Development of planar rigid-elastic coupling tyre model with analytical multi-stiffness sidewall

2018 ◽  
Vol 233 (2) ◽  
pp. 299-316
Author(s):  
Zhihao Liu ◽  
Qinhe Gao
Keyword(s):  
Structural Deformation ◽  
Geometrical Parameters ◽  
Radial Deformation ◽  
Elastic Coupling ◽  
Structural Stiffness ◽  
Inflation Pressure ◽  
Large Section ◽  
Tyre Model ◽  
Section Ratio ◽  
Non Linear

In this study, combining the membrane feature with inflation pressure and the structural deformation caused by sidewall curvature, rigid-elastic coupling tyre model with analytical multi-stiffness sidewall is proposed for a heavy-loaded radial tyre with a large section ratio. The membrane pre-tension of sidewall arc resulting from inflation pressure is investigated. By means of virtual work principle, the structural deformation of sidewall curved arc resulting from the arc curvature, including stretching, bending and shearing deformation is derived. The structural stiffness caused by the sidewall curvature and membrane pre-tension caused by the inflation pressure are combined for the multi-stiffness sidewall model. The influence of the sidewall structural and geometrical parameters on the sidewall multi-stiffness, modal resonant frequency and transfer function is researched and discussed. The non-linear characteristic of sidewall multi-stiffness with respect to the sidewall radial deformation is investigated. Experimental and theoretical results show that: (1) the multi-stiffness of sidewall can characterise the membrane-tension stiffness caused by inflation pressure and the structural stiffness led by the sidewall curvature and material properties; (2) the different multi-stiffnesses of upper and lower sidewall arcs results from the different interval angles; (3) the multi-stiffness of sidewall is non-linear to the radial sidewall deformation. Taking the flexible deformation of tyre carcass and the analytical multi-stiffness of tyre sidewall into consideration, rigid-elastic coupling tyre model with multi-stiffness sidewall is suitable for the heavy-loaded radial tyre with a large section ratio or tyres under impulsive loading and large deformation.

In-Plane Flexible Beam on Elastic Foundation With Combined Sidewall Stiffness Tire Model for Heavy-Loaded Off-Road Tire

2019 ◽  
Vol 141 (6) ◽  
Author(s):  
Zhihao Liu ◽  
Qinhe Gao ◽  
Hailong Niu
Keyword(s):  
Elastic Foundation ◽  
Structural Parameters ◽  
Flexible Beam ◽  
Tire Model ◽  
Structural Stiffness ◽  
Inflation Pressure ◽  
Euler Beam ◽  
Large Section ◽  
Section Ratio ◽  
Beam On Elastic Foundation

Combining the flexible carcass beam and the radial sidewall element, flexible beam on elastic foundation with combined sidewall stiffness tire model is proposed for heavy-loaded off-road tire with a large section ratio. The circumferential vibration of flexible carcass is modeled as Euler beam and the influence of inflation pressure on the circumferential vibration of flexible carcass is investigated with the modal experiment and theoretical modeling. The structural stiffness caused by the sidewall curvature and pretension stiffness caused by the inflation pressure is combined for the radial sidewall element. The influence of the sidewall structural parameters on the combined stiffness of sidewall and modal resonant frequency is researched and discussed. The nonlinear combined stiffness of sidewall is investigated with respect to the radial sidewall deformation. Experimental and theoretical results show that: (1) the combined stiffness of sidewall can character the pretension stiffness caused by inflation pressure and the structural stiffness led by the sidewall curvature and material properties and (2) the combined stiffness of sidewall is nonlinear with respect to the radial sidewall deformation, which is prominent with high inflation pressure. Taking the flexibility characteristic of tire carcass and the nonlinear stiffness of sidewall into consideration, flexible beam on elastic foundation with combined sidewall stiffness tire model is suitable for the heavy-loaded off-road tire with a large section ratio or tires under impulsive loading and large deformation.

scholarly journals Non-stationary extreme value analysis applied to seismic fragility assessment for nuclear safety analysis

2019 ◽  
Author(s):  
Jeremy Rohmer ◽  
Pierre Gehl ◽  
Marine Marcilhac-Fradin ◽  
Yves Guigueno ◽  
Nadia Rahni ◽  
...  
Keyword(s):  
Failure Probability ◽  
Linear Models ◽  
Extreme Value ◽  
Steam Line ◽  
Information Criteria ◽  
Extreme Value Analysis ◽  
Geometrical Parameters ◽  
Value Analysis ◽  
Gev Distribution ◽  
Non Linear

