinusoidal asperities which appear more similar to asperities on a rough surface. For single asperity mechanical response, we propose a Hertz-like analytical solution for purely elastic deformation and a semi-analytical solution based on finite element method (FEM) for elastic–plastic deformation. The asperity interaction is accounted for by discretely utilizing a modified Boussinesq solution without consideration of asperity merger. It is seen that the asperity interaction effect is more than just the delay of contact as shown in the statistical model, it also contributes to the loss of linearity between the contact force and the contact area. Our model also shows that: for elastic contact, using spherical asperities results in a larger average contact pressure than using sinusoids; when plasticity is taken into account, using a sphere to represent asperities results in a softer response as compared with using sinusoids. It is also confirmed that sinusoidal asperities are a much better description than spheres, by comparison with fully resolved FEM simulation results for computer-generated rough surfaces.

Some Applications of CDL-BIEM

1994 ◽  
Author(s):  
Nhan Phan-Thien ◽  
Sangtae Kim
Keyword(s):  
Analytical Solution ◽  
Numerical Method ◽  
Analytical Solutions ◽  
Spherical Inclusion ◽  
Three Dimensional ◽  
Simple Problem ◽  
Benchmark Problem ◽  
Bounding Surface ◽  
Rigid Displacement ◽  
Particulate Solids

This chapter presents some selected three-dimensional applications of the CDL-BIEM in elasticity and Stokes flows, especially to particulate solids for which the method is devised. It is paramount that any numerical method should be validated against known analytical solutions. The method will therefore be benchmarked against known simple solutions of the type reported in chapters 2 and 5. Some selected nontrivial examples, where no analytical solutions are available, will also be presented. The translating sphere is a simple problem with known analytical solution and smooth bounding surface; it is a popular benchmark problem for boundary element codes. Here a rigid spherical inclusion of radius a, centered at x = 0, is displaced by either (1) a constant vector U or (2) acted on by a force F, and we seek the force in the case of problem (1), or the rigid displacement in problem (2).

scholarly journals New Analytical Solutions for Longitudinal Vibration of a Floating Pile in Layered Soils with Radial Heterogeneity

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1294 ◽  
Author(s):  
Zhimeng Liang ◽  
Chunyi Cui ◽  
Kun Meng ◽  
Yu Xin ◽  
Huafu Pei ◽  
...  
Keyword(s):  
Analytical Solution ◽  
Analytical Solutions ◽  
Longitudinal Vibration ◽  
Three Dimensional ◽  
Complex Impedance ◽  
Vibration Characteristics ◽  
Layered Soils ◽  
Transform Method ◽  
Floating Pile ◽  
The Time Domain

Based on the theory of wave propagation in three-dimensional (3D) continuum, a new analytical approach for the longitudinal vibration characteristics of a floating pile in layered soils with radial heterogeneity is developed by employing a viscous-type damping model. Firstly, an analytical solution for the longitudinal complex impedance at the pile head is deduced by employing the Laplace transform and complex stiffness technique with the compatibility conditions of the pile and radially inhomogeneous surrounding soil. Secondly, a semi-analytical solution in the time domain is further acquired by using the inverse Fourier transform method. Furthermore, the corresponding analytical solutions are validated through contrasts with previous solutions. Finally, parametric analyses are underway to investigate the effect of radial heterogeneity of surrounding soils on longitudinal vibration characteristics of floating piles. It is indicated that the proposed approach and corresponding solutions can provide a more wide-ranging application than the simple harmonic vibration for longitudinal vibration analysis of a floating pile in soils.

Simulation of Tensile Behavior in Friction Stir Welded and Superplastically Formed Titanium 6 Al-4V Alloy

2007 ◽  
Author(s):  
Paul D. Edwards ◽  
Daniel G. Sanders ◽  
M. Ramulu
Keyword(s):  
Experimental Study ◽  
Numerical Modeling ◽  
Mechanical Response ◽  
Numerical Models ◽  
Tensile Behavior ◽  
Experimental Results ◽  
Friction Stir ◽  
Modeling Approach ◽  
Simulation Results ◽  
Behavior Characteristics

A hybrid numerical and experimental study was undertaken to evaluate the performance of as Friction Stir Welded (FSW) and Superplastically Formed Friction Stir Welded (SPF-FSW) Titanium joints. This paper presents the numerical models which were developed to simulate mechanical response of as FSW and SPF-FSW joints. The simulation results were then compared to experimentally determined behavior characteristics of the joints to assess the validity of the modeling approach. It was found that the numerical modeling approach presented here have simulated successfully the tensile behavior of a FSW joint agreeing with the experimental results. This method also adequately simulated the tensile behavior of a SPF-FSW joint, but due to geometrical influences, there are discrepancies between the numerical results and experimental observations.

Sign in / Sign up

Export Citation Format

Share Document