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2010 Vol. 31, No. 3
Published:
论文
217
Using delay to control band shift of nonlinear saturation control system
This paper analyzes the band shift caused by the deviation of internal resonance frequency of nonlinear saturation control system. The effects of delay on band shift and bandwidth are studied under consideration. Thus, the band shift can be controlled using an appropriate choice of the delay. The method of multiple scales is employed to obtain the analytical solutions when the primary resonance and 1:2 internal resonance occurs in the system simultaneously. From the examples illustrated, in the original system without delay, the frequency band shifts to the above and below of the primary resonance point caused by the deviation of internal resonance frequency. Moreover, the larger band shift is caused by the larger absolute value of deviation of internal resonance frequency. The performance of vibration suppression about the primary resonance point is reduced for the unreasonable distribution of frequency band. However, the band shift can be eliminated and the bandwidth can be enlarged using an appropriate choice of the delay according to the values of deviation of internal resonance frequency. The larger absolute value of deviation of internal resonance frequency, the more effects of the delay on the band shift and bandwidth will be. The conclusion of this paper provides qualitative and quantitative referenced value to control vibration in the nonlinear vibration system.
2010 Vol. 31 (3): 217-227 [
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590
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228
On the Modeling of SMA fiber Active Thin-Walled Composite Structures
2010 Vol. 31 (3): 228-236 [
Abstract
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638
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550
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237
Research on free energy potential of plastic damage constitutive models
Free energy potential functions, as the most important contents of the standard generalized material model, could be usually expressed as scalar productions of irreversibly thermodynamically variables and their conjugate ones. In this essay, the author analyzed the mathematical and physical meanings of dissipative potential function based upon the definitions and theorems of damage state, process, action and pseudo potential. Then one general method to depict the pseudo potential and its theoretical base of damage process was discussed. Subsequently, we studied the connection among damage action, pseudo potential and free energy. As the result of foregoing research, the writer gave the free energy function compatible with the previous constraint. The elementary discrete equations of continuum damage mechanics were derived from the damage action functional equation based on the variation of the incremental minimization principles.
2010 Vol. 31 (3): 237-243 [
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593
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244
A reduced order modeling of nonlinear electrostatic-mechanical systems based on energy ID approach
To build the reduced order model(ROM) of an electrostatically actuated micro-plate device,a system identification method is proposed. The strain energy and capacitance of the nonlinear system are written as multivariate polynomial functions of the structural modal amplitudes. The unknown coefficients of these polynomials are then computed using ther strain energy data and capacitance data which calculated from a set of steady state,high-order, nonlinear finite element models. The resulting strain energy and capacitance expressions can be used to develop the ROM of the device. The simulation with the ROM has a much lower computational cost. The caulculating results campare well with those from a high-fidelity finite element model, thus this modeling approach is validated.
2010 Vol. 31 (3): 244-251 [
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1239
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252
PROPAGATION BEHAVIORS OF SH WAVES IN ELASTIC LAYER/ PIEZOELECTRIC CYLINDER STRUCTURES WITH
This paper is concerned with the dispersion behaviors of SH waves propagating in elastic layer/piezoelectric cylinder structure with an imperfect interface. The surface of the elastic layer is assumed to be mechanically free. The stress at the interface is continuous, while the displacement is discontinuous. By solving the equations, the solution to the problem is expressed by Bessel function. Using the boundary conditions and the interface conditions, the dispersion equation is derived. The numerical examples are provided to show that the combined effects of the imperfect interface, the ratios of the thickness of the elastic layer to the thickness of the piezoelectric cylinder and the material properties of the piezoelectric cylinder on the dispersion characteristics.
