Finite Element Analysis of Rolling Contact Problems Using Minimum Dissipation of Energy Principle

1998 ◽  
Vol 65 (1) ◽  
pp. 271-273 ◽  
Author(s):  
S. K. Rathore ◽  
N. N. Kishore
Keyword(s):  
Finite Element ◽  
Contact Region ◽  
Contact Problems ◽  
Rolling Contact ◽  
Element Analysis ◽  
Energy Principle ◽  
Dissipation Of Energy ◽  
Rolling Surface ◽  
Strain Stress

In steady rolling motion, the loads and the fields of strain, stress, and deformations do not change with time at the contact region, as the contact region is continuously being formed by a new rolling surface. The principle of minimum dissipation of energy and the concept of traveling finite elements are made use of in solving such problems and the determination of micro-slips. The conditions of contact are discovered by use of the kinematic constraints and the Coulomb’s law of friction. A two-dimensional plane-strain finite element method along with the iterative procedure is used. The results obtained are in good agreement with expected behavior.

Finite Element Analysis of Quasi-static Contact Problems Using Minimum Dissipation of the Energy Principle

1994 ◽  
Vol 61 (3) ◽  
pp. 642-648 ◽  
Author(s):  
N. N. Kishore ◽  
A. Ghosh ◽  
S. K. Rathore ◽  
P. V. Kishore
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
A Priori ◽  
Contact Problems ◽  
Computational Time ◽  
Element Analysis ◽  
Element Mesh ◽  
Energy Principle ◽  
Contact Conditions ◽  
Static Contact

There are many practical situations where two bodies are directly in contact and are subjected to dynamic or varying loads. The contact area and the contact conditions are functions of load and load history and are not known a priori at any load thus making the problems nonlinear. The conditions of contact are determined by the kinematic constraints and the Coulomb’s law of friction. Direct solutions do not give unique results if the load steps are large and the finite element mesh is coarse. In the present work a method using the principle of minimum dissipation of energy is proposed and is applied to finite element analysis of a two-dimensional elastic contact problem under quasi-static loading. A combined incremental and iterative procedure is adopted to solve this problem. The results obtained are in good agreement with physical reasoning. The proposed method obtains new results apart from greatly reducing computational time and efforts.

A Finite Element Analysis of the General Rolling Contact Problem for a Viscoelastic Rubber Cylinder

1988 ◽  
Vol 16 (1) ◽  
pp. 18-43 ◽  
Author(s):  
J. T. Oden ◽  
T. L. Lin ◽  
J. M. Bass
Keyword(s):  
Finite Element ◽  
Variational Principles ◽  
Standing Waves ◽  
Rolling Contact ◽  
Finite Element Models ◽  
Viscoelastic Cylinder ◽  
Element Analysis ◽  
Elastic Rubber ◽  
Frictional Effects ◽  
Rough Foundation

Abstract Mathematical models of finite deformation of a rolling viscoelastic cylinder in contact with a rough foundation are developed in preparation for a general model for rolling tires. Variational principles and finite element models are derived. Numerical results are obtained for a variety of cases, including that of a pure elastic rubber cylinder, a viscoelastic cylinder, the development of standing waves, and frictional effects.

Determination of collapse moment of different angled pipe bends with initial geometric imperfection subjected to in-plane bending moments

2021 ◽  
pp. 095440622199640
Author(s):  
Manish Kumar ◽  
Pronab Roy ◽  
Kallol Khan
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Circular Cross Section ◽  
Initial Imperfection ◽  
Bend Angle ◽  
Bending Moments ◽  
Element Analysis ◽  
Geometric Imperfection ◽  
Initial Geometric Imperfection

From the recent literature, it is revealed that pipe bend geometry deviates from the circular cross-section due to pipe bending process for any bend angle, and this deviation in the cross-section is defined as the initial geometric imperfection. This paper focuses on the determination of collapse moment of different angled pipe bends incorporated with initial geometric imperfection subjected to in-plane closing and opening bending moments. The three-dimensional finite element analysis is accounted for geometric as well as material nonlinearities. Python scripting is implemented for modeling the pipe bends with initial geometry imperfection. The twice-elastic-slope method is adopted to determine the collapse moments. From the results, it is observed that initial imperfection has significant impact on the collapse moment of pipe bends. It can be concluded that the effect of initial imperfection decreases with the decrease in bend angle from 150∘ to 45∘. Based on the finite element results, a simple collapse moment equation is proposed to predict the collapse moment for more accurate cross-section of the different angled pipe bends.

