APPLICATION OF DUAL SERIES EQUATIONS TO WAVY CONTACT BETWEEN PIEZOELECTRIC MATERIALS AND AN ELASTIC SOLID

2014 ◽  
Vol 06 (04) ◽  
pp. 1450046 ◽  
Author(s):  
YUE-TING ZHOU ◽  
ZHENG ZHONG
Keyword(s):  
Integral Equation ◽  
Piezoelectric Materials ◽  
Elastic Solid ◽  
Contact Length ◽  
Elementary Functions ◽  
Isotropic Solid ◽  
Full Contact ◽  
Dual Series Equations ◽  
Loading Case ◽  
The Relationship

In this paper, the wavy contact between piezoelectric materials and an isotropic solid is considered. The Papkovich–Neuber potentials for the isotropic solid and three harmonic functions for piezoelectric materials are also presented. The stated problem is reduced to a pair of dual series equations and then recast as an integral equation of the Abel type. Employing the product relation for trigonometric functions and the Mehler integral yields an exact solution of the reduced Abel type integral equation. The relationship between contact length and the level of loading, and the distribution of the surface normal stress are given in terms of elementary functions. The derived results agree well with the previous ones for the purely elastic solid. It is found that a critical loading exists for the disturbance. For limiting cases, such as the low level of loading case and full contact case, corresponding contact behaviors are presented. Numerical analyses are done to reveal the influence of the level of loading on the contact behaviors.

Indentation of an Elastic Layer by an Array of Punches Moving With Steady Velocity

1971 ◽  
Vol 38 (1) ◽  
pp. 92-98 ◽  
Author(s):  
L. M. Keer ◽  
C. Sve
Keyword(s):  
Integral Equation ◽  
Asymptotic Solution ◽  
Elastic Layer ◽  
Wave Speed ◽  
Plane Elasticity ◽  
Contact Length ◽  
Dual Series Equations ◽  
Infinite Array ◽  
Rayleigh Wave Speed ◽  
Steady Velocity

A solution is presented for the problem of an elastic layer that is indented by an infinite array of punches moving with a steady velocity below the Rayleigh wave speed. The layer is assumed to be loaded symmetrically about its midplane. The equations of plane elasticity are used to develop dual series equations which are reduced to a single Fredholm integral equation. An asymptotic solution to the integral equation is developed for the case when the ratio of contact length to punch spacing is small, and it is compared with a numerical solution. Numerical calculations for the effective stiffness of the layer and the stresses along the midplane are included.

Scattering of SH Wave on Periodic Cracks in an Infinite Plane of Piezoelectric/Piezomagnic Composite Materials

2012 ◽  
Vol 166-169 ◽  
pp. 3364-3368
Author(s):  
Wei Shi ◽  
Li Xia Ma
Keyword(s):  
Stress Intensity Factor ◽  
Integral Equation ◽  
Composite Materials ◽  
Piezoelectric Materials ◽  
Infinite Plane ◽  
Sh Wave ◽  
Scattering Problems ◽  
Sh Waves ◽  
Periodic Cracks ◽  
The Fourier Transform

In this paper, the scattering problems of SH waves on periodic cracks in an infinite of piezoelectric/piezomagnic composite materials bonded to an infinite of homogeneous piezoelectric materials is investigated, the Fourier transform techniques are used to reduce the problem to the solution of Hilbert singular integral equation, the latter is solved by Lobotto-Chebyshev and Gauss integral equation, at last, numerical results showed the effect of the frequency of wave, sizes and so on upon the normalized stress intensity factor.

scholarly journals Dual-series equations formulation for static deformation of plates with a partial internal line support

2007 ◽  
Vol 34 (3) ◽  
pp. 221-248 ◽  
Author(s):  
Yos Sompornjaroensuk ◽  
Kraiwood Kiattikomol
Keyword(s):  
Integral Equation ◽  
Fredholm Integral Equation ◽  
Hankel Transform ◽  
Internal Line ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Distributed Load ◽  
Dual Series Equations ◽  
Finite Hankel Transform ◽  
Standard Techniques

The paper deals with the application of dual-series equations to the problem of rectangular plates having at least two parallel simply supported edges and a partial internal line support located at the centre where the length of internal line support can be varied symmetrically, loaded with a uniformly distributed load. By choosing the proper finite Hankel transform, the dual-series equations can be reduced to the form of a Fredholm integral equation which can be solved conveniently by using standard techniques. The solutions of integral equation and the deformations for each case of the plates are given and discussed in details.

The Solution of Crack Problems by Using Distributed Strain Nuclei

1996 ◽  
Vol 210 (1) ◽  
pp. 23-31 ◽  
Author(s):  
A M Korsunsky ◽  
D A Hills
Keyword(s):  
Integral Equation ◽  
Stress Field ◽  
Singular Integral Equation ◽  
Singular Integral ◽  
Crack Problems ◽  
The Relationship ◽  
Distributed Strain

Crack problems may be solved by first establishing the stress field in the crack's absence and distributing strain nuclei along the line of the crack in order to render its faces traction-free. The relationship between the different possible forms of nucleus and the kinds of singular integral equation to which they lead are explored. The merits of each are then highlighted.

