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2011 Vol. 32, No. 6
Published:
论文
541
Size-dependent Pull-in Voltage of Electrostatically Actuated MEMS
The size-dependent pull-in voltage of electrostatically actuated MEMS is studied using strain gradient elasticity theory. The microbeam model and microplate model are derived respectively via the principle of minimum potential energy. The generalized differential quadrature method and pseudo arclength algorithm are used to solve the high-order PDEs. It is shown that the normalized pull-in voltage predicted by the new models increases nonlinearly with the decrease of the structure thickness, exhibiting size effect (and the size effect is particularly strong when the structural thickness is on the same order of the characteristic material length scale parameter); while the corresponding classical models do not exhibit such a size effect. The two new models may be regarded as extensions of the corresponding classical ones. This study may be helpful to characterize the mechanical properties of small sized MEMS, or guide the design of microstructures for a wide range of potential applications.
2011 Vol. 32 (6): 541-548 [
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536
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549
The Quasi-static Compressive Behaviors of an EPS Foam Particle and an Assembly of Many Enclosed EPS Particles
In this paper, we examined experimentally the quasi-static uniaxial compressive behaviors of a single EPS foam particle and an assembly of many enclosed EPS particles at different loading rates. As a representative light-weight closed-cell foam, the mechanical behavior of EPS particle is strongly influenced by the gases enclosed in the cell. The contribution of the gas inside the foam cells is analyzed in this paper. For a single foam particle, the contribution of the internal gas on its compressive behavior can be described using a gas model proposed by Ashby et al. A constitutive relationship, considering both effects of the inter gas and the loading rate, is proposed for the compressive behavior of a single EPS particle. For an assembly of enclosed EPS particles, it is shown that both the internal gas and the inter-particle gas affect the mechanical behavior of the assembly. A constitutive relationship using the apparent density of the assembly as an internal variable is proposed for describing the mechanical behavior of the assembly.
2011 Vol. 32 (6): 549-556 [
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473
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514
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557
ANALYSIS OF SLIP-BAND TRACE ON SPECIMEN SURFACE OF SINGLE CRYSTAL UNDER TENSION
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Based on crystal plasticity theory, the slip-band trace on the specimen surface of single crystal copper tensioned uniaxially is investigated by applying FEM associated with finite deformation numerical algorithm, and the three dimensional plastic slipping is simulated for single crystal copper specimen tensioned in different orientation. Through the geometric analysis of intersect-line between active crystallographic slip-plane with specimen surface, the different slip-band trace of the specimen surface is calculated and discussed, which is brought by tension in different orientation that leading different slip-planes are activated. According to the analyses of specimen surface slip-band, it is confirmed that the crystalline plasticity simulation is available to research the processes of slip-band trace formed on specimen surface of single crystal.
2011 Vol. 32 (6): 557-565 [
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420
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566
INVESTIGATION OF STATIC AND DYNAMIC FRACTURE BEHAVIOR OF PARTICLE-REINFORCED COMPOSITE MATERIALS BY THE EXTENDED FINITE ELEMENT METHOD
The static and dynamic fracture behavior of particle-reinforced composite materials are investigated by the extended finite element method (XFEM) without tip-enriched functions. We assume that both the matrix and the particles, bounded by perfect interfaces, have the elastic properties. The influence of particle position and particle amount on the stress intensity factors (SIFs) of the matrix-crack-tip are studied. The numerical results clearly show the different failure mechanism in such materials. The results also validate that the method employed in this paper could accurately predict the fracture behavior of particle-reinforced composite materials and could be more easily accepted by the engineering.
2011 Vol. 32 (6): 566-573 [
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432
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574
Shielding effect and emission criterion of a screw dislocation near an interfacial blunt crack in piezoelectric bi-materials
The shielding effect and emission criterion of a screw dislocation near an interfacial blunt crack in piezoelectric bi-materials is dealt with. Utilizing the conformal mapping technique, the closed form solutions are derived for electric displacement fields and stress fields due to a screw dislocation located near the interfacial blunt crack. The stress intensity factor and critical conditions for dislocation emission are also calculated. The influences of the position of the dislocation and morphology of the blunt crack as well as the electric-elastic properties on the shielding effect and emission criterion are discussed in detail. The results show that positive screw dislocations can reduce the stress intensity factor of the interfacial blunt crack tip (shielding effect). The shielding effect decreases with the increase of dislocation azimuth angle and the distance between the dislocation and the crack tip. The critical loads at infinity and critical remote electric displacement for dislocation emission increases with the increment of the emission angle and the curvature radius of the blunt crack tip, and the most probable angle for screw dislocation emission is zero. The present solutions contain previous results as the special cases.
