Elastic Contact Between a Geometrically Anisotropic Bisinusoidal Surface and a Rigid Base

2015 ◽  
Vol 137 (2) ◽  
Author(s):  
Yang Xu ◽  
Amir Rostami ◽  
Robert L. Jackson
Keyword(s):  
Numerical Solutions ◽  
Numerical Models ◽  
Elastic Half Space ◽  
Asymptotic Solutions ◽  
Rigid Base ◽  
Fe Model ◽  
Linear Elastic ◽  
Principal Directions ◽  
Complete Contact ◽  
Elliptic Contact

In the current study, a semi-analytical model for contact between a homogeneous, isotropic, linear elastic half-space with a geometrically anisotropic (wavelengths are different in the two principal directions) bisinusoidal surface on the boundary and a rigid base is developed. Two asymptotic loads to area relations for early and almost complete contact are derived. The Hertz elliptic contact theory is applied to approximate the load to area relation in the early contact. The noncontact regions occur in the almost complete contact are treated as mode-I cracks. Since those cracks are in compression, an approximate relation between the load and noncontact area can be obtained by setting the corresponding stress intensity factor (SIF) to zero. These two asymptotic solutions are validated by two different numerical models, namely, the fast Fourier transform (FFT) model and the finite element (FE) model. A piecewise equation is fit to the numerical solutions to bridge these two asymptotic solutions.

scholarly journals On a Certain Method of Selection of Domain for Finite Element Modelling of the Layered Elastic Half-Space in the Static Analysis of Flexible Pavement

2012 ◽  
Vol 58 (4) ◽  
pp. 477-501
Author(s):  
M. Nagórska
Keyword(s):  
Half Space ◽  
Mechanistic Model ◽  
Elastic Half Space ◽  
Original Method ◽  
Fe Model ◽  
Linear Elastic ◽  
Road Pavement ◽  
Viscoelastic Layers ◽  
Selection Of ◽  
Layered Half Space

AbstractIn the flexible road pavement design a mechanistic model of a multilayered half-space with linear elastic or viscoelastic layers is usually used for the pavement analysis.This paper describes a domain selection for the purpose of a FE model creating of the linear elastic layered half-space and boundary conditions on borders of that domain. This FE model should guarantee that the key components of displacements, stresses and strains obtained using ABAQUS program would be in particular identical with those ones obtained by analytical method using VEROAD program.It to achieve matching results with both methods is relatively easy for stresses and strains. However, for displacements, using FEM to obtain correct results is (understandably) highly problematic due to infinity of half-space. This paper proposes an original method of overcoming these difficulties.

On the Effects of Residual Stress in Microindentation Tests of Soft Tissue Structures

2004 ◽  
Vol 126 (2) ◽  
pp. 276-283 ◽  
Author(s):  
Evan A. Zamir ◽  
Larry A. Taber
Keyword(s):  
Residual Stress ◽  
Soft Tissue ◽  
Elastic Foundation ◽  
Elastic Properties ◽  
Material Properties ◽  
Soft Tissues ◽  
Elastic Half Space ◽  
Fe Model ◽  
Linear Elastic ◽  
Tissue Structures

Microindentation methods are commonly used to determine material properties of soft tissues at the cell or even sub-cellular level. In determining properties from force-displacement (FD) data, it is often assumed that the tissue is initially a stress-free, homogeneous, linear elastic half-space. Residual stress, however, can strongly influence such results. In this paper, we present a new microindentation method for determining both elastic properties and residual stress in soft tissues that, to a first approximation, can be regarded as a pre-stressed layer embedded in or adhered to an underlying relatively soft, elastic foundation. The effects of residual stress are shown using two linear elastic models that approximate specific biological structures. The first model is an axially loaded beam on a relatively soft, elastic foundation (i.e., stress-fiber embedded in cytoplasm), while the second is a radially loaded plate on a foundation (e.g., cell membrane or epithelium). To illustrate our method, we use a nonlinear finite element (FE) model and experimental FD and surface contour data to find elastic properties and residual stress in the early embryonic chick heart, which, in the region near the indenter tip, is approximated as an isotropic circular plate under tension on a foundation. It is shown that the deformation of the surface in a microindentation test can be used along with FD data to estimate material properties, as well as residual stress, in soft tissue structures that can be regarded as a plate under tension on an elastic foundation. This method may not be as useful, however, for structures that behave as a beam on a foundation.

