M. Shaat's blog
https://imechanica.org/blog/34410
enPull-in instability of multi-phase nanocrystalline silicon beams under distributed electrostatic force
https://imechanica.org/node/18334
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/10500">actuated beams; nano-structured materials; nanocrystalline silicon; pull-in voltage; modified couple stress theory</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p class="MsoNormalCxSpFirst"><span>The effects of the material structure on the pull-in instability of nano-actuated beams made of nanocrystalline silicon (Nc-Si) and subjected to a distributed electrostatic force are investigated. Nc-Si is represented as a multi-phase material composed of nano-sized grains, nano voids, and an amorphous-like interface to consider the effects of the interface, grain size, porosity, and the inhomogeneities surface energies on the elastic properties of the composite material. To this end, a size-dependent micromechanical model is developed for multi-phase materials considering the inhomogeneities surface energy effects. An atomic lattice model is also proposed to estimate the elastic modulus of the interface of NcMs. Due to the intensive decrease in the beam’s size, the effects of the grain rotations on the beam strain energy and hence on its rigidity are captured and represented using the modified couple stress theory. Considering all these effects and using Euler-Bernoulli beam theory, the governing equation is derived. A finite difference-based solution is used to determine the pull-in voltage of the actuated beams. A parametric study is then performed to reveal the effects of the porosity, interface, surface energy, and grain rotations on the pull-in instability behavior of actuated nano-beams. </span></p>
<p><span><a href="http://www.sciencedirect.com/science/article/pii/S0020722515000257">http://www.sciencedirect.com/science/article/pii/S0020722515000257</a></span></p>
<p> </p>
</div></div></div>Wed, 20 May 2015 06:43:08 +0000M. Shaat18334 at https://imechanica.orghttps://imechanica.org/node/18334#commentshttps://imechanica.org/crss/node/18334Modeling of mechanical resonators used for nanocrystalline materials characterization and disease diagnosis of HIVs
https://imechanica.org/node/18333
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/10497">Bio-mass sensor</a></div><div class="field-item odd"><a href="/taxonomy/term/7031">material characterization</a></div><div class="field-item even"><a href="/taxonomy/term/10498">disease diagnosis</a></div><div class="field-item odd"><a href="/taxonomy/term/10499">distributed-parameter model</a></div><div class="field-item even"><a href="/taxonomy/term/7481">Frequency Shift</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p class="MsoNormalCxSpFirst"><span><span>The modeling and performance of mechanical resonators used for mass detection of bio-cells, nanocrystalline materials characterization, and disease diagnosis of human immune-viruses (HIVs) are investigated. To simulate the real behavior of these mechanical resonators, a novel distributed-parameter model based on Euler-Bernoulli beam theory is developed. This model is equipped with a micromechanical model and an atomic lattice model to capture the inhomogeneity nature of the material microstructure. Compared with lumped-parameter model predictions, the results show that this developed model best fits with the real behavior of the mechanical resonators when detecting the mass of vaccinia virus. In terms of material characterization, the developed model gives very good estimations for the densities and Young’s moduli of the grain boundary of both the nanocrystalline silicon and nanocrystalline diamond. For disease diagnosis, it is shown that the number of human immune-deficiency virus particles in a liquid sample can be easily detected when using the proposed model. The results also show that the developed model is beneficial and can be used to design mechanical resonators made of nanocrystalline materials with the ability to control the resonators’ sizes and the material structure.</span></span></p>
<p class="MsoNormalCxSpFirst"><span><span>Microsyst Technol </span></span><span>DOI 10.1007/s00542-015-2421-y</span></p>
<p class="MsoNormalCxSpFirst"> </p>
</div></div></div>Wed, 20 May 2015 06:41:12 +0000M. Shaat18333 at https://imechanica.orghttps://imechanica.org/node/18333#commentshttps://imechanica.org/crss/node/18333Effects of grain size and microstructure rigid rotations on the bending behavior of nanocrystalline material beams
https://imechanica.org/node/18332
