Numerical Analysis of Double Contacts of Similar Elastic Materials

2008 ◽  
Vol 75 (6) ◽  
Author(s):  
N. Sundaram ◽  
T. N. Farris
Keyword(s):  
Singular Integral Equations ◽  
Partial Slip ◽  
Load History ◽  
The Finite Element Method ◽  
Compatibility Equation ◽  
Wide Range ◽  
Cauchy Singular Integral ◽  
Isotropic Bodies ◽  
Similar Equation ◽  
Good Agreement

A fast numerical method based on the Cauchy singular integral equations is presented to determine the contact pressure and extents for the contact of two-dimensional similar isotropic bodies when the contact area consists of two separate regions. The partial-slip problem is then solved to determine shear tractions using an equivalence principle. The extents of the contact are not all independent but related to a compatibility equation constraining the displacements of an elastic body in contact with an equivalent rigid body. A similar equation is found for the extents of the stick zones in partial-slip problems. The effects of load history are incorporated into the shear solution. The method is applicable to a wide range of profiles and it provides significant gains in computational efficiency over the finite element method (FEM) for both the pressure and partial-slip problems. The numerical results obtained are compared with that from the FEM for a biquadratic indenter with a single concavity and showed good agreement. Lastly, the transition behavior from double to single contacts in biquadratic profiles is investigated.

Load History Effects on Fretting Contacts of Isotropic Materials

2004 ◽  
Vol 126 (2) ◽  
pp. 385-390 ◽  
Author(s):  
P. T. Rajeev ◽  
H. Murthy ◽  
T. N. Farris
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Singular Integral Equations ◽  
Contact Problems ◽  
Two Dimensional ◽  
Load History ◽  
Jet Engine ◽  
Isotropic Materials ◽  
History Effects ◽  
Cauchy Singular Integral

The load history that blade/disk contacts in jet engine attachment hardware are subject to can be very complex. Using finite element method (FEM) to track changes in the contact tractions due to changing loads can be computationally very expensive. For two-dimensional plane-strain contact problems with friction involving similar/dissimilar isotropic materials, the contact tractions can be related to the initial gap function and the slip function using coupled Cauchy singular integral equations (SIEs). The effect of load history on the contact tractions is illustrated by presenting results for an example fretting “mission.” For the case of dissimilar isotropic materials the mission results show the effect of the coupling between the shear traction and the contact pressure.

FE Design Tool for Laminated Composite Plates

2012 ◽  
Vol 248 ◽  
pp. 379-383
Author(s):  
Rasoul Khandan ◽  
Philip Sewell ◽  
Siamak Noroozi ◽  
Mohammad Reza Ramazani
Keyword(s):  
Composite Materials ◽  
Transverse Shear ◽  
Laminated Composite ◽  
Composite Plates ◽  
Design Tool ◽  
Computational Technique ◽  
The Finite Element Method ◽  
Laminated Composite Plates ◽  
Wide Range ◽  
Good Agreement

Considering the non-linearity, complexity and anisotropy of constitutive equations in composite materials, numerical methods are essential to evaluate the behaviour of this material. The finite element method (FEM) is a powerful computational technique for the solution of differential and integral equations that arise in various fields of engineering and applied science such as composite materials. Here, an FEM tool is designed to analyse non-linearity in the behaviour of composites caused by the effect of transverse shear and twist in laminated composite plates. The tool is established by using FEM for composites in ABAQUS combined with programming in Python to run the tests for all possible fibre orientations in laminated composite plates. It is shown that the tool has the ability to design laminated composite plates by considering the effect of transverse shear and the tool’s output provides results for all different fibre orientations. It is demonstrated that there is good agreement between numerical results obtained from this tool and experimental results. The advantages of the tool give designers the opportunity to use this tool for wide range of products.

Load History Effects on Fretting Contacts of Isotropic Materials

2002 ◽  
Author(s):  
P. T. Rajeev ◽  
H. Murthy ◽  
T. N. Farris
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Singular Integral ◽  
Singular Integral Equations ◽  
Contact Problems ◽  
Load History ◽  
Jet Engine ◽  
Isotropic Materials ◽  
History Effects ◽  
Cauchy Singular Integral

The load history that blade/disk contacts in jet engine attachment hardware are subject to can be very complex. Using Finite Element Method (FEM) to track changes in the contact tractions due to changing loads can be computationally very expensive. For 2D plane strain contact problems with friction involving similar/dissimilar isotropic materials, the contact tractions can be related to the initial gap function and the slip function using coupled Cauchy Singular Integral Equations (SIEs). The effect of load history on the contact tractions is illustrated by presenting results for an example fretting “mission”. For the case of dissimilar isotropic materials the misson results show the effect of the coupling between the shear traction and the contact pressure.