A Strain Energy-Based Equivalent Layer Method for the Prediction of Critical Collapse Pressure of Flexible Risers

2018 ◽  
Author(s):  
Xiao Li ◽  
Xiaoli Jiang ◽  
Hans Hopman
Keyword(s):  
Strain Energy ◽  
Critical Pressure ◽  
Numerical Models ◽  
Fe Model ◽  
Collapse Pressure ◽  
Layer Method ◽  
Flexible Risers ◽  
Collapse Behavior ◽  
Equivalent Properties ◽  
Equivalent Layer

Flexible risers are one kind of flexible pipes that transport fluid between subsea facilities and topside structures. This pipe-like structure consists of multiple layers and its innermost carcass layer is designed for external hydrostatic pressure resistance. For the flexible risers used in ultra-deep water fields, the critical collapse pressure of the carcass layers is one of the dominant factors in their safety design. However, the complexity of the interlocked carcass design introduces significant difficulties and constraints into the engineering analysis. To facilitate the anti-collapse analysis, equivalent layer methods are demanded to help construct an equivalent pipe that performs a similar collapse behavior of the carcass. This paper proposes a strain energy based equivalent layer method which trying to bridge the equivalence between those two structures by considering equivalent geometric and material properties for the equivalent layer. Those properties are determined through strain energy equivalence and membrane stiffness equivalence. The strain energy of the carcass is obtained through numerical models and is then used in a derived equation set to calculate the equivalent properties for the equivalent layer. After all the equivalent properties have been determined, an equivalent layer FE model is built and used to predict the critical pressure of the carcass. The prediction result is compared to that of the full 3D carcass model as well as the equivalent models that built based on other existing equivalent methods, which shows that the proposed equivalent layer method gives a better performance on predicting the critical pressure of the carcass.

Mistuning Modeling and its Validation for Small Turbine Wheels

2013 ◽  
Author(s):  
David Hemberger ◽  
Dietmar Filsinger ◽  
Hans-Jörg Bauer
Keyword(s):  
Amplification Factor ◽  
Numerical Models ◽  
Lower Sensitivity ◽  
Fe Model ◽  
Mode Localization ◽  
Geometric Deviations ◽  
Probabilistic Study ◽  
Calculated Amplitude ◽  
Amplitude Amplification ◽  
The Ideal

The production of bladed structures, e.g. turbine and compressor wheels, is a subject of statistical scatter. The blades are designed to be identical but differ due to small manufacturing tolerances. This so called mistuning can lead to increased vibration amplitudes compared to the ideal tuned case. The object of this study is to create and validate numerical models to evaluate such mistuning effects of turbine wheels for automotive turbocharger applications. As a basis for the numerical analysis vibration measurements under stand-still conditions were carried out by using a laser surface velocimeter (LSV). The scope of this investigation was to identify the mistuning properties of the turbine wheels namely the frequency deviation from the ideal, cyclic symmetrical tuned system. Experimental modal analyses as well as blade by blade measurements were performed. Moreover 3D scanning techniques were employed to determine geometric deviations. Numerical FE models and a simplified multi degree of freedom model (EBM) were created to reproduce the measured mistuning effects. The prediction of mode localization and the calculated amplitude amplification were evaluated. The best results were obtained with a FE model that employs individual sectorial stiffnesses. The results also indicate that the major contribution to mistuning is made by material inhomogeneities and not by geometric deviations from ideal dimensions. With the adjusted FE model a probabilistic study has been performed to investigate the influence of the mistuning on the amplitude amplification factor. It has been found that at a certain level of mistuning the amplification factor remains constant or slightly decreases. By introducing intentional mistuning a lower sensitivity as well as a decrease of the amplitude amplification could be achieved.

scholarly journals Established Numerical Techniques for the Structural Analysis of a Regional Aircraft Landing Gear

2018 ◽  
Vol 2018 ◽  
pp. 1-21 ◽  
Author(s):  
F. Caputo ◽  
A. De Luca ◽  
A. Greco ◽  
A. Marro ◽  
A. Apicella ◽  
...  
Keyword(s):  
Finite Elements ◽  
Numerical Models ◽  
Three Dimensional ◽  
Landing Gear ◽  
Point Of View ◽  
Fe Model ◽  
One Dimensional ◽  
Reaction Forces ◽  
Local Technique ◽  
Stick Model

