A Quadratic Contact Element Passing the Patch Test

2016 ◽  
Vol 681 ◽  
pp. 47-85
Author(s):  
Duc Tue Nguyen ◽  
Gast Rauchs ◽  
Jean Philippe Ponthot
Keyword(s):  
Patch Test ◽  
Contact Pressure ◽  
Penalty Method ◽  
Contact Element ◽  
Two Dimensional ◽  
Penalty Parameter ◽  
Contact Modeling ◽  
Numerical Examples ◽  
Contact Surfaces ◽  
High Penalty

For the two dimensional contact modeling, the standard node-to-segment quadratic contact elements are known to exhibit oscillations of the contact pressure. This situation is particularly critical when using the penalty method with a high penalty parameter because the amplitude of the oscillations increase with increasing penalty parameter. The aim of this article is to present a method for removing the oscillations of contact pressure observed while using quadratic contact element. For this purpose, the nodal forces at the slave and at the master nodes need to be evaluated appropriately. One possibility is to develop a suitable procedure for computing the nodal forces. In that sake, we selected the approach first proposed in [35] in an appropriate manner. After presenting the improved quadratic contact element, some numerical examples are illustrated in this paper to comparethe standard quadratic node-to-segment element with the proposed element. The examples show that the proposed element can strongly reduce the oscillating contact pressure for both plane and curved contact surfaces.

Contact Modeling Technique of a Flexible Piston and Cylinder Using Modal Synthesis Method

2005 ◽  
Author(s):  
W. K. Kim ◽  
S. H. Sohn ◽  
H. J. Cho ◽  
D. S. Bae ◽  
J. H. Choi
Keyword(s):  
Contact Force ◽  
Synthesis Method ◽  
Normal Modes ◽  
Modeling Technique ◽  
Mode Shapes ◽  
Dynamics Analysis ◽  
Contact Modeling ◽  
Static Correction ◽  
Modal Synthesis ◽  
Contact Surfaces

In this paper, contact modeling technique and dynamics analysis of piston and cylinder system are presented by using modal synthesis method. It is very important to select mode shapes representing a global or local behavior of a flexible body due to a specified loading condition. This paper proposes a technique to generate the static correction modes which are nicely representing a motion by a contact force between a piston and cylinder. First normal modes of piston and cylinder under a boundary condition are computed, and then static correction modes due to a contact force applied at contacted nodes are added to the normal modes. Also, this paper proposes an efficient dynamics analysis process while changing the shape of the piston and cylinder. In optimization process or design study, their geometric data can be changed a bit. The slight changes of their contact surfaces make a high variation of the magnitude of a contact force, and it can yield the different dynamic behavior of an engine system. But, since the variations of the normal and correction modes are very small, the re-computation of their normal and correction modes due to the change of contact surfaces can be useless. Until now, whenever their contact surfaces are changed at a design cycle, the modes have been recomputed. Thus, most engineers in industries have been spent many times in very tedious and inefficient design process. In this paper, the normal and correction modes from the basic geometry of the piston and cylinder are computed. If the geometry shape is changed, nodal positions of the original modal model are newly calculated from an interpolation method and changed geometry data. And then the updated nodes are used to compute a precise contact force. The proposed methods illustrated in this investigation have good agreement with results of a nodal synthesis technique and proved that it is very efficient design method.

Numerical solution of two-dimensional first kind Fredholm integral equations by using linear Legendre wavelet

2016 ◽  
Vol 14 (01) ◽  
pp. 1650004 ◽  
Author(s):  
M. Tahami ◽  
A. Askari Hemmat ◽  
S. A. Yousefi
Keyword(s):  
Integral Equation ◽  
Tensor Product ◽  
Numerical Solution ◽  
Fredholm Integral Equation ◽  
Fredholm Integral Equations ◽  
Wavelet Basis ◽  
Two Dimensional ◽  
Legendre Wavelets ◽  
Numerical Examples ◽  
One Dimensional