Axisymmetric Finite-Element Analysis for Interface Migration-Controlled Shape Instabilities of Plate-Like Double-Crystal Grains

2012 ◽  
Vol 460 ◽  
pp. 230-235
Author(s):  
Pei Zhen Huang ◽  
Zhou Zhou Zhang ◽  
Jian Wei Guo ◽  
Jun Sun
Keyword(s):  
Finite Element ◽  
Grain Boundary ◽  
Chemical Potential ◽  
Boundary Energy ◽  
Element Analysis ◽  
Interface Motion ◽  
Double Crystal ◽  
Energy Principle ◽  
Chemical Potential Difference ◽  
Interface Migration

An axisymmetric finite-element method is developed to predict the evolution behavior of microstructures by interface migration. The formulation of the method is conducted on the basis of the energy principle during the interface motion. The computations extend earlier models by accounting in detail for the effects of grain-boundary energy, surface energy and chemical potential difference. The eventual shape of the plate-like double-crystal grain depends on both the initial β and the thermal grooving angle Ψ. For a given β, a critical Ψcexists. When Ψ>Ψc, the eventual shape is one made of two sphere segments with a thermal groove. When Ψ≤Ψc, grain splitting along the grain boundary occurs, and the splitting segments evolve into two spheres, respectively. Both the spheroidization time and the splitting time increase with Ψ and β increasing. The volume shrinkage rate decreases with increasing Ψ.

Determination of Stress Concentration Around an Oblique Hole by a Finite-Element Technique

1983 ◽  
Vol 105 (2) ◽  
pp. 206-212 ◽  
Author(s):  
Hua-Ping Li ◽  
F. Ellyin
Keyword(s):  
Finite Element ◽  
Stress Concentration ◽  
Maximum Stress ◽  
Plate Thickness ◽  
Two Dimensional ◽  
Element Analysis ◽  
The Finite Element Analysis ◽  
Parametric Studies ◽  
Element Technique

A plate weakened by an oblique penetration of a circular cylindrical hole has been investigated. The stress concentration around the hole is determined by a finite-element method. The results are compared with experimental data and other analytical works. Parametric studies of effects of angle of inclination, plate thickness, and width are performed. The maximum stress concentration factor (SCF) obtained from the finite-element analysis is higher than experimental results, and this deviation increases with the increase of angle of skewness. The major reason for this difference is attributed to the shear-action between layers parallel to the plate surface which cannot be directly included in the two-dimensional elements. An empirical formula is derived which accounts for the shear-action and renders the finite-element predictions in line with experimentally observed data.

Elasto-Plastic Coupled Temperature-Displacement Finite Element Analysis of Two-Dimensional Rolling-Sliding Contact With a Translating Heat Source

1991 ◽  
Vol 113 (1) ◽  
pp. 93-101 ◽  
Author(s):  
S. M. Kulkarni ◽  
C. A. Rubin ◽  
G. T. Hahn
Keyword(s):  
Finite Element ◽  
Half Space ◽  
Plastic Material ◽  
Element Model ◽  
Rolling Contact ◽  
Two Dimensional ◽  
Element Analysis ◽  
Element Mesh ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

The present paper, describes a transient translating elasto-plastic thermo-mechanical finite element model to study 2-D frictional rolling contact. Frictional two-dimensional contact is simulated by repeatedly translating a non-uniform thermo-mechanical distribution across the surface of an elasto-plastic half space. The half space is represented by a two dimensional finite element mesh with appropriate boundaries. Calculations are for an elastic-perfectly plastic material and the selected thermo-physical properties are assumed to be temperature independent. The paper presents temperature variations, stress and plastic strain distributions and deformations. Residual tensile stresses are observed. The magnitude and depth of these stresses depends on 1) the temperature gradients and 2) the magnitudes of the normal and tangential tractions.

3-D Elasto-Plastic Contact Finite Element Analysis for Bearings Design

1990 ◽  
Author(s):  
Wang Shigang ◽  
Yu Jun ◽  
Zhou Ji ◽  
Li Mingzhang
Keyword(s):  
Finite Element ◽  
Contact Problem ◽  
Geometrical Nonlinearity ◽  
Contact Problems ◽  
Plastic State ◽  
Element Analysis ◽  
Surface Pressure Distribution ◽  
Tangential Stiffness ◽  
Stiffness Method ◽  
Error Method

Abstract In this paper, A 3-D elasto-plastic contact problem in bearings is studied by Finite Element Method (FEM). A computer program has been developed for this purpose. A trial-error method is employed to cope with the geometrical nonlinearity and a tangential stiffness method is employed to tackle the material nonlinearity appeared in elasto-plastic contact problems. A frictionless contact problem of roller bearings is analysed, the result reveals that in 3-D elasto-plastic state the trend of the contact surface pressure distribution is similar to Hertz problem’s but flater.

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