Usually during the design of landing gear, simplified Finite Element (FE) models, based on one-dimensional finite elements (stick model), are used to investigate the in-service reaction forces involving each subcomponent. After that, the design of such subcomponent is carried out through detailed Global/Local FE analyses where, once at time, each component, modelled with three-dimensional finite elements, is assembled into a one-dimensional finite elements based FE model, representing the whole landing gear under the investigated loading conditions. Moreover, the landing gears are usually investigated also under a kinematic point of view, through the multibody (MB) methods, which allow achieving the reaction forces involving each subcomponent in a very short time. However, simplified stick (FE) and MB models introduce several approximations, providing results far from the real behaviour of the landing gear. Therefore, the first goal of this paper consists of assessing the effectiveness of such approaches against a 3D full-FE model. Three numerical models of the main landing gear of a regional airliner have been developed, according to MB, “stick,” and 3D full-FE methods, respectively. The former has been developed by means of ADAMS® software, the other two by means of NASTRAN® software. Once this assessment phase has been carried out, also the Global/Local technique has verified with regard to the results achieved by the 3D full-FE model. Finally, the dynamic behaviour of the landing gear has been investigated both numerically and experimentally. In particular, Magnaghi Aeronautica S.p.A. Company performed the experimental test, consisting of a drop test according to EASA CS 25 regulations. Concerning the 3D full-FE investigation, the analysis has been simulated by means of Ls-Dyna® software. A good level of accuracy has been achieved by all the developed numerical methods.

A New Approach for Fatigue Damage Modeling of Subsurface-Initiated Spalling in Large Rolling Contacts

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
Aditya A. Walvekar ◽  
Neil Paulson ◽  
Farshid Sadeghi ◽  
Nick Weinzapfel ◽  
Martin Correns ◽  
...  
Keyword(s):  
Fatigue Damage ◽  
Damage Mechanics ◽  
Numerical Models ◽  
Rolling Contact ◽  
Fe Model ◽  
Triangle Mesh ◽  
Computationally Efficient ◽  
New Approach ◽  
Rolling Contacts ◽  
Delaunay Triangle

Large bearings employed in wind turbine applications have half-contact widths that are usually greater than 1 mm. Previous numerical models developed to investigate rolling contact fatigue (RCF) require significant computational effort to study large rolling contacts. This work presents a new computationally efficient approach to investigate RCF life scatter and spall formation in large bearings. The modeling approach incorporates damage mechanics constitutive relations in the finite element (FE) model to capture fatigue damage. It utilizes Voronoi tessellation to account for variability occurring due to the randomness in the material microstructure. However, to make the model computationally efficient, a Delaunay triangle mesh was used in the FE model to compute stresses during a rolling contact pass. The stresses were then mapped onto the Voronoi domain to evaluate the fatigue damage that leads to the formation of surface spall. The Delaunay triangle mesh was dynamically refined around the damaged elements to capture the stress concentration accurately. The new approach was validated against previous numerical model for small rolling contacts. The scatter in the RCF lives and the progression of fatigue spalling for large bearings obtained from the model show good agreement with experimental results available in the open literature. The ratio of L10 lives for different sized bearings computed from the model correlates well with the formula derived from the basic life rating for radial roller bearing as per ISO 281. The model was then extended to study the effect of initial internal voids on RCF life. It was found that for the same initial void density, the L10 life decreases with the increase in the bearing size.

Multiple Region Contact Solutions for a Flat Indenter on a Layered Elastic Half Space: Plane-Strain Case

1989 ◽  
Vol 56 (2) ◽  
pp. 251-262 ◽  
Author(s):  
T. W. Shield ◽  
D. B. Bogy
Keyword(s):  
Plane Strain ◽  
Half Space ◽  
Contact Region ◽  
Integral Transforms ◽  
Elastic Half Space ◽  
Geometrical Parameters ◽  
Restricted Range ◽  
Complete Contact ◽  
The One ◽  
Layered Half Space

The plane-strain problem of a smooth, flat rigid indenter contacting a layered elastic half space is examined. It is mathematically formulated using integral transforms to derive a singular integral equation for the contact pressure, which is solved by expansion in orthogonal polynomials. The solution predicts complete contact between the indenter and the surface of the layered half space only for a restricted range of the material and geometrical parameters. Outside of this range, solutions exist with two or three contact regions. The parameter space divisions between the one, two, or three contact region solutions depend on the material and geometrical parameters and they are found for both the one and two layer cases. As the modulus of the substrate decreases to zero, the two contact region solution predicts the expected result that contact occurs only at the corners of the indenter. The three contact region solution provides an explanation for the nonuniform approach to the half space solution as the layer thickness vanishes.

