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2012 Vol. 33, No. 4
Published:
论文
341
THE DYNAMICS RESPONSE AND STABILITY OF A DIELECTRIC ELASTOMER CYLINDRICAL SHELL UNDER STATIC AND PERIODIC VOTAGE
Abstract：When a voltage is applied between the internal and external surface of a dielectric elastomer cylindrical shell, it thins down, and the same voltage will produce an even higher electric field. The positive feedback may make the dielectric elastomer cylindrical shell to thin down drastically, causing an electrical breakdown. We study the dynamics response and stability of the cylindrical shell which is under static and periodic voltage in this article. We get the ordinary differential equation which describes the movement of cylindrical shell using the neo-Hookean material model. The voltage curves as a function of the deformation with different thickness and different boundary conditions are given, and the critical voltage is found. The cylindrical shell will be destroyed if the applied voltage is greater than the critical value. Addition, we also discuss the thickness and boundary conditions influence on the critical voltage. When a periodic voltage is applied, the movement of the shell is cyclical or intending to cyclical nonlinear vibration. We calculate nature frequency of the cylindrical shell, and get the periodic solutions using the shooting method, analyze the stability of the periodic solutions using the numerical method. The vibration amplitude curves as a function of the incentive frequency of periodic voltage are given. The cylindrical shell occur mutirate resonance, the vibration amplitude jumps at the point of resonance which may cause the cylindrical shell destroyed. We give the time history curves and phase diagrams of the resonance points, and discuss the characteristics of the vibration.
2012 Vol. 33 (4): 341-348 [
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293
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349
Radial basis collocation method for bending problems of beam and plate
Radial basis collocation method is introduced to analyze the bending problems of Timoshenko beam and Reissner-Mindlin plate. Radial basis functions are employed to be the approximation, collocation method is utilized for discretization, and least squares approach is adopted to solve the discretized equations. No mesh will be required in the discretization and resolution and so radial basis collocation method is a truly meshfree method. 1-D radial basis functions can represent all the 2-D or 3-D radial functions which greatly reduce the memory space. No integration will be used in collocation method which improves the computational efficiency. For resolving the problems of thin Timoshenko beam and Reissner-Mindlin plate, analysis demonstrates that radial basis collocation method is free of locking since the shape functions with infinite continuity can satisfy the Kirchhoff constraint conditions, and no stress oscillation will be observed, while conventional finite element method and conventional meshfree methods suffer locking problems. The advantages of this approach include easy discretization and implementation, and possessing exponential convergence and high efficiency. Numerical examples validate the conclusions and the stability of this proposed method.
2012 Vol. 33 (4): 349-357 [
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290
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358
Effect of material properties on the fragmentation of ductile materials under high strainrate tension
By introducing a cohesive fracture model into the Mott[1] momentum diffusion analysis, Grady and Kipp[2] deduced a formula for predicting the average size of the fragments during a ductile fragmentation process. To quantitatively evaluate the accuracy of the Grady-Kipp formula, in this paper, we numerically simulated the fragmentation processes of an elastic-plastic bar undergoing initially uniform high strainrate tensile deformation. The key material parameters, including the fracture energy , the material density , and the strainrate sensitivity c, were varied intentionally for evaluating their effects on the fragmentation process. The average fragment sizes were calculated for a wide range of the prescribed strainrates and the material parameters. It was concluded that the Grady-Kipp model provides reasonably close predictions of the ductile fragment size, though slight deviations exist in the cases when the fundamental assumptions in the Grady-Kipp analysis do not apply.
2012 Vol. 33 (4): 358-369 [
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319
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370
6σ Robustness Optimization Design of the Crashworthiness of Foam-filled Tapered Thin-walled Structure Based on Kriging Method
Aimed at improving the robustness and reliability of optimal result of the foam-filled thin-walled structures’ crashworthiness, the uncertainties existed in the design variables were considered, thereby a robustness optimization method which was based on the experimental design method, Kriging metamodel technique, Monte Carlo method and method was applied into an optimization process of the foam-filled tapered thin-walled structure’s crashworthiness. The result showed that the structure’s crashworthiness was improved, and compared with the certainty optimal result the robust optimal result has higher robustness and reliability. Additionally, this example indicated the practicability of this method.
