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On the Modeling of Contact Problems for Curved and Straight Elastic Thin Continuums with Application to Non-Pneumatic Tires.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	On the Modeling of Contact Problems for Curved and Straight Elastic Thin Continuums with Application to Non-Pneumatic Tires./
Author:	Gasmi, Amir.
Description:	245 p.
Notes:	Source: Dissertation Abstracts International, Volume: 72-11, Section: B, page: 6986.
Contained By:	Dissertation Abstracts International72-11B.
Subject:	Applied Mechanics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3469532
ISBN:	9781124855073

On the Modeling of Contact Problems for Curved and Straight Elastic Thin Continuums with Application to Non-Pneumatic Tires.
Gasmi, Amir.

On the Modeling of Contact Problems for Curved and Straight Elastic Thin Continuums with Application to Non-Pneumatic Tires. - 245 p.

Source: Dissertation Abstracts International, Volume: 72-11, Section: B, page: 6986.

Thesis (Ph.D.)--Clemson University, 2011.

In this dissertation the mathematical modeling of thin elastic curved continua that are brought into contact with a rigid surface is addressed by using higher order beam theories. The motivation for the study is the analytical modeling of non-pneumatic tires whose flexible outer ring is highly orthotropic in nature. The closed form solutions obtained provide physical insight into how the stiffness parameters that define the mechanical behavior of the ring affect performance. As such, this dissertation provides mechanics support and development to the optimal and rational design of a non-pneumatic tire, in addition to providing fundamental contact solutions for related applications.

ISBN: 9781124855073Subjects--Topical Terms:

845450
Applied Mechanics.

On the Modeling of Contact Problems for Curved and Straight Elastic Thin Continuums with Application to Non-Pneumatic Tires.
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020 $a 9781124855073
035 $a (UMI)AAI3469532
035 $a AAI3469532
040 $a UMI $c UMI
100 1 $a Gasmi, Amir. $3 845452
245 1 0 $a On the Modeling of Contact Problems for Curved and Straight Elastic Thin Continuums with Application to Non-Pneumatic Tires.
300 $a 245 p.
500 $a Source: Dissertation Abstracts International, Volume: 72-11, Section: B, page: 6986.
500 $a Adviser: Paul F. Joseph.
502 $a Thesis (Ph.D.)--Clemson University, 2011.
520 $a In this dissertation the mathematical modeling of thin elastic curved continua that are brought into contact with a rigid surface is addressed by using higher order beam theories. The motivation for the study is the analytical modeling of non-pneumatic tires whose flexible outer ring is highly orthotropic in nature. The closed form solutions obtained provide physical insight into how the stiffness parameters that define the mechanical behavior of the ring affect performance. As such, this dissertation provides mechanics support and development to the optimal and rational design of a non-pneumatic tire, in addition to providing fundamental contact solutions for related applications.
520 $a This present study encompasses three major research trends. These trends are (1) development of elementary and higher order orthotropic curved and straight beam theories using the variational principles of mechanics; (2) derivation and solution of the governing equations for contact problems including special cases; and finally (3) completion of extensive parametric analysis to understand the effects of the macroscopic structural key elements of the tire on, for example, the contact patch, rolling resistance and the vertical stiffness.
520 $a The study starts with elementary curved beam theories based on the standard Euler-Bernoulli and Timoshenko beam theory assumptions. The former theory accounts only for circumferential extension and bending, whereas the later theory accounts for deformations due to circumferential extension, bending and transverse shear. Using standard notation for the stiffness parameters, this corresponds to EA, EI and GA, respectively, which are independent of each other. As a first application of the approach, the frictionless contact problem of a shear deformable, extensional ring pressed between two rigid smooth plates is solved analytically. The nonlinear feature of the contact problem is accounted for by considering the contact pressure normal to the rigid surfaces in the deformed configuration. Furthermore, a full parametric analysis of contact pressure is performed and it is revealed that a nearly uniform contact pressure, i.e. a pneumatic like pressure, can be obtained when the primary mode of deformation in the ring is shear.
520 $a The analytical approach for a compressed ring is then extended to a two-dimensional analytical model for a compliant non-pneumatic tire on frictionless, rigid ground. The effect of the spokes, which are distributed continuously in the model and act as linear springs, is accounted for only in tension. From the analysis point of view, when the wheel is loaded at its hub, the following three distinct regions develop: (1) a support region where the hub hangs by the spokes from the upper part of the flexible ring, (2) a free surface region where the spokes buckle and have no effect, and (3) a contact region where the flexible ring is supported by the ground without the effect of the spokes. The angular bounds of these three regions are determined by the spoke angle and the contact angle, which are respectively the angle at which the spokes start to engage in tension and the angle that defines the edge of contact. The solution of this problem for finite extensional stiffness requires an approximate solution procedure, which is achieved using a cosine series.
520 $a An extensive two-dimensional parametric analysis is performed to study the relationships among the contact patch, tire stiffnesses and material properties of the key elements that form the tire. As a practical application of the above solution, the steady state calculation of rolling resistance for a non-pneumatic tire using Fourier series to represent the shear stress is developed. The limitation of the model is studied by comparison with experiment and a more general finite element approach.
520 $a In the above solutions it was noted that using a curved beam theory that only accounts for circumferential extension, bending and transverse shear leads to a maximum stress at the edge of contact, which contradicts the elasticity theory result that contact pressure must be zero at the edge of contact. Therefore, in the next phase of this study the transverse normal strain in the beam is considered, both to address this fundamental discrepancy and to include the effect of a soft tread on a tire. To investigate this effect, higher order straight beam theories which account for both constant and linear transverse normal strain through the beam thickness are derived using the principle of virtual work. The contact problem of a straight beam on a circular rigid smooth surface is then solved for these theories, along with the Timoshenko beam model which assumes zero transverse normal strain. The numerical results for different orthotropic materials show that inclusion of transverse normal deformation has a significant affect on the contact pressure solution, especially when the maximum contact pressure is a key design parameter. The solution using higher order beam theories encompasses two contact pressure trends, that is, a Hertz-like contact pressure results when the half contact length is smaller than the thickness of the beam, and a Timoshenko beam like contact pressure results when the half contact length is much larger than the thickness. This makes the present approach superior to Hertz contact modeling and to elementary beam modeling.
520 $a Finally, a higher order orthotropic curved beam theory which accounts for constant radial strain through the beam thickness is derived using the principle of virtual work. This beam theory therefore accounts for four deformation modes, i.e. radial deformation, transverse shearing, bending and circumferential extension. The frictionless contact of a ring is re-solved using the higher order curved beam theory and compared with the more elementary solution. The limitation of the theories is studied through the comparison of the numerical results obtained using the derived theories, along with those of plane strain elasticity theory obtained using finite elements.
590 $a School code: 0050.
650 4 $a Applied Mechanics. $3 845450
650 4 $a Applied Mathematics. $3 845392
650 4 $a Engineering, Mechanical. $3 845387
690 $a 0346
690 $a 0364
690 $a 0548
710 2 $a Clemson University. $b Mechanical Engineering. $3 845453
773 0 $t Dissertation Abstracts International $g 72-11B.
790 1 0 $a Joseph, Paul F., $e advisor
790 1 0 $a Li, Gang $e committee member
790 1 0 $a Fadel, George M. $e committee member
790 1 0 $a Biggers, Sherrill B. $e committee member
790 1 0 $a Rhyne, Timothy B. $e committee member
790 $a 0050
791 $a Ph.D.
792 $a 2011
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3469532