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/1189">nanocrystalline materials</a></div><div class="field-item odd"><a href="/taxonomy/term/10495">micro/nano beams</a></div><div class="field-item even"><a href="/taxonomy/term/659">nanostructured materials</a></div><div class="field-item odd"><a href="/taxonomy/term/7831">couple stress theory</a></div><div class="field-item even"><a href="/taxonomy/term/10496">grain size effect</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p class="MsoNormalCxSpFirst"><span>Due to the intensive decrease in grain sizes of nanocrystalline materials (NcMs), a large volume fraction of atoms reside in the interface regions between crystals forming an atom-cloud phase with a distinct atomic structure. Moreover, the surface to volume ratio of the grain increases, thus its surface energy will significantly affect the mechanical properties of NcMs. </span></p>
<p> </p>
<p class="MsoNormalCxSpMiddle"><span>Recently, nanocrystalline material (NcM) beams have shown effective performances in MEMS and NEMS applications. In the present paper, effects of the inhomogeneity nature of NcMs in addition to effects of the microstructure rigid rotations on the bending behavior of NcM beams are investigated. At first, a grain size-dependent multi-phase representative volume element (RVE) is proposed to detect the effective elastic properties of NcM beams considering the grain surface energy effects. Then, the modified couple stress theory is employed to capture the microstructure rigid rotation effects on micro/nano Euler-Bernoulli beams.<span> In this sense, the </span>bending rigidity of the beam is adopted for the grain size effects and the microstructure rigid rotation effects. </span></p>
<p class="MsoNormalCxSpMiddle"><span><span><a href="http://www.sciencedirect.com/science/article/pii/S0020740315000624">http://www.sciencedirect.com/science/article/pii/S0020740315000624</a></span></span></p>
<p class="MsoNormalCxSpMiddle"> </p>
</div></div></div>Wed, 20 May 2015 06:36:24 +0000M. Shaat18332 at https://imechanica.orghttps://imechanica.org/node/18332#commentshttps://imechanica.org/crss/node/18332Iterative nonlocal elasticity for Kirchhoff plates
https://imechanica.org/node/18331
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/10494">nonlocal elasticity; iterative solution; Kirchhoff plates; micro/nano plates; micro/nano beams</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p class="MsoNormalCxSpFirst"><span>Recently, the nonlocal elasticity theories have been used in studying the different behaviors of micro/nanostructures. However, there is a complicity in applying the natural boundary conditions in the context of the nonlocal differential elasticity models. Also, the nonlocal integral elasticity could provide a suitable remedy for this type of problems but with paying highly computational efforts.</span></p>
<p> </p>
<p class="MsoNormalCxSpMiddle"><span>In the present work, an iterative-based nonlocal elasticity model is proposed to study the bending behavior of nano-sized Kirchhoff plates, having both essential and natural boundary conditions with less computational efforts compared with conventional nonlocal elasticity methods. The proposed iterative-based nonlocal model is based up on an iterative procedure of the type local prediction/nonlocal correction, in which the nonlocal field is diffused to the local field by imposed-like correction strain energy. The most distinguished feature of this iterative-b<span>ased model is that in each iterative step the local field problem is solved and corrected for the nonlocal field. Therefore, the local boundary conditions are applied, in each iterative step, instead of the nonlocal ones resolving the troubles exist in most of other nonlocal solutions</span>.</span></p>
<p class="MsoNormalCxSpMiddle"> </p>
<p class="MsoNormalCxSpMiddle"><span><span><a href="http://www.sciencedirect.com/science/article/pii/S002074031400366X">http://www.sciencedirect.com/science/article/pii/S002074031400366X</a></span></span></p>
<p class="MsoNormalCxSpMiddle"> </p>
</div></div></div>Wed, 20 May 2015 06:33:54 +0000M. Shaat18331 at https://imechanica.orghttps://imechanica.org/node/18331#commentshttps://imechanica.org/crss/node/18331Physical and Mathematical Representations of Couple Stress Effects on Micro/Nanosolids
https://imechanica.org/node/18330
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/10493">Couple–stress; modified couple–stress; consistent couple–stress; microcontinuum mechanics; linear elasticity.</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>In the present paper, for linear elastic materials, effects of couple stresses on micro/nanosolids are physically discussed and mathematically represented in the context of the classical, the modified and the consistent couple–stress theories. Then, an evaluation is provided showing the validity and the limit of applicability of each one of these theories. At first, the possible couple stress effects on mechanics of particles and on continuum mechanics are represented. Then, a reasoning comparison with examples is performed to discuss and evaluate the way that each one of these theories represents the couple stress effects.</p>
