An analytical solution to the problem of seepage into counterfort drains

1984 ◽  
Vol 21 (4) ◽  
pp. 657-662 ◽  
Author(s):  
Edward Nicholas Bromhead
Keyword(s):  
Finite Element ◽  
Numerical Methods ◽  
Analytical Solution ◽  
Finite Element Methods ◽  
Theoretical Approach ◽  
Small Study ◽  
Full Thickness ◽  
Slope Stabilization ◽  
Design Chart ◽  
And Performance

Recently, J. N. Hutchinson has collected data on the design and performance of trench and counterfort drains. This article presents an analytical solution to one of these cases, that of seepage into counterfort drains which penetrate the full thickness of a layer of soil, down to the impermeable base on which it rests. The soil is assumed to have uniform permeability.The findings of a small study, by Hutchinson, of seepage patterns to such drains, made with the use of finite element methods, are found to be validated by the theoretical approach in this article. This solution also provides a convenient benchmark against which approximate numerical methods can be assessed.Finally, a design chart based on the theory is presented, with examples of its application to the design of counterfort drain installations for slope stabilization.

Equilibrium Profile of Modern Belted Radial Ply Tires: Its Determination and Performance Benefits

2013 ◽  
Vol 41 (2) ◽  
pp. 127-151
Author(s):  
Rudolf F. Bauer
Keyword(s):  
Finite Element ◽  
Aspect Ratio ◽  
Finite Element Methods ◽  
Mathematical Analysis ◽  
Internal Stresses ◽  
Stress Concentrations ◽  
Equilibrium Profiles ◽  
Equilibrium Profile ◽  
And Performance ◽  
Beneficial Property

ABSTRACT The benefits of a tire's equilibrium profile have been suggested by several authors in the published literature, and mathematical procedures were developed that represented well the behavior of bias ply tires. However, for modern belted radial ply tires, and particularly those with a lower aspect ratio, the tire constructions are much more complicated and pose new problems for a mathematical analysis. Solutions to these problems are presented in this paper, and for a modern radial touring tire the equilibrium profile was calculated together with the mold profile to produce such tires. Some construction modifications were then applied to these tires to render their profiles “nonequilibrium.” Finite element methods were used to analyze for stress concentrations and deformations within all tires that did or did not conform to equilibrium profiles. Finally, tires were built and tested to verify the predictions of these analyses. From the analysis of internal stresses and deformations on inflation and loading and from the actual tire tests, the superior durability of tires with an equilibrium profile was established, and hence it is concluded that an equilibrium profile is a beneficial property of modern belted radial ply tires.

An Integral Equation Method for Predicting Acoustic Emission within Enclosures

1985 ◽  
Vol 199 (2) ◽  
pp. 133-137 ◽  
Author(s):  
D T I Francis ◽  
M M Sadek
Keyword(s):  
Integral Equation ◽  
Finite Element ◽  
Acoustic Emission ◽  
Analytical Solution ◽  
Numerical Solution ◽  
Finite Element Methods ◽  
Exact Analytical Solution ◽  
Integral Equation Method ◽  
Absorption Characteristics ◽  
Good Agreement

A method is presented for calculating the acoustic emission of a vibrating body within an enclosure whose surface has known absorption characteristics. It is based on a numerical solution of the Helmholtz integral equation. Solutions are given for the case of a pulsating sphere within a sphere, and good agreement with the exact analytical solution is reported. The method is of value for small and medium scale problems at lower frequencies, where traditional techniques are less reliable. It is also potentially less demanding computationally than finite element methods.

Study on T-Section Aluminium Beam-Columns with Web in Compression

2011 ◽  
Vol 250-253 ◽  
pp. 1786-1789
Author(s):  
Zheng Zhang ◽  
Gui Yun Yan
Keyword(s):  
Finite Element ◽  
Numerical Methods ◽  
Finite Element Methods ◽  
Geometrical Nonlinearity ◽  
Initial Imperfection ◽  
Material Nonlinearity ◽  
Parameter Analysis ◽  
Beam Columns ◽  
Analysis Methods ◽  
The Web

Parameter analysis based on finite element methods was executed to study the in-plane stability capacity of extruded T-section aluminium beam-columns with the tip of the web in bigger compression. The analysis methods considered the effects of material nonlinearity, geometrical nonlinearity, and initial imperfection. The comparisons of calculate results of three kinds of T-sections of weak hardening alloy and strong hardening alloy between GB 50429, proposed formula and numerical methods were executed. And the analytical results show that GB 50429 is safe and suitable, and the modification formula based on GB 50429 is also safe enough and more exact than the former.

