• Advances in concrete construction
• /
• v.15 no.5
• /
• pp.349-358
• /
• 2023

Aim of this work is investigating effect of thickness-stretching formulation on the quasi three-dimensional analysis of micro plate based on a thickness-stretched and shear deformable model through principle of virtual work and micro-scale dependent constitutive relations. Governing differential equations are derived in terms of five unknown functions and the analytical solution is derived using Navier's technique. To explore effect of thickness stretching model on the static results, a comparison between the results with and without thickness stretching effect is presented.

• Advances in nano research
• /
• v.8 no.4
• /
• pp.283-292
• /
• 2020

In the present research, differential quadrature (DQ) method has been utilized for investigating free vibrations of porous functionally graded (FG) micro/nano beams in thermal environments. The exact location of neutral axis in FG material has been assumed where the material properties are described via porosity-dependent power-law functions. A scale factor related to couple stresses has been employed for describing size effect. The formulation of scale-dependent beam has been presented based upon a refined beam theory needless of shear correction factors. The governing equations and the associated boundary conditions have been established via Hamilton's rule and then they are solved implementing DQ method. Several graphs are provided which emphasis on the role of porosity dispersion type, porosity volume, temperature variation, scale factor and FG material index on free vibrational behavior of small scale beams.

• Wind and Structures
• /
• v.26 no.4
• /
• pp.205-214
• /
• 2018

In this paper, the thermo-mechanical buckling characteristics of functionally graded (FG) size-dependent Timoshenko nanobeams subjected to an in-plane thermal loading are investigated by presenting a Navier type solution for the first time. Material properties of FG nanobeam are supposed to vary continuously along the thickness according to the power-law form and the material properties are assumed to be temperature-dependent. The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen. The nonlocal governing equations are derived based on Timoshenko beam theory through Hamilton's principle and they are solved applying analytical solution. According to the numerical results, it is revealed that the proposed modeling can provide accurate critical buckling temperature results of the FG nanobeams as compared to some cases in the literature. The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of the several parameters such as material distribution profile, small scale effects and aspect ratio on the critical buckling temperature of the FG nanobeams in detail. It is explicitly shown that the thermal buckling of a FG nanobeams is significantly influenced by these effects. Numerical results are presented to serve as benchmarks for future analyses of FG nanobeams.

• Advances in aircraft and spacecraft science
• /
• v.5 no.1
• /
• pp.141-164
• /
• 2018

In this paper, the thermal effect on buckling and free vibration characteristics of functionally graded (FG) size-dependent Timoshenko nanobeams subjected to an in-plane thermal loading are investigated by presenting a Navier type solution for the first time. Material properties of FG nanobeam are supposed to vary continuously along the thickness according to the power-law form and the material properties are assumed to be temperature-dependent. The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen. The nonlocal equations of motion are derived based on Timoshenko beam theory through Hamilton's principle and they are solved applying analytical solution. According to the numerical results, it is revealed that the proposed modeling can provide accurate frequency results of the FG nanobeams as compared to some cases in the literature. The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of the several parameters such as thermal effect, material distribution profile, small scale effects, aspect ratio and mode number on the critical buckling temperature and normalized natural frequencies of the temperature-dependent FG nanobeams in detail. It is explicitly shown that the thermal buckling and vibration behaviour of a FG nanobeams is significantly influenced by these effects. Numerical results are presented to serve as benchmarks for future analyses of FG nanobeams.

• Structural Engineering and Mechanics
• /
• v.76 no.1
• /
• pp.27-56
• /
• 2020

In this paper, the deflection and buckling analyses of porous nano-composite piezoelectric plate reinforced by carbon nanotube (CNT) are studied. The equations of equilibrium using energy method are derived from principle of minimum total potential energy. In the research, the non-local strain gradient theory is employed to consider size dependent effect for porous nanocomposite piezoelectric plate. The effects of material length scale parameter, Eringen's nonlocal parameter, porosity coefficient and aspect ratio on the deflection and critical buckling load are investigated. The results indicate that the effect of porosity coefficient on the increase of the deflection and critical buckling load is greatly higher than the other parameters effect, and size effect including nonlocal parameter and the material length scale parameter have a lower effect on the deflection increase with respect to the porosity coefficient, respectively and vice versa for critical buckling load. Porous nanocomposites are used in various engineering fields such as aerospace, medical industries and water refinery.