In one-dimensional problems, the Legendre wavelets are good candidates for approximation. In this paper, we present a numerical method for solving two-dimensional first kind Fredholm integral equation. The method is based upon two-dimensional linear Legendre wavelet basis approximation. By applying tensor product of one-dimensional linear Legendre wavelet we construct a two-dimensional wavelet. Finally, we give some numerical examples.

scholarly journals An evaluation of ultrasonic arrays for the static and dynamic measurement of wheel–rail contact pressure and area

2020 ◽  
Vol 234 (10) ◽  
pp. 1580-1593
Author(s):  
Henry Brunskill ◽  
Andy Hunter ◽  
Lu Zhou ◽  
Rob Dwyer Joyce ◽  
Roger Lewis
Keyword(s):  
Contact Pressure ◽  
Ultrasonic Transducer ◽  
Dynamic Contact ◽  
Pressure Profile ◽  
Calibration Procedure ◽  
Railway Vehicle ◽  
Profile Measurement ◽  
Two Dimensional ◽  
Cross Sectional ◽  
Contact Conditions

The interfacial contact conditions between a railway vehicle wheel and the rail are paramount to the lifespan, safety and smooth operation of any rail network. The wheel–rail interface contact pressure and area conditions have been estimated, calculated and simulated by industry and academia for many years, but a method of accurately measuring dynamic contact conditions has yet to be realised. Methods using pressure-sensitive films and controlled air flow have been employed, but both are limited. Ultrasonic reflectometry is the term given to active ultrasonics in which an ultrasonic transducer is mounted on the outer surface of a component and a sound wave is generated. This ultrasonic wave packet propagates through the host medium and reflects off the contacting interface of interest. The reflected waveform is then detected and contact area and interfacial stiffness information can be extracted from the signal using the quasi-static spring model. Stiffness can be related to contact pressure by performing a simple calibration procedure. Previous contact pressure measurement work has relied on using a focusing transducer and a two-dimensional scanning arrangement which results in a high-resolution image of the wheel–rail contact, but is limited to static loading of a specimen cut from a wheel and rail. The work described in this paper has assessed the feasibility of measuring a dynamic wheel–rail contact patch using an array of 64 ultrasonic elements mounted in the rail. Each element is individually pulsed in sequence to build up a linear cross-sectional pressure profile measurement of the interface. These cross-sectional, line measurements are then processed and collated resulting in a two-dimensional contact pressure profile. Measurements have been taken at different speeds and loads.

scholarly journals Parameter Identification in the Two-Dimensional Riesz Space Fractional Diffusion Equation

2020 ◽  
Vol 4 (3) ◽  
pp. 39
Author(s):  
Rafał Brociek ◽  
Agata Chmielowska ◽  
Damian Słota
Keyword(s):  
Differential Equation ◽  
Diffusion Equation ◽  
Parameter Identification ◽  
Fractional Diffusion ◽  
Riesz Space ◽  
Fractional Diffusion Equation ◽  
Two Dimensional ◽  
Numerical Examples ◽  
Space Fractional Diffusion Equation ◽  
Swarm Intelligence Algorithm

This paper presents the application of the swarm intelligence algorithm for solving the inverse problem concerning the parameter identification. The paper examines the two-dimensional Riesz space fractional diffusion equation. Based on the values of the function (for the fixed points of the domain) which is the solution of the described differential equation, the order of the Riesz derivative and the diffusion coefficient are identified. The paper includes numerical examples illustrating the algorithm’s accuracy.

Two‐dimensional acoustic modeling by a hybrid method

Geophysics ◽  
1985 ◽  
Vol 50 (8) ◽  
pp. 1273-1284 ◽  
Author(s):  
V. Shtivelman
Keyword(s):  
Wave Propagation ◽  
Wave Field ◽  
Inhomogeneous Medium ◽  
Hybrid Method ◽  
Wave Scattering ◽  
Acoustic Modeling ◽  
Two Dimensional ◽  
Numerical Techniques ◽  
Numerical Examples ◽  
Field Computation

This paper follows previous work (Shtivelman, 1984) in which a hybrid method for wave‐field computation was developed. The method combines analytical and numerical techniques and is based upon separation of the processes of wave scattering and wave propagation. The method is further developed and improved; particularly, it is generalized for the case of an inhomogeneous medium above scattering objects (provided the inhomogeneity is weak, i.e., the effects of scattering can be neglected) and is represented by a simpler and more convenient form. Several numerical examples illustrating application of the method to the problems of two‐dimensional acoustic modeling are considered.

