力学学报

The joint probability density function of nonlinear dynamic stochastic response of structures

In nonlinear dynamic response analysis and reliability evaluation of structures, it is of paramount importance to capture the joint probability density function of different response quantities. In the present paper, under the basic thoughts of density evolution, the generalized density evolution equation is extended to derive a two-dimensional partial differential equation governing the joint probability density function. The numerical algorithm is outlined combining the deterministic dynamic response analysis and the finite difference method. Numerical example is conducted to analyze a ten-story frame structure with stochastic parameters subjected to random ground motions. The investigations show that the joint probability density function is irregular like hilly country, while the coefficient of covariance is time variant.Keywords: nonlinear, dynamic response, probability density evolution method, joint probability density function, coefficient of covariance

2006, 38(5): 8-8. doi: 10.6052/0459-1879-2006-5-2005-430

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2006, 38(5): 577-585. doi: 10.6052/0459-1879-2006-5-2005-621

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Numerical Investigation on Shock-Induced Gaseous Detonation in a Straight Duct with Multi-Obstacles

Numerical simulation was carried out to investigate into shock-induced detonation initiation of the premixed H2/O2/N2 gas mixture in a duct with multi rectangular-shaped obstacles. Numerical results show that even if incident shock is not strong enough to induce the direct initiation of combustible gas mixture behind the shock front, the onset of detonation may take place in the cavity between obstacles where is far behind the shock front. Compression wave, expansion wave and shear layer generated from the surface of obstacles play important roles on chemical reaction that triggers the DDT process of detonation. Increasing N2 dilution of combustible gas mixture will influence the profile of wall temperature behind detonation wave and varying the distance between obstacles will results in the changes in the position of detonation initiation.Key words：Detonation initiation, multi-obstacle, cavities in wall

2006, 38(5): 586-592. doi: 10.6052/0459-1879-2006-5-2005-075

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Numerical analysis of Marangoni convection in liquid bridge with liquid encapsulation

The physical and mathematical models of the Marangoni convection in an encapsulated liquid column (or two immiscible coaxial liquid columns) are established. A numerical simulation of the Marangoni convection in the encapsulated liquid column is performed by employing vorticity-streamfunction method and alternative direction implicit scheme based on finite difference. The distributions of temperature and flow field in two immiscible coaxial liquid columns are obtained. It is verified that the liquid encapsulation can reduce the Marangoni convection in the encapsulated liquid bridge. Effects of a series of non-dimensional parameters on Marangoni convection are analyzed.Keywords: liquid bridge with liquid encapsulation, Marangoni convection, numerical analysis, microgravity

2006, 38(5): 593-598. doi: 10.6052/0459-1879-2006-5-2005-351

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2006, 38(5): 599-604. doi: 10.6052/0459-1879-2006-5-2005-100

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Viscous-spring dynamical artificial boundary for saturated porous media

In the dynamic finite element analysis of saturated porous media in unbounded space or half-space, a finite region is usually selected for computing ,so how to deal with the boundries of this finite region is the key procedure for stimulating and analysing the open system. Based on Biot's dynamic theory about saturated porous media,the normal and tangent stress formulaes are deduced for cylindrical waves and spherical waves propagating outward in unbounded saturated porous media.According to the formulaes , the viscous-spring dynamical artificial boundary is developed in this paper on which continuely distributing physical components such as viscous damping or parallel connecting spring and viscous damping are placed on the artificial boundaries to stimulate the affection of unbounded media..The exemples show that the viscous-spring dynamical artificial boundaries have fine accuracy and stability.Key word: saturated porous media, Viscous-spring dynamical artificial boundary, wave motion

2006, 38(5): 605-611. doi: 10.6052/0459-1879-2006-5-2005-403

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Three-dimensional fracture mechanics for transversely isotropic materials

2006, 38(5): 612-617. doi: 10.6052/0459-1879-2006-5-2005-529

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The Elastic-viscoplastic Field At The Mixed-mode Steadily Propagating Crack-Tip Under Compression And Shear

