应用数学和力学

2006 Vol. 27, No. 7

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Deformation Rigidity Analysis of Assumed Stress Modes in Hybrid Elements

ZHANG Can-hui, HUANG Qian, FENG Wei

2006, 27(7): 757-764.

Abstract(2312) PDF(722)

Abstract:
The new methods to determine the zero-energy deformation modes in the hybrid elements and the zero-energy stress modes in their assumed stress fields are presented by the natural deformation modes of the elements. And the formula of the additional element deformation rigidity due to additional mode into the assumed stress field is derived. Based on That, it is concluded in theory that the zero-energy stress mode cannot suppress the zero-energy deformation modes but increase the extra rigidity to the nonzero-energy deformation modes of the element instead. So they should not be employed to assume the stress field. In addition, the parasitic stress modes will produce the spurious parasitic energy and result in the element behaving over rigidity. Thus, they should not be used into the assumed stress field even though they can suppress the zero-energy deformation modes of the element. The numerical examples show the performance of the elements including the zero-energy stress modes or the parasitic stress modes.

Investigation of the Behavior of a Model-Ⅰ Interface Crack in Piezoelectric Materials by Using the Schmidt Method

ZHOU Zhen-gong, WANG Biao

2006, 27(7): 765-774.

Abstract(3005) PDF(634)

Abstract:
The behavior of a Mode-Ⅰ interface crack in piezoelectric materials is investigated under the assumptions that the effect of the crack surface overlapping very near the crack tips is negligible. By use of the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations in which the unknown variables are the jumps of displacements across the crack surfaces. To solve the dual integral equations, the jumps of the displacements across the crack surfaces are expanded in a series of Jacobi polynomials. Contrary to the previous solution of the interface crack in piezoelectric materials, it is found that the stress and the electric displacement singularities of the present interface crack solution are the same as those of the ordinary crack in homogenous materials. The solution can be returned to the exact solution when the upper half plane material is the same as the lower half plane material.

On the Problem of Nearest Common Fixed Point of Nonexpansive Mappings

ZHANG Shi-sheng

2006, 27(7): 775-780.

Abstract(2148) PDF(676)

Abstract:
The purpose is by using the viscosity approximation method to study the cnvergence problem of the iterative scheme for an infinite family of onexpansive mappings and a given contractive mapping in a reflexive Banach space. Under suitable conditions, it was proved that the iterative sequence converges strongly to a common fixed point which was also the unique solution of some variational inequality in a reflexive Banach space. The results presented extend and improve some recent results.

Structural Damage Model of Unsaturated Expansive Soil and Its Application in Multi-Field Couple Analysis on Expansive Soil Slope

LU Zai-hua, CHEN Zheng-han, FANG Xiang-wei, GUO Jian-feng, ZHOU Hai-qing

2006, 27(7): 781-788.

Abstract(2912) PDF(861)

Abstract:
Focused on the sensitivity to climate change and the special mechanical characteristics of undisturbed expansive soil, an elasto-plastic damage constitutive model were proposed based on the mechanics of unsaturated soil and the mechanics of damage. Undisturbed expansive soil was considered as a compound of non-damage part and damaged part. The behavior of the non-damaged part was described using non-linear constitutive model of unsaturated soil. The property of the damaged part was described using a damage evolution equation and two yield surfaces, i. e., loading yield and shear yield. Further more, a consolidation model for unsaturated undisturbed expansive soil was established and a FEM program named UESEPDC was designed. Numerical analysis on solid-liquid-gas triphases and multi-field couple problem was conducted for four stages and the fields of stress, displacement, pore water pressure, pore air pressure, water content and suction in an expansive soil slope were obtained.

Wavelet-Based Estimators of the Mean Regression Function With Long Memory Date

LI Lin-yuan, XIAO Yi-min

2006, 27(7): 789-798.

Abstract(2384) PDF(746)

Abstract:
An asymptotic expansion is provide for the mean integrated squared error (MISE) of nonlinear wavelet-based mean regression function estimators with long memory data. This MISE expansion is shown, when the underlying mean regression function is only piecewise smooth. It is the same with analogous expansion for the kernel estimators. However, for the kernel estimators, this MISE expansion generally fails if the additional smoothness assumption is absent.

Torsional Oscillation of a Rigid Disk in an Infinite Transversely Isotropic Elastic Cylinder

Sakti Pada Barik, Mridula Kanoria, P. K. Chaudhuri

2006, 27(7): 799-804.

