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2010 Vol. 31, No. 4
Published:
论文
325
ELASTIC ANALYSIS OF A SCREW DISLOCATION IN AN ANNULAR COATING LAYER WITH INTERFACE STRESSES
The interaction between a screw dislocation in the nanoscale coating layer (interphase layer) with interface stresses and the circular inhomogeneity and matrix is investigated. The analytical solutions of complex potential functions in the inhomogeneity, the coating layer and the infinite matrix are derived by means of the complex variable method. With the aid of the Peach-Koehler formula, the explicit expression of the image force acting on the screw dislocation is given. The influence of the interface stresses on the image force and the equilibrium position of the dislocation in the coating layer (interphase layer) is mainly discussed. The results show that the impact of the interface stresses on the motion of the dislocation near the interfaces is very significant. Under certain conditions, the presence of the interface stress can change the interaction mechanism between the screw dislocation and inhomogeneity/matrix, and three equilibrium positions can exist for the dislocation in the coating layer. It can be seen that an additional repulsive force or attractive force will act on the dislocation for considering the interface effect, which cause the image force to increase or decrease.
2010 Vol. 31 (4): 325-331 [
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831
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332
Discussions on the Definition and Exactness of Nonlocal Plane Strain and Stress Problems
Within the framework of nonlocal elastic theory, the nonlocal plane strain and stress state are re-defined. Firstly, governing equations of the two states are deduced respectively based on the corresponding simplifying assumptions, and are compared with the classic equations. Secondly, the exactnesses of the two nonlocal plane problems are discussed by means of the strain compatibility conditions. In the discussion, the exactness of nonlocal plane stress state is studied via the Fourier transforms of strain compatibility equations in order to simplify the problem. Finally, some valuable conclusions are obtained on the basis of the analysis.
2010 Vol. 31 (4): 332-338 [
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827
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910
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339
Micromechanics analysis considering the grain size probability distribution
The influence of the reinforced particle size on the mechanics property of the particle reinforced composites was studied. Using fractal theory, the grain size probability distribution was taken into account to amend the departed equivalent inclusion method of the composite micromechanics. A new equivalent force method reflecting the grain size probability distribution was established. Taking concrete as an example, the effects of the volume fraction of composite, the modulus ratio of the inclusion and the matrix, and the resolution of the fractals structure to the mechanics were analyzed. The results show that this new method can be used to study the influence of microstructure on the particle reinforced composite mechanics performance.
2010 Vol. 31 (4): 339-345 [
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721
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346
Large deflection response of fully-clamped circular metal foam sandwich plates
This paper is concerned with the load-carrying capacity of circular sandwich panels subjected to central quasi-static loading. The panel consists of two metallic face-sheets and a core made from metallic foam, and is fully clamped at the edges. The analysis is based on a newly developed yield criterion for the sandwich cross section. The large deflection response is estimated by assuming a velocity field, which is defined according to the initial deformation mode of flat panel and the boundary condition. A finite element simulation has been performed to validate the analytical solution. A parametric study is then carried out to examine the structural response. Good agreement confirms that the quasi-static behavior of circular sandwich plates is well captured by the analytical model
2010 Vol. 31 (4): 346-352 [
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705
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353
Saint-venant end effect for anti-plane deformations of piezoelectric-piezomagnetic sandwich structures
The decay rates of the Saint-Venant end effects of the Sandwich structures composed of the piezoelectric or piezomagnetic material are studied. The main aim is to discover the effect of the boundary conditions and material properties on the decay character. The results show that the piezoelectric and peozomagnetic properties and boundary conditions have obvious effects on the decay rates of the end effects.
2010 Vol. 31 (4): 353-362 [
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1204
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363
Symplectic analysis for elastic wave propagation in sandwich cylinder
The elastic wave propagation problem in orthotropic sandwich cylinder is analyzed with the symplectic algorithm. By properly organizing the variables, the state space formalism is constructed and then the Hamilton matrix is obtained on the basis of the piece-wise constant hypothesis. With the combination of the symplectic mathematic method of the Hamilton system, extended Wittrick-Williams algorithm and the precise integration method, the dispersion relations are achieved for different sandwich cylinders. Comparison with the polynomial method reveals the effectiveness and superiority of the present method in the analysis of wave propagation problem.