, Bo Zhou

Under the assumption that the artifical viscosity cofficient is in inverse proportion to power law of the plastic strain rate.The friction touch effection beween viscosity and crack-tip surface be considerde,the asymptotic solution is established for elastic-viscoplastic field at the mixed-mode propagating crack-tip under comprission and shear.The numerical solution to crack-tip without stress and stain gap is got. The variation of numerical solution are discussed for the mixed-mode under compression and shear according to each parameter.It is shown in numerical results and analysis that for the mixed-mode crack-tip field under compressing and shear is whole plastic without elatic unloaded section,viscosity effection is an important factor when propagating crack-tip field is studied, whether the mixed-mode crack trend to mode I or to mode II,the hydro-statil stresses are added according to the increasing on frictional coefficient. The crack-tip propagating velocity is prevented due to the frictoon on crack face,the tenacity on crack-tip freld become more higher with the more strorger on friction.Keywords: mixed-mode crack-tip under compression and shear; steadily propagating; viscosity effectionelastic-viscoplastic materials

2006, 38(5): 618-625. doi: 10.6052/0459-1879-2006-5-2005-583

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Propagation of Failure Front in Shock-loaded Polycrystalline Alumina

The dynamic failure behaviors of brittle alumina under shock compression were investigated in this paper. Plate impact experiments were carried out on alumina whereas the free surface velocity profiles were measured through VISAR and the recovered samples were scanned with SEM. The failure front manifested to propagate in the material when the particle velocity history at free surface was checked. The dynamic failure mechanism in ceramics was generally probed associated with the consideration to the mesoscopic structural characteristics as well as induced stress distribution singularity within the mesoscope. Dynamic failure properties of the failure front were discussed occurring in the alumina. A dynamic failure model of shock-loaded alumina and the governing equation of failure front propagation along with a respective failure criterion were built up. A numerical results on propagation of failure front in terms of longitudinal and transverse stress in alumina were presented.Key words: alumina, plate impact experiment, failure front, failure model

2006, 38(5): 626-632. doi: 10.6052/0459-1879-2006-5-2005-017

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Multiple Objective Topology Optimal Design of Multiphase Microstructures

The overall behavior of an elastic material with a periodic microstructure is governed by the microstructure whose effective properties are computed using a homogenization method. Improvements in materials performance can be obtained by designing new topologies of microstructures of these materials. The topology and volume fraction of the microstructure determines the effective properties of the materials. A multiple objective function model is presented to optimize the topology of the periodic microstructure with two or three-phase materials. A combination of effective elastic properties is maximized. Constraints on material volume fraction and perimeter control for eliminating the checkerboard are considered without the restriction of prescribed microstructure symmetry. By means of finite element method and convex programming techniques, several examples of optimal design of multiphase microstructures are solved. Influences of volume fraction, mesh dependence and elastic modulus ratio of three-phase materials on the optimal microstructures are discussed. Key words: topology optimization，microstructure design, multiphase materials, Multiple objective function

2006, 38(5): 633-638. doi: 10.6052/0459-1879-2006-5-2005-322

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Combined application of vibration testing and wavelet packet analysis on structural damage alarming

The wavelet packet impulse response function and wavelet packet energy spectrum of the structural dynamic system are proposed to reflect the structural dynamic characteristics, which is obtained by the wavelet packet decomposition of vibration stimulation signal and response signal based on the combination of vibration testing and wavelet packet analysis. Through a vibration testing analysis of a reinforced concrete slab subjected to static loading series, the damage status of the slab during different loading phases are determined based on the calculation of wavelet packet impulse response functions and wavelet packet energy spectrum. The proposed method overcomes the shortcoming that wavelet packet energy spectrum calculated directly from structural dynamic response cannot reflect the structural dynamic characteristics and the experiment results confirmed the feasibility of the method.Key words：damage alarming; vibration testing; wavelet analysis; wavelet packet analysis; wavelet packet energy spectrum

2006, 38(5): 639-644. doi: 10.6052/0459-1879-2006-5-2005-562

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Interval analysis method for response analysis of nonlinear vibration systems with uncertain parameters

Dynamic response of the MDOF nonlinear vibration system with uncertain parameters is studied. Based on interval mathematic, modeling the uncertain parameters as interval numbers, a new method, which approximately estimates the nonlinear dynamic response range with the help of first-order Taylor series, is presented. Comparisons between the interval analysis method and the probability perturbation finite element method in mathematical proof and numerical examples are performed, which show the advantages of the presented method, including less prior information need on uncertain parameters and higher accuracy.