Abstract(2909) PDF(532)

Abstract:
In the present analysis torsional oscillation of a rigid disk in an infinite transversely isotropic elastic cylinder has been considered. The effects of anisotropy in the stress intensity factor have been shown graphically.

Study of Airship Attitude Tracking System

WANG Xiao-liang, SHAN Xue-xiong

2006, 27(7): 805-811.

Abstract(2476) PDF(621)

Abstract:
The attitude tracking control problem for an airship with parameter uncertainties and external disturbances was considered. The mathematical model of the airship attitude is a multi-input multi-output uncertain nonlinear system. Based on the characteristics of this system, a design method of robust output tracking controllers was adopted based on the upper-bounds of the uncertainties. Using the input/ output feedback linearization approach and Liapunov method, a control law was designed, which guarantees that the system output exponentially tracks the given desired output. The controller is easy to compute and complement. Simulation results show that, in the closed-loop system, precise attitude control is accomplished in spite of the uncertainties and external disturbances in the system

Analytical Solutions for Response of Collision of Particle With Conical Rod Caused by Longitudinal Vibration

BAO Si-yuan, DENG Zi-chen

2006, 27(7): 812-818.

Abstract(2662) PDF(728)

Abstract:
The objective is to present analytical solutions of longitudinal impact analysis for slender conical rods struck by a particle and a new method is proposed for conical rod-particle impact analysis, in which the superposition method is used and the response of the rod is presented. These analytical results are exact and can be used to validate the numerical methods or other analytical results. The numerical example shows that one of the advantages of the present method is that the analytical form is very simple. The result is that mass ratio and some variables describing the geometrical shape of rods such as taper, length and radius play an important role in impact dynamic system.

Flow-Induced Internal Resonances and Mode Exchange in Horizontal Cantilevered Pipe Conveying Fluid(Ⅰ)

XU Jian, YANG Qian-biao

2006, 27(7): 819-824.

Abstract(2789) PDF(748)

Abstract:
The Newtonian method is employed to obtain nonlinear mathematical model of motion of a horizontally cantilevered and inflexible pipe conveying fluid. The order magnitudes of relevant physical parameters are analyzed qualitatively to establish a foundation on the further study of the model. The method of multiple scales is used to obtain eigenfunctions of the linear free-vibration modes of the pipe. The boundary conditions yield the characteristic equations from which eigenvalues can be derived. It is found that flow velocity in the pipe may induced the 3:1, 2:1 and 1:1 internal resonances between the first and second modes such that the mechanism of flow-induced internal resonances in the pipe under consideration is explained theoretically. The 3:1 internal resonance first occurs in the system and is, thus, the most important since it corresponds to the minimum critical velocity.

Flow-Induced Internal Resonances and Mode Exchange in Horizontal Cantilevered Pipe Conveying Fluid(Ⅱ)

XU Jian, YANG Qian-biao

2006, 27(7): 825-832.

Abstract(2666) PDF(779)

Abstract:
Based on the nonlinear mathematical model of motion of a horizontally cantilevered rigid pipe conveying fluid, the 3:1 internal resonance induced by the minimum critical velocity is studied in details. With the detuning parameters of internal and primary resonances and the amplitude of the external disturbing excitation varying, the flow in the neighborhood of the critical flow velocity yields that some nonlinearly dynamical behaviors occur in the system such as mode exchange, saddle-node, Hopf and co-dimension 2 bifurcations. Correspondingly, the periodic motion loses its stability by jumping or flutter, and more complicated motions occur in the pipe under consideration. The good agreement between the analytical analysis and the numerical simulation for several parameters ensures the validity and accuracy of the present analysis.

Incremental Harmonic Balance Method for Airfoil Flutter With Multiple Strong Nonlinearities

CAI Ming, LIU Ji-ke, LI Jun

2006, 27(7): 833-838.

Abstract(3387) PDF(1647)

Abstract:
The incremental harmonic balance method was extended to analyze the flutter of systems with multiple structural strong nonlinearities. The strongly nonlinear cubic plunging and pitching stif-f ness terms were considered in the flutter equations of two-dimensional airfoil. First, the equations were transferred into matrix form, then the vibration process was divided into the persistent incremental processes of vibration moments. And the expression of their solutions could be obtained by using a certain amplitude as control parameter in the harmonic balance process, and then the bifurcation, limit cycle flutter phenomena and the number of harmonic terms were analyzed. Finally, numerical results calculated by the Runge-Kutta method were given to verify the results obtained by the proposed procedure. It has been shown that the incremental harmonic method is effective and precise in the analysis of strongly nonlinear flutter with multiple structural nonlinearities.