Numerical analysis of fretting contacts of dissimilar isotropic and anisotropic materials

2002 ◽  
Vol 37 (6) ◽  
pp. 503-517 ◽  
Author(s):  
P. T Rajeev ◽  
T. N Farris
Keyword(s):  
Singular Integral Equations ◽  
Contact Problems ◽  
Anisotropic Materials ◽  
Partial Slip ◽  
Load History ◽  
Plane Shear ◽  
Shear Traction ◽  
Singular Functions ◽  
Out Of Plane ◽  
Anisotropic Bodies

A numerical method is presented to obtain the contact tractions when two dissimilar isotropic or anisotropic bodies are in partial slip contact. The solution to the governing coupled singular integral equations (SIEs) is obtained by incorporating the appropriate singular behaviour for the contact pressure and the shear traction. The edges of the contact zone and the stick zone are determined by iteration such that the constant multipliers of the singular functions vanish. For anisotropic materials the out-of-plane shear traction is assumed to be very small and hence neglected. The solution method has been successfully verified by comparing its results to solutions available in the literature and to the results obtained by the finite element method (FEM). By modifying the slip function to take into account the remote stress on the half-space, the SIE method can be used to analyse fretting contact problems. The resulting technique efficiently accounts for the effect of load history on the contact tractions and the contact and stick zone sizes. The pronounced effect that load history has on the stick zone size is illustrated.

Analysis of the Contact Deformation of Tread Blocks

1992 ◽  
Vol 20 (4) ◽  
pp. 230-253 ◽  
Author(s):  
T. Akasaka ◽  
K. Kabe ◽  
M. Koishi ◽  
M. Kuwashima
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Deformation Behavior ◽  
Contact Deformation ◽  
The Finite Element Method ◽  
The Road ◽  
Loss Of Contact ◽  
Tread Rubber ◽  
Good Agreement ◽  
Rubber Block

Abstract The deformation behavior of a tire in contact with the roadway is complicated, in particular, under the traction and braking conditions. A tread rubber block in contact with the road undergoes compression and shearing forces. These forces may cause the loss of contact at the edges of the block. Theoretical analysis based on the energy method is presented on the contact deformation of a tread rubber block subjected to compressive and shearing forces. Experimental work and numerical calculation by means of the finite element method are conducted to verify the predicted results. Good agreement is obtained among these analytical, numerical, and experimental results.

scholarly journals Separate Universe calibration of the dependence of halo bias on cosmic web anisotropy

2020 ◽  
Vol 499 (3) ◽  
pp. 4418-4431 ◽  
Author(s):  
Sujatha Ramakrishnan ◽  
Aseem Paranjape
Keyword(s):  
Dark Matter ◽  
High Precision ◽  
Gaussian Distribution ◽  
Initial Perturbation ◽  
Analytical Framework ◽  
Web Environment ◽  
Wide Range ◽  
Galaxy Assembly ◽  
Very High ◽  
Good Agreement

ABSTRACT We use the Separate Universe technique to calibrate the dependence of linear and quadratic halo bias b1 and b2 on the local cosmic web environment of dark matter haloes. We do this by measuring the response of halo abundances at fixed mass and cosmic web tidal anisotropy α to an infinite wavelength initial perturbation. We augment our measurements with an analytical framework developed in earlier work that exploits the near-lognormal shape of the distribution of α and results in very high precision calibrations. We present convenient fitting functions for the dependence of b1 and b2 on α over a wide range of halo mass for redshifts 0 ≤ z ≤ 1. Our calibration of b2(α) is the first demonstration to date of the dependence of non-linear bias on the local web environment. Motivated by previous results that showed that α is the primary indicator of halo assembly bias for a number of halo properties beyond halo mass, we then extend our analytical framework to accommodate the dependence of b1 and b2 on any such secondary property that has, or can be monotonically transformed to have, a Gaussian distribution. We demonstrate this technique for the specific case of halo concentration, finding good agreement with previous results. Our calibrations will be useful for a variety of halo model analyses focusing on galaxy assembly bias, as well as analytical forecasts of the potential for using α as a segregating variable in multitracer analyses.