2010 Vol. 31 (3): 252-257 [
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550
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559
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258
An experimental investigation and modeling of stress-strain behavior in 2D weave ceramic matrix composite
stress-strain behavior of 2D weave ceramic matrix composite is studied by experimental and theoretical method. 2D weave structure is simplified as crossply structure and fiber bundle undulation structure; Basing on matrix strength stochastic distributing theory and fiber failure stochastic distributing theory, stress-strain behavior and tangent tensile modulus related to applied load of unidirectional composite (0°ply) are obtained. Utilize the relationship of between crossply and unidirectional ceramic matrix composite stress-strain behavior, when their material is the same, one can obtain stress-strain behavior of crossply ceramic matrix composite. A two-dimensional analytical method is presented for fiber bundle undulation structure. Introduce composite strength model, the undulation structure is divided into sub-elements, in the meantime including linear behavior and non-linear behavior of sub-elements owing to off-axial loading. The failure analysis is carried out considering the failure of different sub-elements in fiber bundle undulation structure. Moreover，stress-strain behavior of undulation structure is obtained. Combine crossply and undulation structure’s stress-strain behavior, stress-strain behavior 2D weave ceramic matrix composite is gained; and theoretical result is well agreed with experimental result.
2010 Vol. 31 (3): 258-268 [
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647
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555
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269
FEM ANALYSES FOR INFLUENCE OF THERMAL WATER DIFFUSIVITY ON THM COUPLING IN UNSATURATED DUAL-POROSITY ROCK MASS
One kind of coupled thermo-hydro-mechanical model of dual-porosity medium for saturated-unsaturated ubiquitous-joint rock mass was established, and also the relative two-dimensional program of finite element method was developed. Taking a hypothetical nuclear waste repository in an unsaturated dual-porosity rock mass as the calculation example, three cases in which the thermal water diffusivities are different were simulated numerically, and the temperatures, pore pressures, saturations, flow velocities and principal stresses in the rock mass were investigated. The results show：the temperature fields and the stress fields of three cases are near the same；when the thermal water diffusivity is larger the nagative pore pressures in near field reach very high values，the nagative fracture pressures decrease to some extent and the saturate degrees change accordingly；if the thermal water diffusivity is small to a certain extent its influence will disappear.
2010 Vol. 31 (3): 269-277 [
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589
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278
Multiaxial High-cycle Fatigue Life Prediction of Welded Joints Based on Structural Stress
In this paper, fatigue stress at welded toes of welded joints is analyzed ,which is under bending and tortion loading. Stress state on critical plane at welded toes is studied with structural stress under in-phase and out-of-phase loading; Multiaxial fatigue life prediction method of welded joints was built based on structural stress and modified Wohler curve mothod;Some tube-to-plate welded joints under multiaxial loading was estimated using the proposed method, the results were compared with fatigue test data from related literature, The proposed method give the best results compared with some multiaxial fatigue prediction methods including Eurocode3 and the method have a good mesh-size insensitive characteristics.
2010 Vol. 31 (3): 278-285 [
Abstract
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598
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530
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286
The Rapidest Unloading in a Fragmentation Process of Brittle Solids
Brittle solids usually break into many pieces (fragmentizes) during a uniform high strain rate expansion process. This paper established a 1-D theoretical model to study the inner unloading of a 1-D brittle solid during a fragmentation process, and developed a method to calculate the average fragment size. Assuming that there exists an array of equally-spaced cracks in the 1-D solid, and the cracks open and develop simultaneously under a rapidly expanding rate. By symmetry, a unit crack body containing a crack is analyzed, with the separation behavior described by a cohesive law, and the dynamic response of the undamaged solid described by the elastodynamic equations. The problem is numerically solved using a differential scheme along the characteristic lines. Stress distributions in the crack body at different times and the average stress across the crack body are gained. The critical time at which the average stress is unloaded to zero is determined. It is found that for a prescribed strain rate, there exists an optimum crack spacing corresponding to the rapidest unloading process. Assuming that in a natural fragmentation process the brittle solid is unloaded in the fastest way, the average fragment size can be estimated. The calculation results show that this fragment size estimation agrees fairly well with the numerical results obtained previously allowing random crack nucleation. Effect of the cohesive fracture law on the average fragment size is also investigated with this “rapidest unloading property”.
