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Analytical closed-form solution to the stress distribution associated with a hole in finite plates subjected to tension has not been obtained yet. Wherefore, a method developed in this paper is based on a Beltrami-Michell methodology analyzing the Kirsch's problem under finite dimensions conditions of both plane stress and plane strain. This aimed ability is achieved by combining the Beltrami-Michell plane equations, isochromatic information on the boundaries only; and the finite difference method into an effectual hybrid method for analyzing rectangular plates of finite width with circular holes. Furthermore, the Beltrami-Michell methodology suggested may be applied on other plate and cut-out forms.
A fractional model generalized from the Zener model is proposed for the prediction of temperature-dependent free recovery behaviors of amorphous shape memory polymers (SMPs). This model differs from the Zener model in that it involves nonlinear differential equations of fractional, not integer, order. The theoretical solution based on this fractional model is utilized to simulate the isothermal and nonisothermal free recovery of an amorphous SMP compared with the one based on the Zener model. The results show a reasonable improvement in the prediction of the strain recovery response of SMP by the fractional calculus method.
This note presents an elasto-capillary model of a cantilever subject to capillary stiction during drying process of removing sacrificial layers in MEMS. Similar to the dynamic analysis of the electrostatic pull-in of electrostatic micro actuators, the cantilever beam tends to be pulled down to the substrate due to the nonlinear capillary force with respect to the gap. The critical one-half gap deformation and the corresponding critical wetting area for pulling down a micro cantilever by surface tension are analytically found herein. The instability situation of a generalized critical deformation for power-law surface force with respect to gap is also predicted accordingly. Some prior MEMS works are exemplified to justify this critical one-half gap deformation for capillary stiction.
The steady-state response to periodic excitation in the linear fractional vibration system was considered by using the fractional derivative operator . First we investigated the response to the harmonic excitation in the form of complex exponential function. The amplitude-frequency relation and phase-frequency relation were derived. The effect of the fractional derivative term on the stiffness and damping was discussed. For the case of periodic excitation, we decompose the periodic excitation into a superposition of harmonic excitations by using the Fourier series, and then utilize the results for harmonic excitations and the principle of superposition, where our adopted tactics avoid appearing a fractional power of negative numbers to overcome the difficulty in fractional case. Finally we demonstrate the proposed method by three numerical examples.
In this paper, a thermoelastic analysis of rotating disks with different thickness profiles made of functionally graded materials (FGMs) subjected to internal pressure is presented. Material properties (except Poisson’s ratio) and disk thickness profile are described by means of two functions namely power and exponential function. A comparative study of thermoelastic analysis is given for material properties and disk thickness profiles. The results of are compared with those obtained by finite element method (FEM) that shows good agreement. The effect of thickness profiles, gradient parameters and angular velocity on the thermoelastic performance of the disk have been studied.
Through silicon via (TSV) is the critical structure for three dimensional (3D) integration, which provides vertical interconnection between stacking dies. In TSV structure, large coefficient differences of thermal expansion exist between silicon substrate, dielectric material, and filled metal. Due to the large thermal mismatch, the high thermal stress occurring at the interface of different materials would result in delamination. Therefore, thermal-mechanical reliability is a key issue for 3D integration. In this study, we investigated the thermal-mechanical stress distribution of TSV under the condition of the accelerated thermal cycling loading by finite element analysis based on a 3D model of TSV structure. Due to the thermal expansion, that the TSV structure squeezed the surface area between TSVs at a high temperature resulted in compressive stresses at the surface area between TSVs. Therefore, a proper distance between the stress-sensitive device and the TSV should be kept. The stress analysis shows that the maximum thermal stress occurs in the outside region of TSV interface and in the annular region of TSV at a high temperature and at a low temperature, respectively. This study helps to obtain a clear thermal stress distribution of TSV and possible failure regions can be determined.
In the present study, a 3-dimensional model was developed to investigate fluid flow in MHD micro-pumps. Initially, 3D governing equations were derived and numerically solved using the finite volume method/SIMPLE algorithm. The case study was a (MHD) micropump built in the year 2000 (channel length: 20mm, channel width: 800μm, channel height: 380μm and electrode length: 4mm). The applied magnetic flux density was 13mT and the electric current was different for various solutions (10 ~ 140mA). The numerical results were verified by experimental and analytical data for several solutions. In addition effects of magnetic field strength, electric current, geometrical parameters of the MHD micropump, electrode length and electrode location on its performance have been investigated. Finally the results has been considered and discussed.