2012 Vol. 33 (4): 370-378 [
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289
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379
Study on thermal expansion properties of viscoelastic resin-based 3D braided composites
First, the viscoelastic properties of 3D braided composites are obtained using the homogenization method and the FEM, and variation of thermal expansion coefficients with time is studied based on the numerical results of relaxation moduli of materials. The influence of braided structures and processing parameters (braided angles、fiber volume fractions) on initial thermal expansion coefficients is presented, and the numerical results agree well with the experimental data. The research work in the paper furnishes the basis for further investigating the thermo-viscoelastic properties of 3D braided composites.
2012 Vol. 33 (4): 379-385 [
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308
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386
Elastic-plastic solutions for circumferential through-cracks at the fixed end of cylindrical shells loaded by bending
Metal cylinder shell structures are very common components in the large complex structure systems. And the end of the shell is usually connected with other components. Due to the heat effect of the welding and real complicated inherent stress, the possibility of engendering fatigue cracks increases. With the application of high toughness material, elastic-plastic crack becomes more popular. However, there is no elastic-plastic theoretical analytical solution to such problem until now. In this paper, a set of complete elastic-plastic solutions for circumferential through-cracks at the fixed end of cylindrical shells loaded by bending, such as the crack tip opening displacement (CTOD) and crack tip opening angle (CTOA), are developed according to the semi-membrane theory of cylindrical shells and with the use of Dugdale model. The proposed solutions are obtained mostly by explicit equations except a few numerical root-finding calculations and could be used for the calculation of crack initiation and stable crack growth, which describe the whole changing process of the structure compliance and ultimate carrying capacity with the presence of the elastic-plastic crack. This method has filled the gap of analytical solution to such engineering problem.
2012 Vol. 33 (4): 386-394 [
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227
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395
STUDY OF FAILURE CRITERION OF ADVANCED HIGH STRENGTH STEEL
he advanced high strength steel (AHSS) realizes the outstanding advantage of strength by transforming its internal different phases. It has become one of the hottest materials for current automotive lightweight researches. However, compared with traditional deep-drawing steels, the widespread use of AHSS in auto-industry is hampered due to its poor ductility, which leads to frequent occurrences of failure in the mode of fracture during the process of stamping. Therefore, the fracture prediction of AHSS becomes one of the focuses of current researchers. The dual phase (DP) steel can be seen as the representative of AHSS. In this paper, the fracture criteria of DP steel under different stress states are investigated by combining experimental and numerical analysis and an appropriate failure criterion is attempted to be established for predicting its fracture behavior.
2012 Vol. 33 (4): 395-403 [
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354
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简报
404
Finite Deformation of Everted Cylindrical Shells Composed of Incompressible neo-Hookean Materials
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The finite deformation problem is examined for an everted cylindrical shell composed of a class of transversely isotropic incompressible neo-Hookean materials about radial direction. The corresponding mathematical model is solved by using the incompressible condition and the semi- inverse method, moreover, the system of nonlinear equations that the inner radius and the axial stretch rate of the everted cylindrical shell must satisfy is obtained by the boundary conditions. The effects of material and structure parameters on the inner radius and the axial stretch rate of the everted cylindrical shell are discussed by numerical examples. The results show that the effect of initial thickness on the inner radius and the axial stretch rate of the everted cylindrical shell is not essential, but of the radial transversely isotropic parameter, especially on the aspect of axial stretch rate.
2012 Vol. 33 (4): 404-407 [
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331
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408
AN IMPROVED HYPERELASTIC CONSTITUTIVE MODEL OF RUBBER MATERIALS
The phenomenological constitutive model of incompressible rubber materials is investigated in this paper. The principal of choosing strain-energy function is discussed. The advantages and disadvantages of several models, including the Neo-Hookean formulation, the Mooney formulation, the three-order Rivlin formulation and the Ogden formulation, is mechanically analyzed. Subsequently, an improved form of Rivlin formulation is proposed as , which has three significant advantages: ① in the case of N=1 and small strain, the new function is the same as the strain-energy of the linear elastic incompressible material, and gives a approximately linear shear deformation and a exact linear tension and compression deformation. ②when N≥2, in the condition of small strain, using the new formulation, the strain-energy and shear stress in simple shear experiment are polynomial with γxy as geometric proportion. While using Rivlin formulation, the strain-energy and shear stress τxy under small deformation are polynomial with (γxy)2 as geometric proportion. Besides, when the deformation is small, Rivlin formulation with N=1 provides constant shear module and non-linear relationship in tension and compression. The improved form, compared with the same order Rivlin formulation, shows significant advantages in prediction of test data in single experiment, and has a good performance in the mutual prediction between different tests.