<p>In the context of the classical couple–stress theory, two higher-order material constants are introduced in addition to the conventional ones to capture the microstructure rigid rotation effects. Recently, two alternative theories, the modified couple–stress and the consistent couple–stress theories, with only one additional material constant are introduced with contradictory points of view. Authors of these two alternative theories gave apparently strong motivations for their opposed points of view. Therefore, through the present paper, it will be convenient to analyze the essential points of view based on which these alternative theories are proposed since they lead to exactly opposed conclusions. Thus their essential points of view are discussed and evaluated showing their consistency with the fundamental concepts of the couple stress effects. </p>
<p>It has been shown that the scientific bases of these two alternative theories are not consistent with the representation of the couple–stress effects on micro/nanocontinua. Based on discussions and results through the paper, both the modified theory and the consistent theory represent, only, simplifications for the classical couple–stress theory but they did not able to well represent the possible effects of couple stresses and they are limited for only two categories of linear elastic materials problems. This demolishes the scientific points of view based on which the two theories are proposed.</p>
<p> </p>
</div></div></div>Wed, 20 May 2015 06:29:47 +0000M. Shaat18330 at https://imechanica.orghttps://imechanica.org/node/18330#commentshttps://imechanica.org/crss/node/18330Nonlinear Size-Dependent Finite Element Analysis of Functionally Graded Elastic Tiny-Bodies
https://imechanica.org/node/14855
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>
This paper is now in Press and available on line at the Intenational Journal of Mechanical Sciences.
</p>
<p>
<span>In this paper, a nonlinear size-dependent finite element model<br />
incorporating surface energy effects is developed to study the mechanical<br />
behavior of tiny elastic functionally graded (FG) bodies. Here the classical<br />
elasticity theory is modified to incorporate the surface energy effects. </span><span>Most of previous studies assumed that the<br />
surface energy depends only on the 2D symmetric infinitesimal surface strains<br />
and neglects the second-order products of surface strains/displacement<br />
gradients. These descriptions assume a small strain deformation of the surface<br />
and neglect the pre-strain that is, already, developed on the surface – before<br />
loading – due the pre-tension stress</span><span><br /></span><span>. Here in this paper, the pre-strain is considered which forces the<br />
surface to a state of large strain after loading instead of small strain. In<br />
this sense, in the presence of initial surface tension, the theory of surface<br />
elasticity is a hybrid formulation characterized by linearized bulk elastic<br />
material and second order finite deformation of the surface. In the proposed<br />
finite element model, <span>the surface energy effect is<br />
taken into account in the derivation of the element stiffness matrix for the<br />
material elements located very close to the boundary surface. </span>The<br />
proposed model is then used to study the effects of surface energy,<span> </span><span>including</span><br />
the 2nd order displacement gradient<span>,</span> on the mechanical behavior of plane-strain functionally<br />
graded elastic body.</span>
</p>
<p>
The paper is available at: <a href="http://www.sciencedirect.com/science/article/pii/S0020740313001689">http://www.sciencedirect.com/science/article/pii/S0020740313001689</a>
</p>
<p>
<a href="http://www.sciencedirect.com/science/article/pii/S0020740313001689"></a>M. Shaat
</p>
<p>Best regards,<br />
-------------------------------------------------------<br />
Mohammed Ibrahim Shaat (M.Shaat) <br />
Research Assistant<br />
Mechanical Engineering Department, Zagazig University, Zagazig 44511, Egypt <br />
E-Mail: <a href="mailto:ShaatScience@yahoo.com">ShaatScience@yahoo.com</a> <br />
Tel: +20 0122 2232469</p>
<p>My Citations: <a id="yui_3_7_2_1_1371552951173_9533" rel="nofollow" href="http://scholar.google.com/citations?user=n2PUAwcAAAAJ" target="_blank">http://scholar.google.com/citations?user=n2PUAwcAAAAJ</a>.</p>
<p>
<span> </span><a rel="nofollow" href="http://www.scopus.com/authid/detail.url?authorId=55553742901" target="_blank">http://www.scopus.com/authid/detail.url?authorId=55553742901</a><span>.</span>
</p>
</div></div></div>Tue, 18 Jun 2013 13:58:01 +0000M. Shaat14855 at https://imechanica.orghttps://imechanica.org/node/14855#commentshttps://imechanica.org/crss/node/14855Finite Element Analysis of Functionally Graded Nano-Scale Films
https://imechanica.org/node/14854
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>
This paper is now in press at Finite Element Analysis and Design International Journal.