• Structural Engineering and Mechanics
• /
• v.71 no.1
• /
• pp.37-43
• /
• 2019

This paper studies application of modified couple stress theory and first order shear deformation theory to magneto-electro-mechanical vibration analysis of three-layered size-dependent curved beam. The curved beam is resting on Pasternak's foundation and is subjected to mechanical, magnetic and electrical loads. Size dependency is accounted by employing a small scale parameter based on modified couple stress theory. The magneto-electro-mechanical preloads are accounted in governing equations to obtain natural frequencies in terms of initial magneto-electro-mechanical loads. The analytical approach is applied to investigate the effect of some important parameters such as opening angle, initial electric and magnetic potentials, small scale parameter, and some geometric dimensionless parameters and direct and shear parameters of elastic foundation on the magneto-electro-elastic vibration responses.

• Advances in materials Research
• /
• v.7 no.1
• /
• pp.1-16
• /
• 2018

Thermal bifurcation buckling behavior of fully clamped Euler-Bernoulli nanobeam built of a through thickness functionally graded material is explored for the first time in the present paper. The variation of material properties of the FG nanobeam are graded along the thickness by a power-law form. Temperature dependency of the material constituents is also taken into consideration. Eringen's nonlocal elasticity model is employed to define the small-scale effects and long-range connections between the particles. The stability equations of the thermally induced FG nanobeam are derived via the principal of the minimum total potential energy and solved analytically for clamped boundary conditions, which lead for more accurate results. Moreover, the obtained buckling loads of FG nanobeam are validated with those existing works. Parametric studies are performed to examine the influences of various parameters such as power-law exponent, small scale effects and beam thickness on the critical thermal buckling load of the temperature-dependent FG nanobeams.

• Proceedings of the Korean Society of Precision Engineering Conference
• /
• 2005.06a
• /
• pp.619-622
• /
• 2005

Purpose of this study is to investigate the size-dependent mechanical properties in micron scale medium. Theories such as the couple stress theory and strain gradient theory explain that the deformation in the micron scale is dependent upon the size of the medium. Specimens of the cantilever type, bridge type and paddle type beam that have thickness of 900, 1000 and 1200 nm and width of 10, 20, 30 and $50{\mu}m$ were fabricated by the MEMS technique. We carried out the bending and torsion test to measure the mechanical properties such as the young's modulus, yield strength and torsional rigidity using the AFM(Atomic Force Microscopy).

• 한국지구물리탐사학회:학술대회논문집
• /
• 2003.11a
• /
• pp.156-161
• /
• 2003

Mechanical behavior of rock joints usually can be characterized by small-scale laboratory shear tests due to economical and technical limitations, but their applicability to the behaviour of rock mass has been always questioned by a number of researchers because of scale effect. Though there have been several researches regarding the scale effect, it has been a controversial problem how to apply the result of small-scale laboratory shear test directly to field design from different conclusions among researchers. In order to grasp the trend of scale effect of shear behavior, a series of direct shear tests on replicas of natural rock joint surfaces made of gypsum cement with different size and roughness were conducted and analyzed. Result showed that as the size of the specimen increased, average peak shear displacement increased, but average shear stiffness and average peak dilation angle decreased. As for the dependency of scale on shear strength, the degree of scale effect was dependent on normal stress and roughness of rock joint. For the condition of low normal stress and high roughness, decrease of average peak shear strength with increasing size of joint was evident.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.19 no.9
• /
• pp.2237-2248
• /
• 1995

In incompressible flow which has multi-length scale, it has a very important effect which dependent variables are used for adaptive grid generation. Among many length scales in incompressible flow, the dependent variables used for the adaptive grid generation should be able to represent the feature of the concerned system. In this paper, by using vorticity and stream function, in addition to velocity components, the smoother and more stable grid generation is possible and these four flow properties represent each scale. The adaptive grid generation for a lid-driven cavity flow with $N_{re}$ =3200 using four flow properties such as velocity components, vorticity, stream function is performed, and the usefulness of using vorticity and stream function as the indicator for adaptive grid generation is shown.