2012 Vol. 33 (4): 408-414 [
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403
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519
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415
Investigation of the vibration response and sound transmission of a micro-perforated plate periodically stiffened by two sets of orthogonal beams
A semi-analytical method to estimate the vibration response and sound transmission of an infinite micro-perforated plate, stiffened by two periodic sets of orthogonal beams, is proposed in this paper. The plate is submerged in water fluid and excited by a plane wave at arbitrary angle of incidence. Based on the velocity boundary condition and acoustic impedance of the micro-perforated plate, the equation of the vibration response of the studied structure is established, which is then expressed in terms of an infinite set of space harmonic amplitudes using the Fourier transforms and space harmonic method. After solving these space harmonic amplitudes numerically, the vibration response and sound transmission coefficient of the perforated plate in the physical space are finally obtained by employing the Fourier inverse transform. Comparisons with sound pressure results of the unstiffened perforated plate of Takahashi illustrate the validity of the proposed approach. In numerical examples, effects of the perforation ratio and periodic beams on the vibration response and acoustic transmission coefficient are investigated.
2012 Vol. 33 (4): 415-422 [
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252
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423
Axisymmetrical Analytical Solution for Vertical Vibration of End-bearing Viscoelastic Pile
Yang Xiao
Regarding the pile and the soil layer as viscoelastic media, the dynamical behavior of vertical vibration of an end-bearing viscoelastic pile in a viscoelastic soil layer is investigated in the frequency domain using methods of the Helmholtz decomposition and variable separation. The axisymmetric analytical solution for the vertical vibration of the pile is obtained, and the analytical expression for the dynamical complex stiffness of the pile top is presented. Responses of dynamic stiffness factor and equivalent damping of pile top with respect to the frequency are shown in figures by means of the numerical method. Influences of the soil’s viscosity, slenderness ratio of pile, modulus ratio of the pile to soil, pile’s Poisson ratio and viscosity on the stiffness factor and equivalent damping are examined. It is revealed that, due to the effect of the transversal deformation of the pile and the radial force of the soil acting on the pile, the dynamic stiffness factor and equivalent damping derived from the axisymmetrical solution are greatly different from those derived from the classic Euler rod model. Therefore, there are some limitations for the applicability of the Euler rod model for analysis of the vertical vibration of the pile, and the axisymmetric model based on the three dimensional viscoelasticity should be employed under some special cases.
2012 Vol. 33 (4): 423-430 [
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244
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459
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431
Bending analysis of orthotropic thin plate on graded elastic foundation
Based on the energy method and variation principle, the bending analysis is presented for orthotropic thin plates on graded elastic foundations subjected to distributed loads using two-parameter foundation model. Firstly, the bending differential equilibrium equation of orthotropic thin plates on graded elastic foundations and the expressions of two elastic parameters of elastic foundation are given by introducing the energy method and variation principle. Then, the displacement reduced function is derived based on the assumption that the normal stress in z-direction is steady through foundation thickness. In the example, the proposed solution is validated by comparing the degenerated results for homogeneous isotropic foundation with Vlazov model. Finally, this paper studies the displacements distributions of the orthotropic thin plate on a graded elastic foundation, whose Young’s modulus obeys a power law through the thickness. The effects of top-bottom surfaces’ Young’s modulus ratio and volume fraction exponent on the variation of displacements of the plate are also examined.
2012 Vol. 33 (4): 431-436 [
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272
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659
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437
CPFEM analysis on growth and interaction behaviors of surface voids
To investigate the growth and interaction behaviors of surface voids, unit cells of void growth and interaction were created, and the effects of crystallographic orientation and depth of void location were studied by using crystal plasticity finite element method(CPFEM). Simulation results show that the void shape and growth direction significantly depend on the crystallographic orientation, and the void growth velocity is dependent on the crystallographic orientation. In general, the grwoth and interaction velocities of hard orientation are larger than that of soft one under the strain controlled boundary condition. With the depth of void location for surface void increasing, the maximal plastic deformation increases, and deformation localization around voids is more serious, and the velocity of void growth accelerates.
2012 Vol. 33 (4): 437-443 [
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298
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499
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优博
444
Theoretical Investigations on Mechanical Behavior of Fracture and Stability for Some Advanced Electromagnetic materials and Structures
Huadong Yong
2012 Vol. 33 (4): 444-448 [
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301
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580
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