</p>
<p>
<span>In<br />
this paper, a size-dependent finite element model, for Mindlin plate theory<br />
accounting for the position of the neutral plane for continuum incorporating<br />
surface energy effect, is proposed to study the bending behavior of ultra-thin<br />
functionally graded (FG) plates.</span><span> </span><span>The<br />
size-dependent mechanical response is very important while the plate thickness<br />
reduces to micro/nano scales. <span>The classical finite<br />
element model is adopted to allow insertion of the surface energy into the<br />
total energy of the plate. </span>Bulk stresses on the surfaces are required to<br />
satisfy the surface balance conditions involving surface stresses. Therefore,<br />
unlike the classical continuum plate models, the bulk transverse normal stress<br />
is preserved here. <span>Moreover, unlike most of previous<br />
studies in the literature, the exact neutral plane position is pre-determined<br />
and considered for FG plates. </span>A series of continuum governing<br />
differential equations which include surface energy and neutral plane position<br />
effects are derived. A comparison between the continuum analysis of FG<br />
ultra-thin plates with and without incorporating surface energy effects is<br />
presented.</span>
</p>
<p>
M. Shaat
</p>
<p>Best regards,<br />
-------------------------------------------------------<br />
Mohammed Ibrahim Shaat (M.Shaat) <br />
Research Assistant<br />
Mechanical Engineering Department, Zagazig University, Zagazig 44511, Egypt <br />
E-Mail: <a href="mailto:ShaatScience@yahoo.com">ShaatScience@yahoo.com</a> <br />
Tel: +20 0122 2232469</p>
<p>My Citations: <a id="yui_3_7_2_1_1371552951173_9533" rel="nofollow" href="http://scholar.google.com/citations?user=n2PUAwcAAAAJ" target="_blank">http://scholar.google.com/citations?user=n2PUAwcAAAAJ</a>.</p>
<p>
<span> </span><a rel="nofollow" href="http://www.scopus.com/authid/detail.url?authorId=55553742901" target="_blank">http://www.scopus.com/authid/detail.url?authorId=55553742901</a><span>.</span>
</p>
</div></div></div>Tue, 18 Jun 2013 13:48:57 +0000M. Shaat14854 at https://imechanica.orghttps://imechanica.org/node/14854#commentshttps://imechanica.org/crss/node/14854Nonlinear Size-Dependent Analysis of Elastic Tiny-Bodies
https://imechanica.org/node/14310
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p class="MsoNormalCxSpFirst">
<span>Many researchers have studied the effect of surface energy on the<br />
elastic behavior of nano-structural elements based on Gurtin and Murdoch surface<br />
model. Many of them, however, assumed that the surface energy depends only on<br />
the 2D symmetric infinitesimal surface strains and neglects the second-order<br />
products of surface strains/displacement gradients. Moreover, there are some<br />
researchers assumed that the surface energy is independent on infinitesimal<br />
rotation tensor and neglected all rotation </span><span>ω</span><span><br /></span><span>-related terms. These<br />
previous descriptions of the surface stresses lack an important key point.<br />
These descriptions assume a small strain deformation of the surface and neglect<br />
the pre-strain that is, already, developed on the surface – before loading –<br />
due the pre-tension stress </span><span></span><span>σ</span><span>0</span><span><br /></span><span>. Consequently, considering the pre-strain, which is associated with the<br />
deformation of the surface from the initial surface area to the deformed<br />
surface area before loading, forces the surface to a state of large strain<br />
after loading instead of small strain. Consequently, the accurate description<br />
of surface elasticity is to consider the surface pre-strain, so a large strain<br />
is assumed for surface strains while the bulk remain under small strain. This<br />
forces us to exploit the Lagrangian surface description to consider the surface<br />
pre-strain. </span>
</p>
<p>
</p>
</div></div></div>Fri, 08 Mar 2013 13:06:13 +0000M. Shaat14310 at https://imechanica.orghttps://imechanica.org/node/14310#commentshttps://imechanica.org/crss/node/14310Size-dependent analysis of functionally graded ultra-thin films
https://imechanica.org/node/13625
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/8167">functionally graded plates; surface energy effect; ultra-thin films; size-dependent analysis; finite element analysis; nano plates</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p align="justify">
</p><p>This paper is accepted at Structural Engineering and Mechanics; <em>An international journal</em>.</p>