scholarly journals Analysis and optimization of cooling channels performances for industrial extrusion dies

2021 ◽  
Author(s):  
Riccardo Pelacci ◽  
Marco Negozio ◽  
Barbara Reggiani ◽  
Lorenzo Donati ◽  
Luca Tomesani
Keyword(s):  
Liquid Nitrogen ◽  
Numerical Models ◽  
Extrusion Process ◽  
Die Design ◽  
Design Stage ◽  
Fe Model ◽  
Cooling Efficiency ◽  
Channel Design ◽  
Liquid Nitrogen Cooling ◽  
Experimental Trials

Liquid nitrogen cooling is widely used in the extrusion industrial practice in order to increase the production rate, to reduce the die temperature and to avoid defects on the profile exit surfaces resulting from an excessive heating. However, the efficiency of the cooling is deeply affected by position and design of the liquid nitrogen channel so that numerical modelling is gaining an increasing industrial interest in relation to the possibility offered to optimize the channel design without expensive and time-consuming experimental trials. In this work, a numerical FE model developed within COMSOL Multiphysics® is proposed and validated against experimental trials performed in industrial environment. The model combines the 3D simulation of the extrusion process with a 1D model of the cooling channel thus allowing the testing of a number of different solutions at the die design stage. The global aim of this work is the assessment of the liquid nitrogen cooling efficiency in the extrusion of an industrial aluminum profile and the proof of the potentials offered by numerical models to get an optimized channel design in terms of cooling efficiency, die thermal balancing and reduction of liquid nitrogen consumption.

Numerical solutions to wave interaction with rubblemound breakwaters

1990 ◽  
Vol 17 (2) ◽  
pp. 252-261 ◽  
Author(s):  
Kevin R. Hall
Keyword(s):  
Numerical Modelling ◽  
Numerical Solution ◽  
Numerical Solutions ◽  
Scale Effects ◽  
Numerical Models ◽  
Internal Flow ◽  
Wave Interaction ◽  
Theoretical Development ◽  
Porous Media Flow ◽  
Complex Flow

The interaction of a wave with a rubblemound breakwater results in a complex flow field which is both nonlinear and turbulent, particularly within a region close to the surface of the structure. Numerical models describing internal flow in a rubblemound breakwater are becoming increasingly important, particularly as the influence of scale effects on internal flow in physical hydraulic models are becoming understood as important. A number of numerical models to predict the internal breakwater flow kinematics have been produced in the past two decades. This paper provides a review of the state-of-the-art of numerical modelling of wave interaction with rubblemound breakwaters. Details of the theoretical development and the resulting numerical solution techniques are presented. Methods for incorporating secondary effects such as two-phase (air–water) flow, inertia, and unbalanced boundary conditions are discussed. Limitations of the models resulting from the validity of the assumptions made in order to effect a numerical solution are discussed. Key words: breakwaters, internal flow, porous media flow, numerical modelling, rubblemound breakwaters.

On the relation between ice thickness changes and glacier speed-up, with application to Pine Island Glacier in West Antarctica 

2021 ◽  
Author(s):  
Jan De Rydt ◽  
Ronja Reese ◽  
Fernando Paolo ◽  
G Hilmar Gudmundsson
Keyword(s):  
Numerical Solutions ◽  
Numerical Models ◽  
Flow Speed ◽  
Ice Thickness ◽  
West Antarctica ◽  
Ice Shelf ◽  
Ice Flow ◽  
Spatially Distributed ◽  
Speed Up ◽  
Induced Changes

<p>Pine Island Glacier in West Antarctica is among the fastest changing glaciers worldwide. Much of its fast-flowing central trunk is thinning and accelerating, a process thought to have been triggered by ocean-induced changes in ice-shelf buttressing. The measured acceleration in response to perturbations in ice thickness is a non-trivial manifestation of several poorly-understood physical processes, including the transmission of stresses between the ice and underlying bed. To enable robust projections of future ice flow, it is imperative that numerical models include an accurate representation of these processes. Here we combine the latest data with analytical and numerical solutions of SSA ice flow to show that the recent increase in flow speed of Pine Island Glacier is only compatible with observed patterns of thinning if a spatially distributed, predominantly plastic bed underlies large parts of the central glacier and its upstream tributaries.</p>

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