This paper is former part of serial studies to investigate the influence of design parameters of tapered-spool type restrictors on static characteristics of hydrostatic bearing. The flow rates passing restrictors can determine the static characteristics of hydrostatic bearings. In this part an analytical method which includes formulas and solving is utilized to simulate dimensionless flow rate in both single-action and double-action tapered-spool restrictors. The numerical results illustrate the variations of flow rates with respect to the change of pressure and pressure difference, respectively. The findings give that the design parameters of tapered-spool restrictors and the useful range of recess pressure. The following part will depend on this paper results to study load capacity and static stiffness of hydrostatic bearing compensated by tapered-spool restrictor.
This study including two parts investigates the influence of design parameters of tapered-spool restrictors and hydrostatic planar bearing on static characteristics of load capacity and static stiffness. The former part provides guides for the design of single-action and double-action tapered-spool restrictors. This part provides design guides for planar hydrostatic bearing and for matching up with tapered-spool restrictor. The equations of flow continuity are utilized to determine the film thickness for open-type planar bearing and worktable displacement for closed-type planar bearing with respect to the recess pressure, respectively. The load capacity can be obtained by multiplying recess pressure by effective area of bearing pad. Furthermore, the static stiffness can be obtained by differentiating the recess pressure with respect to film thickness or worktable displacement. The finding results give that the usage range of recess pressure, and the availability ranges of design parameters of restrictor and bearing parameters. Which are found for getting the maximum stiffness.
This study presents the influence of heat and mass transfer on peristaltic transport of Finitely Extensible Nonlinear Elastic Peterlin (FENE-P) fluid in the presence of chemical reaction. It is assumed that all the fluid properties, except the density are constant. The Boussinesq approximation which relates density change to temperature and concentration changes is used in formulating buoyancy force terms in the momentum equation. Moreover, we neglect viscous dissipation and include diffusion-thermal (Dufour) and thermal-diffusion (Soret) effects in the present analysis. By the consideration of such important aspects the flow equations become highly nonlinear and coupled. In order to make the problem tractable we have adopted widely used assumptions of long wave length and low Reynolds number. An exact solution of the simplified coupled linear equations for the temperature and concentration has been obtained whereas numerical solution is obtained for dimensionless stream function and pressure gradient. The effects of different parameters on velocity field, temperature and concentration fields and trapping phenomenon are highlighted through various graphs. Numerical integration has been performed to analyze pressure rise per wavelength.
The possibility of cooling enhancement of flat plate heat pipes (FPHPs) by tilting was examined experimentally in this study. All of the FPHPs were made of Al and were partially filled with acetone. They had the same size of 120 mm (length) by 36 mm (width) by 2.5 mm (thickness) and the same liquid filling ratio of 25.1%. The effects of six tilting angles of -30°, -15°, -10°, 0°, 45°, and 90° were explored. The results showed that the thermal resistance decreased and the effective thermal conductivity increased when the tilting angle was increased. By increasing the tilting angle from 0° to 45° and further to 90°, the maximum effective thermal conductivity increased by a factor of 1.205 from 4561 W/mK to 5497 W/mK and of 1.212 to 5530 W/mK, respectively. The corresponding maximum heat transport capability increased by a factor of 2.89 from 39.8 W to 115 W and of 3.27 to 130 W. Hence, by proper tilting into positve angles, cooling enhancement of the FPHPs can be greatly achieved.
The journal bearings which are designed for heavy-duty operations could experience different lubricant density due to high bearing loads. In the present work, hydrodynamic behaviour of finite length journal bearings under laminar and isoviscous flow with variable density are investigated. For this purpose, three-dimensional continuity and momentum equations along with a proper density-pressure relation are solved numerically, using CFD technique. Also, an appropriate cavitation model based on mass conservation is involved in the computation. Because of complex geometry of journal bearing, a conformal mapping is employed to generate an orthogonal grid and the governing equations are transformed in the computational domain. Since the degree of oil compressibility can be depended to the type of lubricant, typical mineral and synthetic oils treatments are modelled, separately. Results indicate that the oil compressibility effect leads to increasing load carrying capacity such that this increase is slightly more for the synthetic oil.
In the present paper the propagation of torsional surface waves is discussed in an inhomogeneous elastic layer lying over a fluid saturated porous half space. The inhomogeneity in rigidity and density in the inhomogeneous layer plays an important role in the propagation of torsional surface waves. The presence of fluid in the pores diminishes the velocity. Further, it is seen that if the layer becomes homogeneous and the porous half space is replaced by a homogeneous half space, the velocity of the torsional surface waves coincides with that of Love wave. The effect of inhomogeneity factors and porosity factor on the phase velocity of torsional surface wave is delimitated by means of graphs.