2006, 38(5): 645-651. doi: 10.6052/0459-1879-2006-5-2005-361

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Evaluation of damping ratio of the small-amplitude liquid sloshing within the cylindrical container with a ring baffle

The damping ratio is an important parameter in the research on fuel sloshing of spacecraft. In this paper, the liquid sloshing in the cylindrical container with rigid and elastic ring baffles are emulated by finite element method respectively, based on the hypothesis of ideal linear potential flow and the damping mechanism adopted in recent dissertations. Compared with the experiments of NASA, the frequency derived by the finite element method coincide with that of NASA well, while there is a considerable discrepancy with the damping ratio. Finally, the comparison of the flow fields of viscous liquid sloshing in a rectangle tank with a baffle and those without baffle emulated by ALE finite element method show that one important form of the "drag" that the baffle applying to the liquid is vortex. Key word：sloshing, frequency, damping ratio, baffle, tank, liquid-solid interactionALE finite element method

2006, 38(5): 660-667. doi: 10.6052/0459-1879-2006-5-2005-439

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The effects of second-order slip-flow on the steady performance of micro gas bearing

The effects of slip flow on the steady mechanicalperformances of the micro gas bearing are discussed. Considering thedimensional characters of the micro bearing and judging from the flow'sKnudsen number, the flow in the bearing is in the slip regime instead of thecontinuous regime. The modified Reynold's equations of first-order slip-flowand second-order slip-flow for the micro gas bearing are obtained. Solving theReynold's equations for the continuous regime and the two slip regimes with thefinite difference method (FDM), the gas pressure distributions, the non-dimensional load capacities and attitude angles are obtained.The comparisons of the load capacities and attitude angles between the threeregimes are made, and it is shown that the mechanical performance withthe slipregime distinctly differs with that of the continuous regime. Ananalysis illustrates that the slip flow regime has great effects on thesteady mechanical performances of the micro bearing. The second-orderslip-flow model can produce a good result for high eccentricity ratio operation.

2006, 38(5): 668-673. doi: 10.6052/0459-1879-2006-5-2005-226

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Theoretical analysis of the three balls system with multiple impact

2006, 38(5): 674-681. doi: 10.6052/0459-1879-2006-5-2005-357

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A method of symplectic enginsolutions in Stokes flow

In this paper, two dimensional Stokes flow are reduced to the determination of eigenvalues andeigensolutions with the aid of Hamiltonian system. The close method of the symplectic enginsolution ispresented based on the completeness of the space of symplectic enginsolutions. The results explain that basicflows can be described by zero-enginvalue enginsolutions and end effects for Stokes flow by enginsolutions ofnon-zero-enginvalues. Numerical results reveal some rules of symplectic enginvalues and enginsolutions.Numerical examples show that the irregular flow of the ends of the pipeline is decayed. At the same time, themethod is a path for solving the other problem.Key Words: Stokes flow；Incompressible fluid； Hamiltonian system； symplectic

2006, 38(5): 682-687. doi: 10.6052/0459-1879-2006-5-2005-576

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Crack tip field in functional gradient material with exponential variation of elastic constants for the case ν≠0

The present paper derives the solution of the crack tip field in functional gradient material with exponential variation of elastic constants for the case 0. The crack is located on the Oxis (Fig.1). From the result in the Appendix VIII, only the exponential term exp(ax) is discussed. On the basis of exact mathematical theory, it has been found that although the exponential term is exp(ax) in the constitutive equations, yet it becomes exp(ax/2+ak11/2y/2-kr/2) and exp(ax/2-ak11/2y/2-kr/2) in the exact relation. For some numerical solutions, considering the results of the exact relation, they become explained more easily. Further study must focus on the influence of the large deformation.

