scholarly journals Endless elastic beam travelling on a moving rough surface with zones of stick and sliding

2021 ◽  
Author(s):  
Yury Vetyukov
Keyword(s):  
Finite Element ◽  
Boundary Value Problem ◽  
Characteristic Time ◽  
Nonlinear Boundary ◽  
Elastic Beam ◽  
Stationary Regime ◽  
Self Similarity ◽  
Present Contribution ◽  
Element Simulation ◽  
Rough Plane

AbstractWe study the planar deformation of a beam that travels across a given control domain supported by a moving rough plane, which is a prototype for various technological processes. A sufficiently small misalignment between the guideways at the ends of the domain results in a stationary regime of motion, which features a zone of sticking contact near the entry to the control domain, followed by infinitely many segments of transverse sliding with alternating directions. Self-similarity of this solution of an essentially nonlinear boundary value problem is the primary novel result of the present contribution. Closed-form analytic results are validated against a finite element simulation of the transient evolution process, which demonstrates stability of the obtained solution and provides insights regarding the characteristic time scales of establishing of subsequent zones of sliding.

scholarly journals Endless Elastic Beam Travelling on a Moving Rough Surface With Zones of Stick and Sliding

2021 ◽  
Author(s):  
Yury Vetyukov
Keyword(s):  
Finite Element ◽  
Boundary Value Problem ◽  
Characteristic Time ◽  
Nonlinear Boundary ◽  
Elastic Beam ◽  
Stationary Regime ◽  
Self Similarity ◽  
Present Contribution ◽  
Element Simulation ◽  
Rough Plane

Abstract We study the planar deformation of a beam that travels across a given control domain supported by a moving rough plane, which is a prototype for various technological processes. A sufficiently small misalignment between the guideways at the ends of the domain results into a stationary regime of motion, which features a zone of sticking contact near the entry to the control domain followed by infinitely many segments of transverse sliding with alternating directions. Self-similarity of this solution of an essentially nonlinear boundary value problem is the primary novel result of the present contribution. Closed-form analytic results are validated against a finite element simulation of the transient evolution process, which demonstrates stability of the obtained solution and provides insights regarding the characteristic time scales of establishing of subsequent zones of sliding.

Electromagnetic Sheet Metal Feeder

2014 ◽  
Vol 611-612 ◽  
pp. 939-946 ◽  
Author(s):  
Sergej Teichrib ◽  
Richard Krimm ◽  
Bernd Arno Behrens
Keyword(s):  
Finite Element ◽  
Sheet Metal ◽  
Experimental Measurements ◽  
Sheet Metals ◽  
Mechanical Contact ◽  
Present Contribution ◽  
New Approach ◽  
Sheet Surface ◽  
Element Simulation ◽  
Continuous Feeding

For a continuous feeding of sheet metals in forming press lines mechanical roll and gripper feeders are used. Typical resulting problems are the damage of the sheet surface due to the mechanical contact. The present contribution deals with the investigations of an electromagnetic material feeder for electric conductive sheet metals. The concept is based on the principle of an asynchronous linear motor. Here the sheet metal acts directly as the secondary part. The new approach was first analysed and designed by means of finite element simulation. With experimental measurements the simulations could be validated using a demonstrator of the electromagnetic feeder. The results indicate that the feeding forces of partially 1000 N can be doubled in comparison to conventional mechanical roll feeders.

scholarly journals The Solvability and Numerical Simulation for the Elastic Beam Problems with Nonlinear Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Qun Gao
Keyword(s):  
Numerical Simulation ◽  
Boundary Value Problem ◽  
Fourth Order ◽  
Multiple Solutions ◽  
Nonlinear Boundary ◽  
Elastic Beam ◽  
Nonlinear Boundary Conditions ◽  
Beam Equation ◽  
Three Solutions ◽  
New Criteria

We study the existence of multiple solutions for a fourth-order nonlinear boundary value problem. We give some new criteria for guaranteeing that the fourth-order elastic beam equation with a perturbed term has at least three solutions. The proof is based on some three critical points theorems of B. Ricceri. Furthermore, numerical simulations are also presented.

Hypo-Elastic vs Hyper-Elastic Constitutive Equation for Textile Materials at Meso-Scale

2014 ◽  
Vol 611-612 ◽  
pp. 243-249 ◽  
Author(s):  
Emmanuelle Vidal-Sallé ◽  
Charlotte Florimond ◽  
Adrien Charmetant ◽  
Philippe Boisse
Keyword(s):  
Finite Element ◽  
Constitutive Modelling ◽  
Mesoscopic Scale ◽  
Present Contribution ◽  
Textile Materials ◽  
The Past ◽  
Element Simulation ◽  
Hyper Elastic ◽  
Material Forming ◽  
Nonlinear Continuum

The increasing use of finite element simulation in the field of composite material forming involved in the past few years a large among of research on the constitutive modelling of textile material at the mesoscopic scale (i.e. the scale of individual fibre tow). Up to now, a consensus does not exist on the most appropriate approach. The present contribution aims on the comparison between hypo-and hyper-elastic approaches to describe the mechanical behaviour of a single tow in the framework of nonlinear continuum mechanics. A particular attention is paid to the ease of implementation in standard finite element codes.

scholarly journals On the existence of equilibrium states of an elastic beam on a nonlinear foundation

1993 ◽  
Vol 16 (1) ◽  
pp. 193-198
Author(s):  
M. B. M. Elgindi ◽  
D. H. Y. Yen
Keyword(s):  
Boundary Value Problem ◽  
Axial Compression ◽  
Existence And Uniqueness ◽  
Nonlinear Boundary ◽  
Nonlinear Eigenvalue Problem ◽  
Boundary Value ◽  
Elastic Beam ◽  
Equilibrium States ◽  
Nonlinear Boundary Value Problem ◽  
Nonlinear Boundary Value

This paper concerns the existence and uniqueness of equilibrium states of a beam-column with hinged ends which is acted upon by axial compression and lateral forces and is in contact with a semi-infinite medium acting as a foundation. The problem is formulated as a fourth-order nonlinear boundary value problem in which the source of the nonlinearity comes from the lateral constraint (the foundation). Treating the equation of equilibrium as a nonlinear eigenvalue problem we prove the existence of a pair of eigenvalue/eigenfunction for each arbitrary prescribed energy level. Treating the equilibrium equation as a nonlinear boundary value problem we prove the existence and uniqueness of solution for a certain range of the acting axial compression force.

Predicting Mixing Volumes in Serial Transport in Pipelines

2002 ◽  
Vol 124 (2) ◽  
pp. 528-534 ◽  
Author(s):  
F. B. Freitas Rachid ◽  
J. H. Carneiro de Araujo ◽  
R. M. Baptista
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Value Problem ◽  
Field Test ◽  
Nonlinear Boundary ◽  
Time Dependent ◽  
Dispersion Coefficients ◽  
Flow Rates ◽  
Theoretical Predictions ◽  
Dependent Flow

This paper presents a model for predicting the contaminated mixing volume arising in pipeline batch transfers without physical separators. The proposed technique represents an improvement over the existing methods since it takes into account time-dependent flow rates and accurate concentration-varying axial dispersion coefficients. The governing equation of the model forms a nonlinear boundary-value problem that is solved by a finite element method coupled to the Newton’s method. A comparison among the theoretical predictions of this method, a field test, and other classical procedures show that the proposed method exhibits the best estimate over the whole range of admissible concentrations investigated.

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