Study on the Relationship Between Interaction Factors and Stress Intensity Factor for Elliptical Flaws

2017 ◽  
Author(s):  
Kisaburo Azuma ◽  
Yinsheng Li ◽  
Kunio Hasegawa
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Crack Front ◽  
Elastic Solid ◽  
Element Analysis ◽  
Linear Elastic ◽  
Close Proximity ◽  
Interaction Factors ◽  
The Relationship

The interaction of multiple flaws in close proximity to one another may increase the stress intensity factor of the flaw in structures and components. This interaction effect is not distributed uniformly along the crack front. For instance, the strongest interaction is generally observed at the point closest to a neighboring flaw. For this reason, the closest point could show a higher value of the stress intensity factor than all other points in some cases, even if the original value at the point of the single flaw is relatively low. To clarify the condition when the closest point shows the maximum stress intensity factor, we investigated the interaction of two similar elliptical flaws in an infinite model subjected to remote tension loading. The stress intensity factor of the elliptical flaws was obtained by performing finite element analysis of a linear elastic solid. The results indicated that the interaction factors along the crack front can be expressed by a simple empirical formula. Finally, we show the relationship between geometrical features of the flaw and the stress intensity factor at the closest point to a neighboring flaw.

Contact Stresses Between an Elastic Cylinder and a Layered Elastic Solid

1974 ◽  
Vol 96 (2) ◽  
pp. 250-257 ◽  
Author(s):  
P. K. Gupta ◽  
J. A. Walowit
Keyword(s):  
Integral Equation ◽  
Layer Thickness ◽  
Contact Pressure ◽  
Contact Zone ◽  
Numerical Solutions ◽  
Elastic Solid ◽  
Elastic Cylinder ◽  
Elastic Solids ◽  
Actual Contact ◽  
Wide Range

The generalized plane strain problem of the contact of layered elastic solids is reduced to an integral equation using Green’s function approach. Approximate numerical solutions are obtained by replacing the integral equation by a matrix inversion when the trapezoidal rule is used to represent the integral. Results for determining the actual contact pressure at the center of the contact zone and size of contact zone for a wide range of layer thicknesses are presented for two most practical cases, (i) when the indenter is rigid, and (ii) when the indenter is elastic having a modulus of elasticity equal to that of the substrate of the indented body. When the layer is softer than the substrate it is found that the actual contact pressure distribution is very closely determined by a weighted sum of elliptic and parabolic functions. For a substrate softer than the layer the pressures substantially deviate from an elliptical or parabolic behavior, for the cases when the layer thickness is finite. The analysis checks with the Hertzian solution in the extreme cases when the layer thickness either tends to zero or approaches infinity.

scholarly journals Free Motion of Particles in the Lobachevskii Space in Terms of the Scattering Theory

2019 ◽  
Vol 64 (12) ◽  
pp. 1108
Author(s):  
Yu. A. Kurochkin
Keyword(s):  
Integral Equation ◽  
Scattering Amplitude ◽  
Separation Of Variables ◽  
Free Particle ◽  
Three Dimensional ◽  
Lobachevskii Space ◽  
Analytical Functions ◽  
Axis Of Symmetry ◽  
Cartesian Coordinate ◽  
The Relationship

The problem of the motion of a free particle in the three-dimensional Lobachevskii space are interpreted as scattering by the space. The quantum-mechanical case is considered on the basis of the integral equation derived from the Schr¨odinger equation. After the separation of variables in a quasi-Cartesian coordinate system, the integral equation is derived for the momentum component along the axis of symmetry of a horosphere, which coincides with the z axis. The relationship between the scattering amplitude and analytical functions is established. The methods of iteration and finite differences are used to solve the integral equation.

scholarly journals Sustainability of Civil Structures through the Application of Smart Materials: A Review

Materials ◽  
2021 ◽  
Vol 14 (17) ◽  
pp. 4824
Author(s):  
Alireza Tabrizikahou ◽  
Mieczysław Kuczma ◽  
Piotr Nowotarski ◽  
Małgorzata Kwiatek ◽  
Ahad Javanmardi
Keyword(s):  
Shape Memory ◽  
Smart Materials ◽  
Significant Relationship ◽  
Piezoelectric Materials ◽  
Structural Characteristics ◽  
Design Methods ◽  
Seismic Events ◽  
Civil Structures ◽  
Comprehensive Review ◽  
The Relationship

Every year, structural flaws or breakdowns cause thousands of people to be harmed and cost billions of dollars owing to the limitations of design methods and materials to withstand extreme earthquakes. Since earthquakes have a significant effect on sustainability factors, there is a contradiction between these constraints and the growing need for more sustainable structures. There has been a significant attempt to circumvent these constraints by developing various techniques and materials. One of these viable possibilities is the application of smart structures and materials such as shape memory and piezoelectric materials. Many scholars have examined the use of these materials and their structural characteristics up to this point, but the relationship between sustainability considerations and the deployment of smart materials has received little attention. Therefore, through a review of previous experimental, numerical, and conceptual studies, this paper attempts to draw a more significant relationship between smart materials and structural sustainability. First, the significant impact of seismic events on structural sustainability and its major aspects are described. It is then followed by an overview of the fundamentals of smart material’s behaviour and properties. Finally, after a comprehensive review of the most recent applications of smart materials in structures, the influence of their deployment on sustainability issues is discussed. The findings of this study are intended to assist researchers in properly addressing sustainability considerations in any research and implementation of smart materials by establishing a more explicit relationship between these two concepts.

Improved piezoelectricity in ternary potassium–sodium niobate lead-free ceramics with large strain

2020 ◽  
Vol 8 (8) ◽  
pp. 2838-2846 ◽  
Author(s):  
Bo Wu ◽  
Jian Ma ◽  
Wenjuan Wu ◽  
Min Chen
Keyword(s):  
Piezoelectric Materials ◽  
Large Strain ◽  
Lead Free ◽  
Sodium Niobate ◽  
Practical Application ◽  
Potassium Sodium Niobate ◽  
Balanced Development ◽  
Lead Free Ceramics ◽  
Relationship Of ◽  
The Relationship

We decode the relationship of balanced development between piezoelectric and strain properties, which would promote the practical application of lead-free piezoelectric materials.

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