Axisymmetric Boussinesq problem of a transversely isotropic half space with surface effects

2018 ◽  
Vol 24 (5) ◽  
pp. 1425-1437 ◽  
Author(s):  
Jing Jin Shen
Keyword(s):  
Half Space ◽  
Mixed Boundary ◽  
Contact Stiffness ◽  
Surface Elasticity ◽  
Transversely Isotropic ◽  
Surface Effects ◽  
Building Blocks ◽  
Material Anisotropy ◽  
Residual Surface Stress ◽  
Special Cases

A transversely isotropic half space with surface effects subjected to axisymmetric loadings is investigated in terms of the Lekhnitskii formulism. Surface effects including residual surface stress and surface elasticity are introduced by using the Gurtin–Murdoch continuum model. With the aid of the Hankel transforms, solutions corresponding to several different axisymmetic loadings are derived and used to determine the influence of surface effects on contact stiffness in nanoindentations. Numerical results are provided to show the influence of surface effects and material anisotropy on the material behaviours. Meanwhile, the obtained analytical Green’s functions for two special cases can be used as building blocks for further mixed boundary value problems.

Contact Stress Analysis of a Layered Transversely Isotropic Half-Space

1992 ◽  
Vol 114 (2) ◽  
pp. 253-261 ◽  
Author(s):  
C. H. Kuo ◽  
L. M. Keer
Keyword(s):  
Half Space ◽  
Mixed Boundary ◽  
Contact Region ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Hankel Transform ◽  
Elastic Half Space ◽  
Contact Stresses ◽  
Stress Components ◽  
Contact Failure

The three-dimensional problem of contact between a spherical indenter and a multi-layered structure bonded to an elastic half-space is investigated. The layers and half-space are assumed to be composed of transversely isotropic materials. By the use of Hankel transforms, the mixed boundary value problem is reduced to an integral equation, which is solved numerically to determine the contact stresses and contact region. The interior displacement and stress fields in both the layer and half-space can be calculated from the inverse Hankel transform used with the solved contact stresses prescribed over the contact region. The stress components, which may be related to the contact failure of coatings, are discussed for various coating thicknesses.

Surface Effects on the Buckling of Piezoelectric Nanobeams

2012 ◽  
Vol 486 ◽  
pp. 519-523 ◽  
Author(s):  
Kai Fa Wang ◽  
Bao Lin Wang
Keyword(s):  
Shear Deformation ◽  
Electric Potential ◽  
Surface Stress ◽  
Surface Elasticity ◽  
Beam Theory ◽  
Surface Effects ◽  
Residual Surface Stress ◽  
Buckling Behavior ◽  
Stress Surface ◽  
Piezoelectric Nanobeam

In this paper, we analyze the influence of surface effects including residual surface stress, surface piezoelectric and surface elasticity on the buckling behavior of piezoelectric nanobeams by using the Timoshenko beam theory and surface piezoelectricity model. The critical electric potential for buckling of piezoelectric nanobeams with different boundary condition is obtained analytically. From the results, it is found that the surface piezoelectric reduces the critical electric potential. However, a positive residual surface stress increases the critical electric potential. In addition, the shear deformation reduces the critical electric potential, and the influence of shear deformation become more significant for a stubby piezoelectric nanobeam.

Surface Effects on Large Deflection of Nanobeams Subjected to a Follower Load

2020 ◽  
Vol 12 (06) ◽  
pp. 2050067
Author(s):  
Yun Xing ◽  
Yi Han ◽  
Hua Liu ◽  
Jialing Yang
Keyword(s):  
Large Deformation ◽  
Surface Stress ◽  
Large Deflection ◽  
Surface Effect ◽  
Surface Elasticity ◽  
Surface Effects ◽  
Surface Residual Stress ◽  
Residual Surface Stress ◽  
Deformation Problem ◽  
Cross Sectional Dimension

As a basic element of the micro/nanodevices, nanobeams have remarkable physical properties and have attracted considerable attention in the previous studies. However, previous publications did not study the large deformation problem of nanobeams under follower loading when the surface effect becomes significant and especially for the influence of surface effect on mechanical behaviors of the nanobeams under follower loading remains unclear. In this paper, we investigated the large deformation behavior of nanobeams subjected to follower loads in consideration of the surface effects. The mechanical model of large deflection of extensible cantilever nanobeams under follower loading is presented in combination with the surface elasticity and residual surface stress, and then a MATLAB program of shooting method with a technique for determining the initial value was developed to solve the problems. The results indicate that the surface effects have an important influence on the large deflection of nanobeams under follower loading: when the surface residual stress is positive, the maximums of displacement in horizontal and vertical directions and the rotation angle of the free end become lager, but the corresponding follower force related to those maximums becomes smaller. When the residual surface stress is negative, the results are the opposite. In addition, the influence of the cross-sectional dimension of the nanobeams under follower loading on surface effects was discussed. This work is beneficial to understand the mechanism of large deformation of nanobeams with surface effects subjected to follower loads, and can also provide inspirations to design advanced nanomaterials and nanoscaled devices.