2006, 38(5): 688-691. doi: 10.6052/0459-1879-2006-5-2005-350

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Anisotropic yield criterion based on microplane effective stress vector

In this paper, based on microplane model, the damagevariable is defined as the reduction of loading area on microplanes, whichis an scalar-valued ODF(Orientation Distribution Function). Kachanov'seffective stress in one dimension is generalized to three dimension byintroducing the concept of effective stress vector on microplanes. Accordingto the concept of microplane effective stress vector, the integral relationsbetween macro stress tensor, its invariants and stress vector onmicroplances for virgin material are generalized to damaged material byreplacing invariants of macro stress tensor as its effective counterparts.For damaged material, macro effective stress tensor and its invariants canbe expressed as the functions of macro nominal stress tensor and fabrictensors of microplane damage. An anisotropic yield criterion is obtained fordamaged materials by extending Drucker-Prager yield criterion. It is shownthat macro effective stress tensor has the same form with Murakami'seffective stress tensor and the anisotropic yield criterion has the sameform with the phenomenological yield criterion proposed by Liu et al. Whenhydrostatic stress has no influence on material yield such as metals, theanisotropic yield criterion has the same form with Hill's anisotropic yieldcriterion.

2006, 38(5): 692-697. doi: 10.6052/0459-1879-2006-5-2005-467

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The mixed-mode propagation of fatigue crack in CTS specimen

In this paper, the mixed-mode fatigue tests are carried out with the CTSspecimen (Compact-Tension-Shear) and the mixed-mode loading device developedby Richard [1]. Three loading angles and two materials are selected in theexperiments. The effect of loading angle on the crack propagation isanalyzed numerically and experimentally. According to the experimentalresults, the fatigue crack growth rate is related to the loading angle. Forthe same initial equivalent stress intensity factor (combination of thestress intensity factor in mode I and in mode II), the crack grows slowestunder pure mode I loading. The photos of crack bifurcation and the resultsof the crack growth rate in different specimens under different mixed-modeloadings are presented. Furthermore, a numerical model of fatigue crackpropagation is proposed on the basis of the experimental results to evaluatethe influences of loading mode on the crack growth rate. The validation ofthe model is performed on the steel specimens under mixed mode loading. Thenumerical evaluations are in good agreement with the experimental results.

2006, 38(5): 698-704. doi: 10.6052/0459-1879-2006-5-2005-441

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An adaptive importance sampling algorithm and its application for multiple failure modes

For failure probability calculation of system with multiple failure modes,an adaptive importance sampling algorithm is developed. The importancesampling function for each failure mode is sought and optimized by means ofthe simulated annealing method. During the optimization of the importancesampling function, the variance of the failure probability evaluation isdecreased. For the system with multiple failure modes, a weighted mixingimportance sampling function is proposed, in which the contribution of eachfailure mode to the system failure probability is represented appropriately.When not all basic variables are included in the limit state equation ofsome failure modes, an extended algorithm is presented to unify the basicvariables in all failure modes, hence the weighted mixing importancesampling can be implemented successfully in the case. The variances and thecoefficients of variation are derived for the failure probabilityevaluation. The feasibility and the rationality of the presented method areillustrated by numerical example and engineering example.

2006, 38(5): 705-711. doi: 10.6052/0459-1879-2006-5-2005-023

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Transfer matrix method for 2-dimension system

Taking vibration characteristics of thin plate for example,the transfer matrix method for 2-dimension system is developed. On the basisof the transfer matrices of lumped mass and mass less beam, the transfermatrix of sub-structure which is arranged in column is acquired. By means ofthe transfer matrix method for 2-dimension system, the overall transferequation of plate can be obtained easily, then the characteristics equationunder arbitrary boundary condition can be got. Numerical solution ofvibration characteristics of thin plate with transverse vibration arecomputed under two boundary conditions. The computational results show thatthe transfer matrix method can be applied to dynamics problems of twodimension system similar to thin plate, and the dynamic equations of globalsystem is not indispensable.

2006, 38(5): 712-720. doi: 10.6052/0459-1879-2006-5-2005-429

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