2010 Vol. 31 (4): 363-368 [
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1354
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536
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369
Crystal Nucleus Method for Material Design
It is difficult to determine the initial density distribution of design domain and take the optimization algorithm convergenced when designing material with specified performance using the method of inversed homogenization. Crystallon can usually be used to accelerate the growth of crystal when making cultured crystal. Suggested from this physical process, a new method called crystal nucleus method used to determine the initial density distribution was proposed. After discribed the conception of crystal nucleus method, some issues about this method were discussed. These issues included how to determine the value of power exponent in SIMP model, how to select the filtering domain, the influences of the position of crystal nucleus and the type of object function to the optimal microstructrure of material with specified performance. Several examples of material design with described and extreme performances showed the effectiveness of crystal nucleus method.
2010 Vol. 31 (4): 369-378 [
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676
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572
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379
Approximate analytical solutions for transient response of visco-elastic laminated cantilever plate
The series composed by two-dimension beam mode function is used to approximate the transverse displacement function of visco-elastic cantilevered plate, and the transverse deformation of the plate on which a concentrated force is acted is calculated by using Ritz’s method. By solving Lagrange’s equation, the frequencies and model loss factors of free vibration of the plate are obtained, then transient response of visco-elastic cantilevered plate, when the concentrated force is withdrew suddenly, is obtained by using the method of mode superposition. Also the effects of loss factor, module and thickness of viscoelastic layer on the response are analyzed.
2010 Vol. 31 (4): 379-384 [
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694
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646
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385
The scattering of SH wave on a vertical crack in a coated piezoelectric strip
The scattering of elastic waves is an important method in researching the defects and parameter of materials.Many applications in industry utilize a piezoelectric layered composite plate with a crack. In this paper, the scattering of SH wave by a finite crack in a piezoelectric strip is considered(shown in Figure$1$). The piezoelectric layer is bonded between two half plate of functionally grated materials(FGMs). The shear modulus and the mass density of FGMs are assumed to be of exponential form, and the crack is vertical to the interfaces. Based on the Fourier integral transform and the boundary conditions, the solution is obtained in terms of a Cauchy singular integral equation. The Cauchy singular integral equation can be solved by the approximation of Chebyshev polynomials. Numerical results for the normalized dynamic stress intensive factors (NDSIF) are carried out for an example. The effects of geometric parameters and frequency of SH wave on the NDSIF are plotted out and discussed.
2010 Vol. 31 (4): 385-391 [
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688
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681
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392
The Analytic Solving for Nonlinear Torsional Wave Equation in Non-Circular Cross-Sectional Rod
The exact solving problem of nonlinear torsional wave equation in non-circular cross-sectional rod is investigated. Using the method of direct integral together with differential transformation, an implicit general solution of the nonlinear torsional wave equation are obtained. Through analyzing arbitrary integral constants and coefficients of the known equation, various solutions of this equation are given, including trigonometric function solution, hyperbolic function solution, exponential function solution, elliptic function solution and their composite function. These solutions correspond to solitary waves, shock waves and periodical waves and so on.
2010 Vol. 31 (4): 392-396 [
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1406
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534
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397
Mathematical Model for Dynamics of Incompressible Saturated Poroelastic Timoshenko Beam
Based on the theory of saturated porous media, a mathematical model for dynamics of the transversely isotropic saturated poroelastic Timoshenko beam is established with assumption that fluid in pores moves only in the axial direction of the beam. Under some limiting cases, this mathematical model can be degenerated into Euler-Bernoulli Model, Rayleigh Model and Shear Model of the poroelastic beam respectively. With the mathematical model presented, the natural frequencies and attenuations for free vibration and the dynamical behavior of the simply-supported poroelastic Timoshenko beam, with two ends permeable and subjected to the step load are investigated. The variations of the deflections, bending moments of the poroelastic beam and the equivalent couples of the pore fluid pressure are shown in figures and are compared with the results of the simply-supported poroelastic Euler-Bernoulli beam. The influences of the interaction coefficient between the solid skeleton and the slenderness ratio of the beam are discussed. It is shown that the interaction coefficient plays a role as viscidity. The amplitudes of deflection attenuate more rapidly with the increasing of the interaction coefficient, and the deflection approaches to that of the static response. Furthermore, the deflection amplitude and period of the poroelastic Euler-Bernoulli beam are smaller than those of the poroelastic Timoshenko beam, and the limit values of the bending moments are the same for the poroelastic Euler-Bernoulli beam and Timoshenko beam.