<p>In this paper, the first-order shear deformation theory (FSDT) (Mindlin) for continuum incorporating surface energy is exploited to study the static behavior of ultra-thin functionally graded (FG) plates. The size-dependent mechanical response is very important while the plate thickness reduces to micro/nano scales. Bulk stresses on the surfaces are required to satisfy the surface balance conditions involving surface stresses. Unlike the classical continuum plate models, the bulk transverse normal stress is preserved here. By incorporating the surface energies into the principle of minimum potential energy, a series of continuum governing differential equations which include intrinsic length scales are derived. The modifications over the classical continuum stiffness are also obtained. To illustrate the application of the theory, simply supported micro/nano scaled rectangular films subjected to a transverse mechanical load are investigated. Numerical examples are presented to present the effects of surface energies on the behavior of functionally graded (FG) film, whose effective elastic moduli of its bulk material are represented by the simple power law. The proposed model is then used for a comparison between the continuum analysis of FG ultra-thin plates with and without incorporating surface effects. Also, the transverse shear strain effect is studied by a comparison between the FG plate behavior based on Kirchhoff and Mindlin assumptions. In our analysis the residual surface tension under unstrained conditions and the surface Lame constants are expected to be the same for the upper and lower surfaces of the FG plate. The proposed model is verified by previous work.</p>
</div></div></div>Fri, 09 Nov 2012 17:34:08 +0000M. Shaat13625 at https://imechanica.orghttps://imechanica.org/node/13625#commentshttps://imechanica.org/crss/node/13625Effect of Surface Energy on Mechanical Behaviour of Nano Structural Elements
https://imechanica.org/node/13308
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/597">mechanics of materials</a></div><div class="field-item odd"><a href="/taxonomy/term/7920">Size-dependent analysis</a></div><div class="field-item even"><a href="/taxonomy/term/7998">Nano structural elements</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p class="MsoNormalCxSpFirst">
<span>Extremely small size of nano-structures such as beams, sheets and<br />
plates, which are commonly used as components in Nanoelectromechanical Systems<br />
(NEMS), presents a significant challenge to the researchers of nano-mechanics.<br />
Several studies have been developed on the mechanical behavior of nano-sized<br />
bars, tubes, sheets and plates. The results of these studies show that the<br />
elastic modulii of such nano-structural elements depend on their size.<br />
Unfortunately, classical elasticity lacks an intrinsic length scale and thus<br />
cannot be used to model the size effect. Atomistic simulation, however it is<br />
very powerful, needs intensive computations.</span>
</p>
<p class="MsoNormalCxSpMiddle">
<span>All physical theories possess a certain domain of applicability outside<br />
which they fail to predict the physical phenomena with reasonable accuracy.<br />
While the boundaries of these domains are not known precisely, often the<br />
failure of a given mathematical model is indicated by its prediction that<br />
deviate considerably from experimental results or obviously displayed<br />
mathematical singularities. The domain of applicability of a theory is a<br />
formation of some internal characteristic length and time scales of the media<br />
for which it is constructed. When these scales are sufficiently small compared<br />
to the corresponding external scales then the classical field theories give<br />
successful results; otherwise they fail to apply. For each theory, the domain<br />
of application defines the level of the considered constituents and the<br />
appropriate processes of interactions between these constituents. The<br />
components below this level would not be accounted for and consequently, the<br />
interaction process between these components and the other ones would be<br />
avoided also. As an obvious example, for a macro-scale body the surface<br />
component of the body is very small relative to the volume of the solid. Thus,<br />
we can neglect the surface, as component of the continuum and focus our<br />
attention only on the bulk solid. On the contrary, for a tiny body the surface<br />
is very comparable to the bulk volume. Therefore, it should be taken into<br />
consideration and deserves to pay a considerable attention to its<br />
characteristics and the processes of interactions with the bulk of the<br />
continuum. </span>
</p>
<p class="MsoNormalCxSpMiddle">
<span>The same issue can be observed when we study the mechanical deformation<br />
of a macro –scale elastic continuum. In this case, it will be sufficient to<br />
investigate the behavior on the level of particles as already happened in the<br />
classical continuum mechanics theories. On the contrary, for nano-scale systems<br />
we have to deal with the atomic discrete nature of the system. Thus, we have to<br />
concern primarily with the level of microstructure elements and investigate<br />