2011 Vol. 32 (6): 574-580 [
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399
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581
PEM based acoustic radiation analysis from random excited structures
DOI:
Based on FEM, BEM and PEM, acoustic radiation analysis from random excited structures is investigated in this paper. A new method is presented to calculate random acoustic radiation analysis. FEM is used to calculate structural responses, and BEM is used to calculate structural acoustic radiation. PEM combined with FEM and BEM is used to solve the problem on random acoustic radiation. Numerical examples show accuracy and efficiency of the presented method.
2011 Vol. 32 (6): 581-587 [
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398
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526
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588
Study of thermoelasticity of an infinite metal film during laser heating
An ultrafast thermoelasticity based on hyperbolic two-step heat conduction model with electron-phonon interaction is used to investigate thermomechanical response (including temperatures, stresses and displacements) of an infinite metal film impacted under femtosecond laser pulses by using finite element method (FEM). The heat conduction effect of lattice is taken into account. Finite element governing equations are established and solved in time domain directly. The results, including electron and lattice temperatures, stresses and displacements, are presented graphically and compared with literatures. The results show that FEM method can be used to solve this kind of problem. The influences of hot-electron blast on displacements and stresses are studied and the results show that the hot-electron blast should be considered in the analysis.
2011 Vol. 32 (6): 588-594 [
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428
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474
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595
Integrated Optimization Design of Structure and Material of Composite Guide Vane
By combining composite microstructure optimization with structure optimization, an integrated optimization design of structure and material of composite guide vane was developed. With the microstructure analysis model of plain weave braided composite, micromechanical finite element method was used to predict mechanical property, thermosetting coupling method was used to analyze turbine guide vane. During integrated optimization of structure and material procedure, design variables include microstructure parameter and macrostructure parameter, and the objective was mass of vane, also required to satisfy stress and displacement constraints.
2011 Vol. 32 (6): 595-602 [
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421
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493
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603
Vibration Characteristics of Cylindrical Shell treated with Active Constrained Layer Damping
A finite element dynamic model for cylindrical shell treated with active constrained layer damping (ACLD) is established based on the constitutive equations of elastic, viscoelastic and piezoelectric materials by energy approach . The proportion and differential control system considering the self-sensing voltage from the sensor layer is developed. The active constrained layer damping (ACLD) shells including nature frequencies, loss factors and responses in frequency domain are investigated. The influence of some key parameters, such as the covering ratio of ACLD patches, the thickness of VEM and the control gains, on the shell vibration characteristics is discussed. The results show that ACLD patches should be bonded on the different locations on the surface of the cylindrical shell in order to surpress vibration for different modes; the covering ratio of ACLD patches, the thickness of VEM and control gains have direct effect on the vibration amplitude. The Optimization of these parameters including the placement of ACLD patches, the covering ratio of ACLD patches, the thickness of VEM and control gains in ACLD technique can effectively surpress the vibration of cylindrical shells. Therefore, the ACLD technique demonstrates the potential applications in engineering.
2011 Vol. 32 (6): 603-610 [
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344
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495
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611
On the analytic solution of Hamiltonian canonical equation for rectangular moderately thick plate problem
A complete symplectic eigenfunction expansion of rectangular moderately thick plate problem with two simply-supported opposite sides is proposed by using Fourier analysis method. The eigenfunctions of the Hamiltonian operator arising from the considering problem are directly solved with the help of Mathematica software. The completeness of the eigenfunctions is then proved, providing the theoretical guarantee of using separation of variables to solve the problems. The analytic solution is obtained with the proved expansion theorem. A numerical example shows the correctness of the result.
2011 Vol. 32 (6): 611-618 [
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467
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492
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简报
619
The effect of Stone-Wales topological defects on the tensile mechanical properties of single graphene sheets
The effect of Stone-Wales (SW) defects on the tensile mechanical properties and deformation mechanism of the zigzag and armchair single graphene sheets was investigated using molecular dynamics simulation with Tersoff bond-order interatomic potential. The numerical simulation results show that there is no effect on the Young’s modulus of the two chiral graphene sheets due to the presence of single SW defect, while the effects on the tensile strength, strain and deformation mechanism are dependent on the chirality of graphene. For armchair graphene sheets, single SW defect is observed to reduce the tensile stress and limit tensile strain by as much as 5.04% and 7.07%, respectively. It is also found that SW defect serves as nucleation site for fracture under tension. However, for zigzag graphene sheets, single SW defect has no effect on the mechanical properties and deformation mechanism.