2010 Vol. 31 (3): 286-295 [
Abstract
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648
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704
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296
STUDY ON INFLUENCE OF PORE DISTRIBUTION ON CONTACT STRENGTH OF THICK-WALLED CELLULAR STRUCTURES
Materials of H59 brass has been chosen for the preparation of cylindrical specimens which contain one pore, two pores, three pores and four pores, and YE-600 hydraulic pressure testing machine has been used for compression tests on these specimens. The effects of pore distribution on contact strength of thick-walled cellular structures have been discussed, and the damage mechanism of cellular structures has been explored by finite element method. The results show that: the level distribution approach of two pores is superior to the vertical approach; oblique equilateral triangle distribution approach of three pores is better than the equilateral triangle approach; square distribution approach of four pores is superior to the diamond approach; the increasing of pore distribution radius and the number of pores will improve the contact strength of thick-walled cellular structures; cracks generated in the edge of pore which is the nearest away from the initial point of contact; the cracks were caused by the largest principal stretching stress and expanded along the zone of pores stress concentration.
2010 Vol. 31 (3): 296-301 [
Abstract
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564
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560
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302
The transform method based on adaptive radial-based importance sampling for reliability sensitivity analysis with correlative normal variables
For the reliability sensitivity estimation with correlative normal variables, the Transform Method (TM) based on Monte Carlo simulation have been established firstly through transforming the correlative normal variables into independent ones, and its variances is analyzed also. In order to improve the efficiency of the reliability sensitivity analysis, the TM based on Monte Carlo simulation are combined with the adaptive radial-based importance sampling (ARBIS) method respectively, and the ARBIS-based TM is established for the reliability sensitivity analysis with correlative normal variables. Using information provided by the required samples for the reliability sensitivity estimation, the optimal radials of the ARBIS based method can be determined by gradual iteration. Furthermore, in the determination of the optimal radial, due to the interpolation constructed by the most probable point (MPP) in the failure domain of the each iteration, the robustness and the accuracy of the ARBIS based method are improved greatly. Since the universality and the robustness of the Monte Carlo simulation and the high efficiency of the radial-based importance sampling are propagated to the ARBIS-based TM, the established method is strongly applicable to the highly non-linear implicit limit state equation, systems with multiple failure modes in series, in parallel or in mixed states, and the multiple MPPs. The results of the illustrations adequately demonstrate the robustness, efficiency, accuracy and universality of the established ARBIS-based method.
2010 Vol. 31 (3): 302-309 [
Abstract
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610
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462
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简报
310
BOUNDARY ELEMENT ANALYSIS OF STRESS INTENSITY FACTORS OF V-NOTCH IN BONDED BI-MATERIALS
A new way to determinate the singularity stress field near the V-notch tip in bonded bi-materials by the boundary element method is proposed. A small sector around the V-notch tip is dug out from the V-notch structures. The displacements and stresses in this small sector are expressed as the linear combinations of finite terms of the series expansion with several singularity orders. The combination coefficients are the generalized stress intensity factors of the V-notch. Then the expressions of displacements and stresses are substituted into the boundary integral equations which are established in the V-notch structures without the tip sector. The combination coefficients can be obtained by solving the discretized boundary integral equations. Two examples demonstrate the efficiency of the present method.
2010 Vol. 31 (3): 310-318 [
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585
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550
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319
Barycentric finite element method and its application in elasticity theory
Abstract The basis functions of mean value interpolation on arbitrary polygonal element are constructed by geometric method. The formations of the basis functions were identical. The barycentric finite element method (BFEM) was brought by the Galerkin method. And the BFEM was applied in elasticity problems. The functions of BFEM were conforming on irregular polygons. Because of the property, essential boundary conditions can be imposed exactly. The functions have uniform expression for different edge number polygons, consequently the programs could be written conveniently. This provides greater flexibility to solve partial differential equations on complicated geometries. In this paper, BFEM was used in elasticity problems — the patch test, cantilever beam and the effective moduli of composite material. In the patch test, the error was realized the machine precision accuracy. The numerical results using the BFEM were in good agreement with beam theory predictions. The moduli of the composite material were simulated by BFEM. Compared the theory predictions and solution of FEM, the results showed the good consistency and had reasonable changing trend.
2010 Vol. 31 (3): 319-324 [
Abstract
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647
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551
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