different interaction processes between those elements.</span>
</p>
<p class="MsoNormalCxSpMiddle">
<span>Unfortunately, classical continuum mechanics is explicitly designed to<br />
be size-independent which may reflect the breakdown of classical continuum<br />
mechanics at nano-scale sizes. One of the physical reasons for the breakdown of<br />
classical continuum mechanics at nano-scale sizes is the surface effects.</span>
</p>
<p class="MsoNormalCxSpMiddle">
<span>Atoms at a free surface experience a different local environment than do<br />
atoms in the bulk of a material. As a result, the energy associated with these<br />
atoms will be different from that of the atoms in the bulk. The excess energy<br />
associated with surface atoms is called surface free energy. In classical<br />
continuum mechanics, such surface free energy is typically neglected because it<br />
is associated with only a few layers of atoms near the surface and the ratio of<br />
the volume occupied by the surface atoms and the total volume of material of<br />
interest is extremely small. However, for ultra-thin films, the thickness of<br />
the films reduces to micro/nano scales; hence the effects of surface energy<br />
become significant and need more interest.</span>
</p>
</div></div></div>Sun, 30 Sep 2012 17:40:43 +0000M. Shaat13308 at https://imechanica.orghttps://imechanica.org/node/13308#commentshttps://imechanica.org/crss/node/13308A first-order shear deformation finite element model for analysis of laminated composite and the equivalent FG plates
https://imechanica.org/node/13136
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>In this paper, the first-order shear deformation plate (FSDT) model is exploited to investigate the mechanical behavior of laminated composite and functional graded plates. Three approaches are developed to transform the laminated composite plate, with stepped material properties, to an equivalent functionally graded (FG) plate with a continuous property function across the plate thickness. Such transformations are used to determine the details of a functional graded plate equivalent to the original laminated one. In addition it may provide an easy and efficient way to investigate the behavior of multilayer composite plates, with direct and less computational efforts. A comparative study has been developed to compare the effectiveness of the three proposed transformation procedures.<br />
Available online at: <a href="http://www.sciencedirect.com/science/article/pii/S2090447911000128">http://www.sciencedirect.com/science/article/pii/S2090447911000128</a>.</p>
</div></div></div>Fri, 14 Sep 2012 17:57:11 +0000M. Shaat13136 at https://imechanica.orghttps://imechanica.org/node/13136#commentshttps://imechanica.org/crss/node/13136Bending Behavior of Functionally Graded Plates; Including Surface Effects
https://imechanica.org/node/13103
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>
In this research study, Mindlin plate theory, accounting for the neutral plane position, of laminated composite and functionally graded (FG) plates is formulated for continuums subjected to thermo-mechanical loads with/without incorporating surface energy effects. The size-dependent mechanical response is very important while the plate thickness reduces to micro/nano scales. The mechanical response of ultra-thin FG plates is studied based on Gurtin and Murdoch surface conditions. A series of continuum governing differential equations which include surface energy and neutral plane position effects are derived. The obtained modifications over the classical Mindlin model are involved at both equivalent material stiffnesses and the governing equations. To illustrate application of the model, a simply supported laminated composite and functionally graded plates of multi-scales subjected to a transverse mechanical load and thermal excitation are discussed. A finite element model is presented to clarify the effects of constituent material properties and surface energies on the behavior of FG plates, whose effective elastic moduli are represented by the simple power law. The proposed finite element model is then used for a comparison between the continuum analysis of FG ultra-thin plates with and without incorporating surface effects. A parametric study is also presented to clarify the effects of plate dimensions, mechanical and thermal material properties on the behavior of the FG plate.
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Available online at:<br /><a href="http://www.lap-publishing.com/catalog/details/store/gb/book/978-3-659-20379-4/bending-behavior-of-functionally-graded-plates?search=functionally%20graded">www.lap-publishing.com/catalog/details/store/gb/book/978-3-659-20379-4/b...</a>.
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</div></div></div>Sun, 09 Sep 2012 22:00:50 +0000M. Shaat13103 at https://imechanica.orghttps://imechanica.org/node/13103#commentshttps://imechanica.org/crss/node/13103