2011 Vol. 32 (6): 619-624 [
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712
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625
FRACTURE ANALYSIS OF TWO COLLINEAR CRACKS FOR A FUNCTIONALLY GRADED ORTHOTROPIC COATING--SUBSTRATE STRUCTURE
Ding Sheng-Hu;
This paper investigates the mode I crack problem of two collinear cracks for a functionally graded orthotropic coating bonded to a homogeneous substrate. A new bi-parameter exponential function was introduced to simulate the continuous variation of material properties. The principal directions of orthotropy are parallel and perpendicular to the boundaries of the strip. By using integral transforms, the problem was reduced as a system of Cauchy singular integral equations of the first kind. The local stress field was obtained. The influences of parameters such as the material constants and the geometry parameters on the stress intensity factors (SIFs) are studied.
2011 Vol. 32 (6): 625-629 [
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401
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458
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630
An improved basic deformation mode method for zero-energy mode suppression of hybrid element
Basic deformation mode method is very effective to construct the assumed stress field for hybrid elements. However, this method only provides the necessary condition for a zero-energy mode free element. In this work it is shown that due to the coupled effect between various basic modes, the basic deformation method has a severe limitation for zero-energy mode free element construction. Subsequently by using the positive definiteness property of flexibility matrix the sufficient and necessary condition for determination of zero energy modes is presented. Moreover the assumed stress method is improved for coupled basic modes by means of the linear independence of special inner product vectors and it is applicable to arbitrary element shapes. Numerical examples of 2D 4-ndoe elements show that the proposed method is very effective.
2011 Vol. 32 (6): 630-637 [
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459
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499
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638
THE INTERACTION BETWEEN A SCREW DISLOCATION INSIDE THE INHOMOGENEITY AND AN ELASTIC ELLIPTICAL INHOMOGENEITY WHICH CONTAINS A CONFOCAL RIGID CORE UNDER LONGITUDINAL SHEAR
Abstract The interaction between a screw dislocation inside the inhomogeneity and an elastic elliptical inhomogeneity which contains a confocal rigid core under longitudinal shear is investigated. By using the technical of conformal mapping and the method of analytic continuation, the stress fields of matrix and inhomogeneity is obtained explicitly in the series form, and the image force acting on the screw dislocation is obtained. The maximum interfacial stresses and the ratio of the two elliptical interfaces under longitudinal shear are calculated. As a result, the analysis and discussion show that the influence of the rigid core on the interaction effects between a screw dislocation and an elliptical inhomogeneity is significant. It can repel the dislocation , and make it reach the interface of the elastic inclusion constantly when the inhomogeneity is stiff. If the inhomogeneity is soft, there is a stable equilibrium position. As the dislocation is in between the rigid core and the stable equilibrium position , the dislocation will shift near the interface of the elastic inclusion. When the dislocation is in between the stable equilibrium position and the interface of the elastic inclusion , the dislocation will leave away from the interface. The result also show that the ratio of the long and short axes of the inhomogeneity has the noticeable influence on the interaction between the screw dislocation and the inhomogeneity. When the dislocation is on the nearby rigid core, the repulsive force of the core to the dislocation decreased significantly with the ratio of the long and short axes of the inhomogeneity decreases.
2011 Vol. 32 (6): 638-645 [
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416
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680
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646
Study on structural non-probabilistic reliability index under convex models and its solution methods
In the circumstances of hardly defining precise probability distributions of uncertainties when only a limited number of sample information is available, the non-probabilistic reliability based on convex models serves as an effective approach for structural safety assessment. Based on the multi-ellipsoid model description for bounds of uncertainties in material properties, geometric dimensions and loading conditions, a min-max mathematical definition of the non-probabilistic reliability index is presented by using the normalized transformation and the generalized infinity norm measurement. The presented non-probabilistic reliability index can be regarded as the relative “length” ratio of the structural allowable variation range to the reference variation range. By approximating the limit-state function with linear expansion, an explicit iterative algorithm is presented for seeking the non-probabilistic reliability index conveniently. Numerical examples are given to illustrate the validity and efficiency of the present iterative approach.
2011 Vol. 32 (6): 646-654 [
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440
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727
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655
DYNAMIC RESPONSE OF LINING IN SATURATED FOUNDATION SUBJECTED TO SUDDEN INTERNAL UNIFORM LOADING
Buried lined tunnels are often subject to internal dynamic loading, such as blast loading and impact loading. The dynamic stress concentration of lining structure due to various dynamic sources is a special concern in practical engineering. Based on Biot’s dynamic theory, the expressions of the displacements, stresses and pore pressures of saturated soil and those of the displacements and stresses of lining have been derived with the method of the wave function expansion and Laplace transform. Employing the complex variable functions and conformal mapping method, the arbitrary boundary is mapped circular boundary and the solution on dynamic response of lining with arbitrary shapes has been obtained based on the inner boundary condition of the lining and the continuity conditions between the soil and the lining. With the numerical integration of inverse Laplace transforms, the numerical solution on the dynamic response of an elliptic lining and a cylindrical one is presented respectively.
2011 Vol. 32 (6): 655-664 [
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414
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432
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