scholarly journals TORSIONAL SHEAR STRESS IN PRISMATIC BEAMS WITH ARBITRARY CROSS-SECTIONS USING FINITE ELEMENT METHOD

2021 ◽  
Vol 30 (2) ◽  
Author(s):  
Dang-Bao Tran
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Shear Stress ◽  
Numerical Methods ◽  
Analytical Solution ◽  
Numerical Method ◽  
Cross Sections ◽  
Structural Element ◽  
Quadrilateral Elements ◽  
Torsional Shear

Determining the shear stress of a structural element caused by torsion is a vital problem. The analytical solution of the Saint-Venant torsion is only suitable for simple cross-sections. The numerical method to evaluate the shear stress of complicated cross-sections is indispensable. Many numerical methods have been studied by scientists. Among these studies, Gruttmann proposed an excellent numerical method, which inherited the Saint-Venant theory. However, the use of isoparametric four-noded quadrilateral elements made the method not to reach the best optimization. The objective of this paper is to improve Gruttmann‘s method by using isoparametric eight-noded quadrilateral elements. MATLAB is the language for programming the numerical method. The validated examples have demonstrated that the author’s numerical method is more effective than Gruttmann‘s method.

Application of Finite Element Methods to Lubrication: Squeeze Films Between Porous Surfaces

1976 ◽  
Vol 98 (1) ◽  
pp. 175-179 ◽  
Author(s):  
B. E. Eidelberg ◽  
J. F. Booker
Keyword(s):  
Finite Element ◽  
Analytical Solution ◽  
Finite Element Methods ◽  
Fluid Film ◽  
Anisotropic Permeability ◽  
Porous Region ◽  
Porous Surfaces ◽  
Irregular Geometry

Finite element methods are applied to the analysis of squeeze films between porous surfaces. Planar elements in the fluid film region are joined with solid elements in the porous region to ensure continuity of pressures and flows. The formulation is valid for problems with irregular geometry and nonhomogeneous anisotropic permeability. A simple example with uniform properties demonstrates convergence to a previous analytical solution. More complex examples illustrate the power and versatility of the method.

scholarly journals Numerical behavior of singular two-point boundary value problems in a comparative way

2017 ◽  
Vol 7 (3) ◽  
pp. 288-292
Author(s):  
Selmahan Selim ◽  
Gözde Elver ◽  
Murat Sari
Keyword(s):  
Finite Element ◽  
Numerical Methods ◽  
Boundary Value Problems ◽  
Finite Element Methods ◽  
Model Equation ◽  
Boundary Value ◽  
Point Boundary ◽  
Numerical Techniques ◽  
Physical Processes ◽  
Advantages And Disadvantages

This article concentrates on discovering numerical behavior of the singular two-point boundary value problems through various numerical techniques. This is carried out in a comparative way by mainly using differential quadrature and finite element methods. Also a discussion has been done by means of advantages and disadvantages of the numerical methods of interest.To properly understand the behavior of the physical processes represented by the model equation, the calculated solutions have been discussed in detail. 

scholarly journals The accuracy of numerical methods for the analysis of electrostatic fields

2021 ◽  
Vol 7 (1) ◽  
pp. 59-70
Author(s):  
Vladimir N. Taran ◽  
Maxim V. Shevlyugin ◽  
Aleksey V. Shandybin
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Methods ◽  
Analytical Solution ◽  
Electromagnetic Fields ◽  
The Finite Element Method ◽  
Electrostatic Fields ◽  
Improve Accuracy ◽  
Real Objects ◽  
Element Method

Aim: Estimation of the accuracy of the numerical method relative to the analytical solution. Methods: This article reports on studies of the accuracy of numerical calculations based on the finite element method. The variational scheme of the method is considered. Results: The dependences of errors on the number of simplexes used are obtained and analyzed. The authors noted ways to further improve accuracy. Conclusion: The article gives recommendations on the possible application of the finite element method in solving problems of calculating the electromagnetic fields of real objects.

scholarly journals NUMERICAL SIMULATION OF LAMB WAVE PROPOGATION IN ISOTROPIC LAYER

2019 ◽  
Vol 15 (2) ◽  
pp. 14-23
Author(s):  
Anna Avershyeva ◽  
Sergey Kuznetsov
Keyword(s):  
Numerical Simulation ◽  
Finite Element ◽  
Numerical Methods ◽  
Analytical Solution ◽  
Finite Element Modeling ◽  
Lamb Wave ◽  
Lamb Waves ◽  
Solution Stability ◽  
Isotropic Layer ◽  
Simulation Parameters

Propagation of Lamb waves in an elastic isotropic layer is studied by analytical and numerical methods. The influence of numerical simulation parameters on the solution stability is analyzed. The results of the finite element modeling and the analytical solution are compared.

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