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2011 Vol. 32, No. 5
Published:
论文
433
Molecular dynamics study of the tensile mechanical behavior of metallic nanowires with different orientation
The mechanical properties and the extensional deformation of the single-crystalline Cu nanowires with FCC crystal lattice are analyzed. The elastic modulus and yield strength in three different directions of <100>, <110> and <111> are investigated by the quasi-static classic MD (Molecular dynamics) simulation of the nanowires under tension at room temperature. The discuss about the stress-strain relation and the tension -deformation mechanism of the nanowires, which in term of the structure evolution and the resolved shear stress，is carried out. It is found that the <111> Cu nanowires is highest in strength, while the <110> is worst, and the <100> is best in ductility, the <111> and <110> is similar poor Nanowires have different mechanical properties in different tensile directions
2011 Vol. 32 (5): 433-439 [
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543
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440
The Dislocation Model of Superlattice and Dynamic Stabilities for system
DOI:
The dynamic behaviours in the vicinity of the interface for the superlattice is discussed in the classical mechanics frame and based on Seeger equation.It is indicated that the motion and the accomulation of the dislocations by the bifurcation and chaos may be gived rise to the layer or the fracture of the superlattice;and also it is indicated that putting the superlattice of growing process in the suitable sound field reduce stress to minimum, or suitable regulating a parameters of the system, then the dynamic stabilities of the system may be ensured.At first,introducing damping term,the Seeger equation described the general dislocation motion may be reduced to the generalized pendulum equation described superlattice system.The properties of the phase plane for a non-peturbated system are ananysed by means of Jacobian elliptic function and the elliptic integral, and the solution of the equation and a period of the dislocation motion for this system may be expressed exactly。Secondary, the global bifurcation and a chaotic behaviours with the Smale horseshoe for the 3-kind orbit in a phase plane are analysed by Melnikov method.The critical condition of the system entered in a bifurcation or a chaoc is found。It show that the critical condition is related to the parameters of the system, then suitable regulating a parameters of the system,the bifurcation or the chaos can be avoided or controlled in principle，then the stabilities of the growing process and the perfect of the superlattice materials may be further ensured
2011 Vol. 32 (5): 440-445 [
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399
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446
Study on Distribution of Interfacial Stresses in Bimaterial Corners of Edge-bounded Quarter-planes with Stress Singularity at Interface Tip
The distribution of interfacial stresses in bimaterial corners of edge-bonded quarter-planes is investigated with a particular attention to the distribution of interfacial stresses in the vicinity of the singular tip of bimaterial corners. It is found that, closely near the singular tip, the difference between the rigorous solution and the asymptotic solution of edge-bonded quarter-planes (Bogy, 1970) is a damping stress oscillation stress with tiny amplitude, and it quickly attenuates towards the tip. The starting position of the damping oscillating stress is defined as a transition point. Beyond the transition point, the asymptotic solution is continuously decreasing to zero, and it remarkably deviates from the rigorous solution. From the tip to the transition point, the rigorous solution just equals the sum of the asymptotic solution plus the damping oscillating stress. The segment from the tip to the transition point is called the asymptotic part. From the transition point to infinity, the asymptotic solution is no longer valid, and the interfacial stresses must be determined through the rigorous solution. The segment from the transition point to infinity is called the basic part. Therefore the curve of interfacial stress is divided into the asymptotic part and the basic part by the transition point. The transition point has a particular significance as it is the joining of the asymptotic part with the basic part. By substituting the coordinate of the transition point into the asymptotic expression, a relationship between the stress intensity factor in the asymptotic part and the interfacial stress at the transition point is deduced. It is believed that the knowledge about the transition point and the relationship between the stress intensity factor in the asymptotic part and the interfacial stress at the transition point will benefit to the development of a criterion of the interfacial initial debonding for bimaterial corners with singularity.
2011 Vol. 32 (5): 446-458 [
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425
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459
Delamination in thermohyperelastic plastic IC packaging material
Popcorn delamination failure of plastic electronic packages made of thermohyperelastic material featuring Gent-Thomas, during the solder-reflow process, resulted from the integrated effects of vapor pressure induced by the moisture and thermal stress induced by heat mismatch was studied.Using the theory of cavity formation and unstable void growth in incompressible hyper-elastic material, we gained an analytical relationship between void growth and the sum of the vapor pressure and thermal stress. Numerical analysis shows that popcorn failure won’t occur when the moisture in voids is in single vapor phase during the solder-reflow process on condition that plastic electronic packages absorb little moisture; plastic electronic packages produce popcorn failure when the vapor pressure maintains saturation state during the solder-reflow process on condition that plastic electronic packages absorb sufficient moisture.