Abstract. Fragility curves (FC) are key tools for seismic probabilistic safety assessments that are performed at the level of the nuclear power plant (NPP). These statistical methods relate the probabilistic seismic hazard loading at the given site and the required performance of the NPP safety functions. In the present study, we investigate how the tools of non-stationary extreme value analysis can be used to model in a flexible manner the tail behaviour of the engineering demand parameter as a function of the considered intensity measure. We focus the analysis on the dynamic response of an anchored steam line and of a supporting structure under seismic solicitations. The failure criterion is linked to the exceedance of the maximum equivalent stress at a given location of the steam line. A series of three-component ground-motion records (~ 300) were applied at the base of the model to perform non-linear time history analyses. The set of numerical results was then used to derive a FC, which relates the failure probability to the variation of peak ground acceleration (PGA). The probabilistic model of the FC is selected via information criteria completed by diagnostics on the residuals, which support the choice of the generalized extreme value GEV distribution (instead of the widely used log-normal model). The GEV distribution is here non-stationary and the relationships of the GEV parameters (location, scale and shape) are established with respect to PGA using smooth non-linear models. The procedure is data-driven, which avoids the introduction of any a priori assumption on the shape/form of these relationships. To account for the uncertainties in the mechanical and geometrical parameters of the structures (elastic stiffness, damping, pipeline thicknesses, etc.), the FC is further constructed by integrating these uncertain parameters. A penalisation procedure is proposed to set to zero the variables of little influence in the smooth non-linear models. This enables us to outline which of these parametric uncertainties have negligible influence on the failure probability as well as the nature of the influence (linear, non-linear, decreasing, increasing, etc.) with respect to each of the GEV parameters.

scholarly journals Experimental Characterization of Tensairity Beams

2019 ◽  
Vol 8 (3) ◽  
pp. 6150-6154
Keyword(s):  
Experimental Investigation ◽  
Structural Stiffness ◽  
Experimental Characterization ◽  
Inflation Pressure ◽  
High Agreement ◽  
Distributed Load ◽  
Structural Concept ◽  
Full Scale Tests ◽  
Favorable Conditions

Tensairity is a new structural concept towards a sustainable architecture, combined from struts, cables, and an airbeam. In Tensairity, each bearing component is working in the most favorable conditions: struts are only compressed, cables are only tensioned and the airbeam stabilizes the system. Thus, Tensairity beam will be much lighter than a conventional beam. The bearing capacity of this type of beam depends not only on the material property but also on the inflation pressure in the airbeam and the tension in the cable. And this tension strongly depends on the cable anchoring method. This paper presents an experimental investigation aimed to the bending of a Tensairity beam submitted to a homogeneous distributed load. Prototypes in full-scale tests of Tensairity beams will be manufactured. Effect of inflation pressure, airbeam size, and cable anchoring method to structural stiffness will be studied experimentally. The obtained experimental results are in high agreement with those of an independent theory.

Non-linear elastic ring tyre model using the absolute nodal coordinate formulation

2009 ◽  
Vol 223 (3) ◽  
pp. 211-219 ◽  
Author(s):  
H Sugiyama ◽  
Y Suda
Keyword(s):  
Moving Boundary ◽  
Absolute Nodal Coordinate Formulation ◽  
Elastic Ring ◽  
Tyre Model ◽  
Inertia Effects ◽  
Absolute Nodal Coordinate ◽  
Linear Elastic ◽  
Proposed Model ◽  
Road Surfaces ◽  
Non Linear

In this investigation, a non-linear elastic ring tyre model is developed. The elastic deformation of the tyre belt is modelled using the finite element absolute nodal coordinate formulation that allows for describing large rotational motion and the non-linear inertia effects; the curved structure of the tyre belt; and moving boundary resulting from the tread and road interaction. Using a concept of elastic ring tyre models, the sidewall flexibility of a tyre is modelled using circumferential and radial springs and dampers defined between the belt and rim, while the tangential tyre force is modelled using friction elements defined at contact nodes defined within the curved belt elements. Numerical examples are presented in order to demonstrate the use of the flexible tyre model developed in this investigation. Good agreements are demonstrated in the tyre vibration characteristics obtained using the experiments and the proposed model. It is presented that the proposed tyre model can be used for assessing dynamic characteristics of tyres in high frequency ranges resulting from the interaction to uneven road surfaces.