Synchronous Effect of Slipping Heavy Loads on a Ro-Ro Ship Rolling in Waves

ZHANG Yin-long, SHEN Qing, CHEN Xu-jun

2006, 27(7): 839-844.

Abstract(2922) PDF(754)

Abstract:
Common effect of wave and slip of internal vehicles will make rolling of the roll-on ship serious. This is one of the important reasons for overturn of ro-ro ships. The multibody system with a floating base is composed of ro-ro ship and slipping vehicles. The rolling angle of the ship and the transverse displacements of the slipping vehicles on desk are taken as freedoms. Making use of the analysis of apparent gravitation and apparent buoyancy, the wave rolling moment is derived. By means of dynamic method of multibody system, dynamic equations of the system are established. Taking a certain channel ferry as an example, a set of numerical calculation hase been carried out for rolling response of the multibody system with a floating base of a ro-ro ship and displacements response of the slipping vehicles under common effect of free slipping vehicles and wave, and a conclusion has been drawn that the motion of the numerous free slipping heavy loads will trend to be synchronous under restraining of the side-wall bulkhead with time because of repeated collision.

Research on Damage Model of Control Fissure in Perilous Rock

CHEN Hong-kai, TANG Hong-mei, YE Si-qiao

2006, 27(7): 845-851.

Abstract(2712) PDF(827)

Abstract:
Hitherto, perilous rock is the weakest topic in disaster studies. Specially, damage of con trol fissure under loads is one key technique in study of developing mechanism of perilous rock. Dam age division of end area of control fissure was defined, then calculation methods of timed-Poisson s ratio and timed-Young s modulus were established in damage mechanics theory. Further, the damage constitutive equation of control fissure is set up, which founds important basis to numerical simulation for control fissure to develop.

Nonexistence of Global Solutions of a Nonlinear Hyperbolic Equation With Material Damping

SONG Chang-ming

2006, 27(7): 852-858.

Abstract(2772) PDF(771)

Abstract:
Concerns with the nonexistence of global solutions to the initial boundary value problem for a nonlinear hyperbolic equation with material damping. Nonexistence theorems of global solutions to the above problem are proved by the energy method, Jensen inequality and the concavity method, respectively. As applications of our main results, three examples are given.

Simulation of the Sedimentation of Two Circular Particles With Collision Considered in a Vertical Channel

WANG Ye-long

2006, 27(7): 859-866.

Abstract(2540) PDF(702)

Abstract:
D2Q9 model of Lattice Boltzmann equation method was used to simulate the sedimentation of two circular particles in a bounded two dimension channel. The characteristics of the sedimentation shows some periodicity for the Reynolds number Re chosen, 0.1~20. The larger the Reynolds number, the stronger the interaction between the two particles and the larger the transversal displacements. For large Re, the two particles leading alternately; for small Re, the initially leading particle will keep its leading position and for moderate Re, the initially upper particle will get leading position and keep it. The influence of the initially relative position of the two particles on sedimentation is small. The width of the channel won't change the characteristics of the sedimentation as a whole, but will change the period of the sedimentation. The wider the channel, the longer the period will be.

Boundary Integral Formula for the Elastic Plane Problem of Exterior Circular Domain

DONG Zheng-zhu, LI Shun-cai, YU De-hao

2006, 27(7): 867-873.

Abstract(2641) PDF(647)

Abstract:
After the stress function and its normal derivative on the boundary for the plane problem of exterior circular domain are expanded into Laurent series, comparing them with the Laurent series of the complex stress function and making use of some formulas in Fourier series and in the convolutions, the boundary integral formula of the stress function is derived further. Then the stress function can be obtained directly by the integration of the stress function and its normal derivative on the boundary. Some examples are given. It shows that the boundary integral formula of the stress function is convenient to be used for solving the elastic plane problem of exterior circular domain.

A Level-Value Estimation Method for Solving Global Optimization

WU Dong-hua, YU Wu-yang, TIAN Wei-wen, ZHANG Lian-sheng

2006, 27(7): 874-882.

Abstract(2683) PDF(983)

Abstract:
A level-value estimation method was illustrated for solving the constrained global optimization problem. The equivalence between the root of a modified variance equation and the optimal value of the original optimization problem is shown. An alternate algorithm based on the Newton's method is presented and its implementable approach's convergence is proved. Preliminary numerical results indicate that the method is effective.