2011 Vol. 32 (5): 459-464 [
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431
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465
Analysis of Sound Radiation of Double Stiffened Shells Connected by Different Structures
The vibration characteristics of two types of linked structure between outer shell and inner shell of double stiffened cylindrical shells, namely annular plates and splints are studied. The annular plates’ vibration is treated as both extensional and bending vibration, as only extensional vibration and as only radial vibration respectively. The splints’ vibration is treated as extensional vibration, as only radial vibration and as pole’s vibration respectively. The comparison of each structure type’s three methods shows that different methods have different precision. The conclusion that the splints linked double shells have similar sound radiation with the annular plate’s connected ones when the there is no space between each splint in the circumferential direction is discussed.
2011 Vol. 32 (5): 465-474 [
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393
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475
Boundary Effect on Bifurcation Buckling of Functionally Graded Material Circular Cylindrical Shells in Thermal Environment
DOI:
Based on prebuckling consistent theory, the effect of boundary constraints on the bifurcation buckling for functionally graded material circular cylindrical shells subjected to axial compression in thermal environment is investigated. The analytic solution is obtained for prebuckling deformation coupling thermal and mechanical loading as well as initial geometrical imperfects. The nonlinear eigen value problem is derived by combining the approach of separating variables with the technique of finite difference to solve the governing equations of bifurcation buckling. The temperature dependence of material properties is taken into account in the analysis, the influence of temperature gradient along thickness, initial geometrical imperfection, volume fraction of material composite in the critical axial compressive loads is examined with respect to simply supported ends and clamped ends respectively. The results show that temperature sensitivity and imperfection sensitivity corresponding to clamped ends are stronger than those in simply supported ends, but become weaker with the increase of temperature gradient, and the volume fraction of material composite exerts little influence on imperfection sensitivity irrespective to boundary conditions at ends. Also it is revealed that the effect of boundary constraints on bifurcation buckling abates with the rise of amplitude of initial geometrical imperfections.
2011 Vol. 32 (5): 475-482 [
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402
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483
Static Response of Timoshenko Sandwich Beam Made of Functionally Graded Materials under Thermal Loads
DOI:
By accurately considering the axial extension and transverse shear deformation in the sense of theory of Timoshenko beam, geometrically nonlinear governing equations for functionally graded sandwich beams subjected to thermal loads were formulated. By using a shooting method, the obtained boundary value problem of nonlinear differential equations was numerically solved and thermal buckling and post-buckling response of transversely non-uniformly heated FGM Timoshenko sandwich beams with fixed-fixed edges were obtained. The effects of material gradient property, surface layer thickness and temperature parameter on the buckling deformation and the tension-bending coupling deformation of the beam were discussed in details, and the distribution patterns of temperature function above thickness of sandwich beam are plotted.
2011 Vol. 32 (5): 483-492 [
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409
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493
Application of meshless natural element method to dynamic elastoplastic analysis
A new algorithm for dynamic elastoplastic analysis is put forward on the basis of the meshless natural element method. The natural element method (NEM) is a recently developed meshless method and is essentially the Galerkin method based on natural neighbour interpolation. Compared with the meshless methods based on the moving least squares approximation, The NEM possesses notable advantages in the enforcement of essential boundary conditions. The space domain is discretized with the NEM and the discretized governing equations for dynamic elastoplastic analysis are derived using weighted residual technique. Then the predictor-corrector form of the Newmark algorithm is employed to solve the discretized governing equations. At last, numerical examples are presented to demonstrate the effectiveness and accuracy of the proposed method for dynamic elastoplastic analysis.
2011 Vol. 32 (5): 493-499 [
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459
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500
Analysis of 3D linear elasticity problems directly on geometric model with the boundary face method
DOI:
This paper presents the boundary face method (BFM) based on boundary integral equations for solving 3D linear elasticity problems directly on geometric model. In the method, both boundary integration and variable approximation are performed in the parametric space of each boundary face. The geometric data at Gaussian integration points, such as the coordinates, the Jacobians and the out normals are calculated directly from the faces rather than from elements, and thus no geometric error will be introduced. The BFM has real potential to completely integrate with CAD system, because its implementation can be directly based on a CAD model through its boundary representation data. The structures with local small features are directly used for analysis, when all of geometry features are kept accurately according to their size in the real-world-coordinate system, instead of simplification for them. Numerical examples problems have demonstrated that the proposed method effectively simulates thin shell based on 3D elastic theory and the complicated structure with detailed configurations in a simply way, and also provides more accurate results when compared with the finite element method (FEM).