2010 Vol. 31 (4): 397-405 [
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1457
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763
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简报
406
Decrement-dimensional Precise Time Integration of 2-D transient heat conduction equation for Functionally Graded Materials
An efficient algorithm（Decrement-dimensional Precise Time Integration method, DPTI） of two-dimensional transient heat conduction equation is presented for Functionally Graded Materials(FGMs) based on the Precise Time Integration method (PTI). DPTI realizes the matrix storage optimization which solves the problem of large-scale coefficient matrix H when calculating the transfer matrix T which PTI surfers. DPTI also make full use of the similarity of the equation after decreased dimension to reduce the computation time greatly which achieve the optimization of the computational efficiency. The numerical examples are presented to demonstrate the effectiveness and reliability of the proposed method.
2010 Vol. 31 (4): 406-410 [
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729
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623
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411
ANALYTIC SOLUTION OF PLANE ELASTICITY OF EPPIPTICAL HOLE IN ONE-DIMENSIONAL ORTHORHOMBIC QUASICRYSTALS
By introducing the generalized conformal transformation and using the complex variable function method , the analytic solution of the plane elasticity problem of elliptical hole in one-dinensional orthorhombic quasicrystals were obtained and derived complex repesentation of stress displacement . In some special conditions,the elliptical hole can be turned into a Griffith crack and the SIFs of crack tips can be obtained. The plane elasticity problem of elliptical hole in 1D orthorhombic QCs could extended for 1D tetragonal QCs and the analytic solution of plane elasticity problem of elliptical hole in 1D tetragonal QCs. The elliptical hole can be also turned into a Griffith crack in specical conditions and the SIFs also be obtained.
2010 Vol. 31 (4): 411-416 [
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709
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695
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417
Compare of Time Domain Method with Frequency Domain Methodin Nonlinear Flutter Analysis for Panels of Supersonic Airplane
The nonlinear flutter responses of heated panels in supersonic airflow are studied. The aeroelastic model of three-dimensional panels considering thermal effect is established by the use of von Karman large deflection strain-displacement formulations, quasi-steady first-order piston theory aerodynamics and the principle of virtual work. The governing equations in structural node degree of freedom are expressed in the function of linear modal coordinates. The amplitude and frequency of panel flutter response is obtained using both frequency domain method and time domain numerical integration. The numerical results show that the time domain method is consistant with the frequency domain method when panel flutter response is simply harmonic limit cycle oscillation.
2010 Vol. 31 (4): 417-421 [
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765
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600
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422
An Implementation of the Multi-Transmitting Formula for Numerical Simulation of Wave Motion
A scheme for implementing one of the widely used absorbing boundary conditions (ABCs)—Multi-Transmitting Formula (MTF) is proposed by combining MTF into the control equation of the interior nodes adjacent to the artificial boundary. Compared with the original scheme, the new one improves not only accuracy of the boundary condition, reduces the computational domain, but also reveals clearly a relation between the order of truncation error of the ABC and the extended mesh solution, which is commonly used as a benchmark to test ABCs. Limitation is then clarified for improving accuracy of numerical simulation of wave motion via increasing the accuracy order of an ABC. The performance of the new scheme, original one and Givoli-Neta ABC are finally compared via numerical examples concerning a semi-infinite wave guide, and resulted in that the first scheme is better than the other two.
2010 Vol. 31 (4): 422-426 [
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683
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622
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427
An Application of the Meshless Radial Point Interpolation Method to the Structural Topology Optimization Design
In this paper, a structural topology optimization design is investigated based on the meshless radial point interpolation method (RPIM). Considering the relative density of Gauss quadrature points as a design variable, and the minimization of compliance as an objective function, the updating scheme for the design variable is created by using the solid isotropic microstructures with penalization (SIMP) and the optimality criteria method. The filter method is applied to eliminate the checkerboard pattern with the point state. The effects of different parameters on the topology optimization design are in detail discussed. Numerical examples show that the proposed approach is feasible and efficient for the topology optimization design.
2010 Vol. 31 (4): 427-432 [
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1456
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748
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