scholarly journals Study of Influence of Width to Thickness Ratio in Sheet Metals on Bendability under Ambient and Superimposed Hydrostatic Pressure

2021 ◽  
Vol 2 (3) ◽  
pp. 542-558
Author(s):  
Mohammadmehdi Shahzamanian ◽  
David Lloyd ◽  
Amir Partovi ◽  
Peidong Wu
Keyword(s):  
Hydrostatic Pressure ◽  
Stress Ratio ◽  
Fracture Strain ◽  
Stress Triaxiality ◽  
Volumetric Strain ◽  
Thickness Ratio ◽  
Sheet Metals ◽  
The Finite Element Method ◽  
Bending Strain ◽  
Good Agreement

The effect of the width to thickness ratio on the bendability of sheet metal is investigated using the finite element method (FEM) employing the Gurson–Tvergaard–Needleman (GTN) model. Strain path changes in the sheet with change in the width/thickness ratio. It is shown that bendability and fracture strain increase significantly by decrease in the width/thickness ratio. The stress state is almost uniaxial when the stress ratio (α) is close to zero for narrow sheets. Stress ratio is nothing but the major stress to minor stress ratio. This delays the growth and coalescence of micro-voids as the volumetric strain and stress triaxiality (pressure/effective stress) decrease. On the other hand, ductility decreases with increase in α for wider sheets. Fracture bending strain is calculated and, as expected, it increases with decrease in the width/thickness ratio. Furthermore, a brief study is performed to understand the effect of superimposed hydrostatic pressure on fracture strain for various sheet metals with different width/thickness ratios. It is found that the superimposed hydrostatic pressure increases the ductility, and that the effect of the width/thickness ratio in metals on ductility is as significant as the effect of superimposed hydrostatic pressure. Numerical results are found to be in good agreement with experimental observations.

Evaluation of Trinder's Glucose Oxidase Method for Measuring Glucose in Serum and Urine

1975 ◽  
Vol 21 (12) ◽  
pp. 1754-1760 ◽  
Author(s):  
John A Lott ◽  
Kathie Turner
Keyword(s):  
Glucose Oxidase ◽  
Oxidase Activity ◽  
Color Reaction ◽  
Critical Variable ◽  
Wide Range ◽  
Serum And Urine ◽  
Good Agreement

Abstract Trinder's method for glucose has nearly all the attributes of an ideal automated colorimetric glucose oxidase procedure. The chemicals used in the color reaction with peroxidase are readily available, the solutions are stable and can be prepared by the user, the method is highly specific and largely free of interferences, the sensitivity can be adjusted by the user to cover a wide range of glucose concentrations, and the reagents are not hazardous. We found very good agreement between results by this method and by the hexokinase and Beckman Glucose Analyzer methods. The method has been modified and adapted to the AutoAnalyzer I and SMA 6/60 (Technicon) with manifolds that give very little interaction between specimens. A study of the method by the simplex technique revealed that the glucose oxidase activity in the reagent is the most critical variable.

Estimation of the Thermodynamic Properties of Branched Hydrocarbons

2000 ◽  
Vol 122 (3) ◽  
pp. 147-152 ◽  
Author(s):  
Hui He ◽  
Mohamad Metghalchi ◽  
James C. Keck
Keyword(s):  
Thermodynamic Properties ◽  
Degrees Of Freedom ◽  
Statistical Thermodynamic ◽  
Motion Modes ◽  
Branched Alkanes ◽  
Branched Hydrocarbons ◽  
Wide Range ◽  
On Line ◽  
Kinetic Calculations ◽  
Good Agreement

A simple model has been developed to estimate the sensible thermodynamic properties such as Gibbs free energy, enthalpy, heat capacity, and entropy of hydrocarbons over a wide range of temperatures with special attention to the branched molecules. The model is based on statistical thermodynamic expressions incorporating translational, rotational and vibrational motions of the atoms. A method to determine the number of degrees of freedom for different motion modes (bending and torsion) has been established. Branched rotational groups, such as CH3 and OH, have been considered. A modification of the characteristic temperatures for different motion mode has been made which improves the agreement with the exact values for simple cases. The properties of branched alkanes up to 2,3,4,-trimthylpentane have been calculated and the results are in good agreement with the experimental data. A relatively small number of parameters are needed in this model to estimate the sensible thermodynamic properties of a wide range of species. The model may also be used to estimate the properties of molecules and their isomers, which have not been measured, and is simple enough to be easily programmed as a subroutine for on-line kinetic calculations. [S0195-0738(00)00902-X]

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