Rayleigh waves in transversely isotropic thermoelastic diffusive half-space

2008 ◽  
Vol 86 (9) ◽  
pp. 1133-1143 ◽  
Author(s):  
R Kumar ◽  
T Kansal
Keyword(s):  
Half Space ◽  
Rayleigh Waves ◽  
Chemical Potential ◽  
Transversely Isotropic ◽  
Surface Wave Propagation ◽  
Surface Displacements ◽  
Special Cases ◽  
Secular Equations ◽  
The Media ◽  
Straight Lines

The present investigation is devoted to the study of the propagation of Rayleigh waves in a homogeneous, transversely isotropic, thermoelastic diffusive half-space subjected to stress-free, thermally insulated and (or) isothermal, and chemical potential boundary conditions, in the context of the theory of coupled thermoelastic diffusion. Secular equations for surface-wave propagation in the media being considered are derived. The surface-particle paths during the motion are found to be elliptical, but degenerate into straight lines in case where there is no phase difference between the horizontal and vertical components of the surface displacements. The phase velocity; attenuation coefficient; specific loss of energy; and the amplitudes of surface displacements, temperature change, and concentration are computed numerically and presented graphically to depict the anisotropy and diffusion effects. Some special cases of frequency equations are also deduced from the present investigation. PACS Nos.: 62.20.–x, 62.20.D–, 62.20.de, 62.20.dj, 62.20.dq, 62.30.+d, 66.10.C–, 66.10.cd, 66.10.cg, 66.30.–h

POSTBUCKLING OF PIEZOELECTRIC NANOBEAMS WITH SURFACE EFFECTS

2012 ◽  
Vol 04 (02) ◽  
pp. 1250018 ◽  
Author(s):  
YUHANG LI ◽  
CHI CHEN ◽  
BO FANG ◽  
JIAZHONG ZHANG ◽  
JIZHOU SONG
Keyword(s):  
Electric Field ◽  
Significant Role ◽  
Energy Method ◽  
Material Properties ◽  
Surface Stress ◽  
Surface Elasticity ◽  
Surface Effects ◽  
Surface Material ◽  
Residual Surface Stress ◽  
Piezoelectric Nanobeam

Surface effects, including surface elasticity, surface piezoelectricity and residual surface stress, on the postbuckling of piezoelectric nanobeams due to an electric field are investigated using an energy method in this paper. The critical buckling voltage and amplitude are obtained analytically in terms of the bulk and surface material properties and geometric parameters. The results show that surface effects play a significant role in the postbuckling of piezoelectric nanobeams. It is found that the influences of surface piezoelectricity and residual surface stress are more prominent than the surface elasticity. These results might be helpful for designing piezoelectric nanobeam-based devices.

scholarly journals Wave Propagation in a Micropolar Transversely Isotropic Generalized Thermoelastic Half-Space

2014 ◽  
Vol 19 (2) ◽  
pp. 247-257
Author(s):  
R.R. Gupta
Keyword(s):  
Phase Velocity ◽  
Half Space ◽  
Attenuation Coefficient ◽  
Rayleigh Waves ◽  
Generalized Thermoelasticity ◽  
Transversely Isotropic ◽  
Thermoelastic Properties ◽  
Special Cases ◽  
Generalized Thermoelastic ◽  
Phase Velocity And Attenuation

Abstract Rayleigh waves in a half-space exhibiting microplar transversely isotropic generalized thermoelastic properties based on the Lord-Shulman (L-S), Green and Lindsay (G-L) and Coupled thermoelasticty (C-T) theories are discussed. The phase velocity and attenuation coefficient in the previous three different theories have been obtained. A comparison is carried out of the phase velocity, attenuation coefficient and specific loss as calculated from the different theories of generalized thermoelasticity along with the comparison of anisotropy. The amplitudes of displacements, microrotation, stresses and temperature distribution were also obtained. The results obtained and the conclusions drawn are discussed numerically and illustrated graphically. Relevant results of previous investigations are deduced as special cases.

Love Waves in a Piezoelectric Half-Space with an Anisotropic Elastic Layer

2011 ◽  
Vol 117-119 ◽  
pp. 1160-1163 ◽  
Author(s):  
Qian Yang ◽  
Yan Ping Kong ◽  
Jin Xi Liu
Keyword(s):  
Phase Velocity ◽  
Half Space ◽  
Orthotropic Material ◽  
Elastic Layer ◽  
Transversely Isotropic ◽  
Love Waves ◽  
Dispersion Characteristics ◽  
Material Anisotropy ◽  
Symmetric Plane ◽  
Anisotropic Elastic

This work is concerned with the dispersion characteristics of Love waves propagating in a layered structure consisting of an anisotropic elastic layer and a piezoelectric half-space. The layer processes one symmetric plane, while the half-space is transversely isotropic. The explicit dispersion equation is derived. As an example, an inclined orthotropic material is chosen as an elastic layer to reveal the effect of material anisotropy on the dispersion behaviors. The numerical results show that the phase velocity is strongly influenced by the anisotropic degree.

Surface Effects on the Buckling of Nanowires Based on Modified Core-Shell Model

2014 ◽  
Vol 901 ◽  
pp. 3-9
Author(s):  
Hai Yan Yao ◽  
Guo Hong Yun
Keyword(s):  
Critical Load ◽  
Surface Stress ◽  
Surface Elasticity ◽  
Surface Effects ◽  
Core Shell ◽  
Nanowire Diameter ◽  
Residual Surface Stress ◽  
Work Surface ◽  
Effective Elasticity ◽  
S Model

In this work, surface effects including surface elasticity and residual surface stress on the buckling of nanowires are theoretically investigated. Based on modified core-shell (MC-S) model, the effective elasticity incorporating surface elasticity effect of the nanowire is derived, and by using the generalized Young-Laplace equation the residual surface stress is accounted for. The ratio of critical load with and without surface effects are obtained for a nanowire loaded in uniaxial compression. Taking silver (Ag) nanowires as an example, the analyzed results demonstrate that the influence of surface effects on the critical load of buckling becomes more and more significant as the nanowire diameter decreases. Moreover, it is shown that the influence of residual surface stress on the critical load is more prominent than that of surface elasticity.

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