2011 Vol. 32 (5): 500-506 [
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416
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简报
507
Thermo-mechanical-order coupling in the mechanical behaviors of liquid crystal elastomers under uniaxial stretch
DOI:
The thermo-mechanical-order coupling in the mechanical behaviors of the liquid crystal elastomers under the uniaxial stretch along the director is investigated based on the stress-strain constitutive equation and the mechanical-order coupling equation. Due to the mechanical-order coupling, the order parameter is increased by the stretch, which thus influences the stress-strain relation of the liquid crystal elastomers, and leads to the result that the stress at the same stretch is reduced. This influence varies with the temperature. Because the order parameter decreases with the temperature, the stretch decreases with the temperature when the nominal stress is fixed; and the stress increases with the temperature when the stretch is fixed. The dependence on temperature for both situations is nonlinear.
2011 Vol. 32 (5): 507-512 [
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639
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513
A VIRTUAL JOINT ELEMENT METHOD FOR NUMERICAL SIMULATION OF QUASI-BRITTLE MATERIAL FAILURE PROCESS
The combination of finite deformation element and virtual joint element is introduced to simulate the failure process of quasi-brittle materials. First, based on accurate finite deformation theory, with the second Piola-Kirchhoff stress and Green-Lagrange strain as the energy conjugate stress and strain, the stiffness matrix of virtual joint element is derived; then, correctness and rationality of the virtual joint element is verified using an numerical example and the height range of the element is given after the comparison between the numerical results with and without the joint element; finally, the method is used to simulate the crack propagation of a concrete three-point beam, the result is consistent with that of document. The method proposed in the paper provides a new approach for the numerical simulation of failure process of structures.
2011 Vol. 32 (5): 513-519 [
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664
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520
THE DYNAMICAL BEHAVIOUR OF CANTILEVERED FLEXIBLE PLATES SUBJECTED TO AXIAL FLOW WITH FLUID-STRUCTURE INTERACTION
A theoretical and experimental study has been conducted to investigate this topic. The partial differential equations of motion based on the inextensibility assumption are derived for a cantilevered plate subjected to axial flow. The partial differential equations of motion of the plate are discretized using the Galerkin method. The complex modal analysis is adopted to analyze the dynamical behaviour of this system. The non-dimensional critical flow velocities are predicted, time traces and oscillation mode shapes are shown, the relationship between damping, frequency and flow velocity for the first three modes are also discussed, and the theoretical values are also compared with the experimental results in this paper. It is shown that cantilevered plates lose stability via a Hopf bifurcation and develops divergence. Typically, the free motions of the plates are damped in their first mode by the small flow velocities, and then are subject to flutter in their second mode at higher flow velocities; at slightly higher flow velocities, the plates flutter in third mode; meanwhile, a temporary second and third coupled-mode flutter is shown to occur.
2011 Vol. 32 (5): 520-526 [
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418
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527
Topology Optimization of Continuum Structures Subjected to Forced Vibration Based on the Element Free Galerkin Method
In this paper, the element free Galerkin method (EFG) is applied to carry out the topology optimization of the continuum structures subjected to a forced vibration. Considering the relative density of nodes as design variables, the minimization of dynamic compliance as an objective function, the mathematical formulation of the topology optimization is developed using the SIMP (solid isotropic microstructures with penalization) interpolation scheme. Sensitivity of the objective function is derived based on the adjoint method. The optimization formulation is solved by the optimality criteria method. Numerical examples show that the proposed approach is feasible and efficient for the topology optimization of the continuum structures subjected to a forced vibration.
2011 Vol. 32 (5): 527-533 [
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492
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534
Mechanical analysis of uniform slender beam acted by uniform couple
An interested slender beam with constant section and material is established whose low and above surfaces are acted by reversed uniform distributed shear stresses. In engineering beam theory these loads are equivalent with uniform distributed couple. Timoshenko beam theory is used to develop the analytical results of the deflection and stress distribution of this model. And in comparison with the numerical results obtained by finite element method, some useful conclusions can be acquired: 1) when shear force is not equal to zero in boundary conditions, the shear effect need to be taken into account for the analyses of bending deflection and normal stress, i.e. Euler beam theory is not competent. 2) when boundary conditions contain zero shear force, Euler beam theory can be used in the analyses of bending deflection and normal stress. 3) The distribution of the shear stress in the cross-section is parabolic with the height coordinate as usual. When shear force is zero, the shear stress may be zero due to the effect of this surface load. The direction of the shear stress in same cross section can be altered.
2011 Vol. 32 (5): 534-540 [
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464
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356
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