A Design Method and the Performance of Two-Dimensional Turbine Cascades for High Subsonic Flow

1971 ◽  
Author(s):  
A. Uenishi
Keyword(s):  
Approximate Solution ◽  
Pressure Distribution ◽  
Subsonic Flow ◽  
Design Method ◽  
Two Dimensional ◽  
Hodograph Method ◽  
Numerical Examples ◽  
Turbine Cascades ◽  
Measured Pressure ◽  
High Subsonic Flow

This paper deals with a hodograph method for design of turbine cascades in high subsonic flow and an approximate solution to a gas, specific heat ratio γ = −1 (the Karman-Tsien approximation) and γ > 1 (the gas obeying the adiabatic law). Numerical examples and a comparison of theoretical and measured pressure distribution for profiles designed by this method are given. Further, a better criterion for design to improve cascade efficiency is also presented.

scholarly journals A Two Dimensional Discrete Mollification Operator and the Numerical Solution of an Inverse Source Problem

Axioms ◽  
2018 ◽  
Vol 7 (4) ◽  
pp. 89 ◽  
Author(s):  
Manuel Echeverry ◽  
Carlos Mejía
Keyword(s):  
Inverse Problem ◽  
Source Term ◽  
Fractional Diffusion ◽  
Inverse Source Problem ◽  
Two Dimensional ◽  
Regularization Procedure ◽  
Numerical Examples ◽  
Convergence Results ◽  
Time Fractional Diffusion Equation ◽  
Operator Convergence

We consider a two-dimensional time fractional diffusion equation and address the important inverse problem consisting of the identification of an ingredient in the source term. The fractional derivative is in the sense of Caputo. The necessary regularization procedure is provided by a two-dimensional discrete mollification operator. Convergence results and illustrative numerical examples are included.

Free Vibration Analysis of Cable Structures Using Isogeometric Approach

2017 ◽  
Vol 14 (03) ◽  
pp. 1750033 ◽  
Author(s):  
Son Thai ◽  
Nam-Il Kim ◽  
Jaehong Lee
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Penalty Method ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Basis Functions ◽  
Displacement Fields ◽  
Numerical Examples ◽  
B Splines ◽  
Cable Structures

This paper presents a free vibration analysis of cable structures based on the isogeometric approach. The nonuniform rational B-splines (NURBS) basis functions are employed to represent both the exact geometry of cable and displacement fields. In order to enrich the basis functions, the [Formula: see text]-, [Formula: see text]- and [Formula: see text]-refinement strategies are implemented. Therefore, these refinement schemes increase the accuracy of solution fields. For determining the static configuration of slack cables as a reference configuration, the well-known penalty method is used. Three numerical examples for slack and taut cable structures are presented in which different refinement schemes are utilized to obtain the converged results. The accuracy and reliability of the present numerical method are verified by comparing the natural frequencies with the results given by other researchers.

Solution of Plane Problems of Elasticity Utilizing Partitioning Concepts

1973 ◽  
Vol 40 (3) ◽  
pp. 767-772 ◽  
Author(s):  
O. L. Bowie ◽  
C. E. Freese ◽  
D. M. Neal
Keyword(s):  
Analytic Function ◽  
Power Series ◽  
Collocation Method ◽  
Stress Function ◽  
Function Theory ◽  
Series Expansions ◽  
Two Dimensional ◽  
Numerical Examples ◽  
Power Series Expansions

A partitioning plan combined with the modified mapping-collocation method is presented for the solution of awkward configurations in two-dimensional problems of elasticity. It is shown that continuation arguments taken from analytic function theory can be applied in the discrete to “stitch” several power series expansions of the stress function in appropriate subregions of the geometry. The effectiveness of such a plan is illustrated by several numerical examples.

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