scholarly journals Mathematical Model of Influence of Geometric Parameters on Wave Gear Teeth Wear

2021 ◽  
Vol 346 ◽  
pp. 03016
Author(s):  
I. Ye. Lyuminarskiy ◽  
S.Ye. Lyuminarskiy ◽  
Ye. S. Lyuminarskaya
Keyword(s):  
Mathematical Model ◽  
Wear Resistance ◽  
Geometric Parameters ◽  
Geometrical Parameters ◽  
Radial Deformation ◽  
Gear Teeth ◽  
Wave Generator ◽  
Average Wear ◽  
Gear Wheels ◽  
The Given

The object of the research is a wave gear with a cam wave generator. One of the requirements for wave gears is to increase the wear resistance of the teeth flanks. A mathematical model that makes it possible to assess the influence of the geometrical parameters of the gear on the teeth wear is proposed in this work. To assess the specified effect, the maximum and average wear coefficients are introduced. To calculate these coefficients, a spatial mathematical model of a wave gear is used, taking into account the volumetric and contact deformations of gear wheels and a flexible bearing. Using the developed technique, the dependences of the wear coefficients on the radial deformation and the length of the flexible gear were obtained. The given dependences increase the knowledge concerning the influence of geometric parameters on the wave gear teeth wear.

Study on the key issues of the wheel-spoke shaped pretension structure system

2016 ◽  
Author(s):  
Yueqiang Zhang ◽  
Zheng Zhang ◽  
Jiemin Ding
Keyword(s):  
Geometrical Parameters ◽  
Structural Stiffness ◽  
Structure System ◽  
Compression Ring ◽  
Key Issues ◽  
Structural Boundary ◽  
Ratio Range

<p>The wheel-spoke shaped pretension structure which is one of the architects' favorite structure types has the advantages of reasonable stress, beautiful design, and it can fit with the architectural aesthetics smoothly. Through studying on the geometrical parameters of the wheel-spoke shaped pretension structure, we find out the rational ratio range of compression ring outside to the tension ring inside. In order to improve the structures' bearing performance, we also bring out the idea that the structural boundary can be misaligned with the architectural boundary. Besides, we find that the support column in the place of the compression ring outside can improve structural stiffness, and we analysis the column's influence to the structural bearing performance. At last, by studying the suspended column's influence to the structural bearing performance and architectural sight line, we figure out the suspended column's rational height.</p>

scholarly journals Oscillations of a Beam on a Non-Linear Elastic Foundation under Periodic Loads

2006 ◽  
Vol 13 (4-5) ◽  
pp. 273-284 ◽  
Author(s):  
Donald Mark Santee ◽  
Paulo Batista Gonçalves
Keyword(s):  
Mathematical Model ◽  
Elastic Foundation ◽  
Period Doubling ◽  
Algebraic Expression ◽  
Geometrical Parameters ◽  
Flexible Beam ◽  
Algebraic Relation ◽  
Structural Element ◽  
Linear Elastic ◽  
Non Linear

The complexity of the response of a beam resting on a nonlinear elastic foundation makes the design of this structural element rather challenging. Particularly because, apparently, there is no algebraic relation for its load bearing capacity as a function of the problem parameters. Such an algebraic relation would be desirable for design purposes. Our aim is to obtain this relation explicitly. Initially, a mathematical model of a flexible beam resting on a non-linear elastic foundation is presented, and its non-linear vibrations and instabilities are investigated using several numerical methods. At a second stage, a parametric study is carried out, using analytical and semi-analytical perturbation methods. So, the influence of the various physical and geometrical parameters of the mathematical model on the non-linear response of the beam is evaluated, in particular, the relation between the natural frequency and the vibration amplitude and the first period doubling and saddle-node bifurcations. These two instability phenomena are the two basic mechanisms associated with the loss of stability of the beam. Finally Melnikov's method is used to determine an algebraic expression for the boundary that separates a safe from an unsafe region in the force parameters space. It is shown that this can be used as a basis for a reliable engineering design criterion.

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