应用数学和力学

2004 Vol. 25, No. 11

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On the Receptivity of Pipe Poiseuille Flow With a Bump on the Wall Under the Periodical Pressure

WANG Zhi-liang, ZHOU Zhe-wei

2004, 25(11): 1101-1112.

Abstract(2167) PDF(470)

Abstract:
Asymptotic method was a dopted to obtain a receptivity model for a pipe Poiseuille flow under periodical pressure, the wall of the pipe with a bump. Bi-orthogonal eigen-function systems and Chebyshev collocation method were used to resolve the problem. Various spatial modes and the receptivity coefficients were obtained. The results show that different modes dominate the flow in different stages, which is comparable with the phenomena observed in experiments.

Nonlinear Dynamic Stability of Composite Laminated Plates

WEI De-min, YANG Gui-tong

2004, 25(11): 1113-1116.

Abstract(2536) PDF(998)

Abstract:
Catastrophe theory was applied to the investigation of nonlinear dynamic stability of composite laminated plates. The influence of large deflection, initial imperfection, support conditions and ply-angle of the fibers were considered. The catastrophic models and the critical conditions of dynamic buckling of composite laminated plates are obtained.

Dynamical Formation of Cavity in a Composed Hyper-Elastic Sphere

REN Jiu-sheng, CHENG Chang-jun

2004, 25(11): 1117-1123.

Abstract(2673) PDF(676)

Abstract:
The dynamical formation of cavity in a hyper-elastic sphere composed of two materials with the incompressible strain energy function, subjected a suddenly applied uniform radial tensile boundary dead-load, was studied following the theory of finite deformation dynamics. Besides a trivial solution corresponding to the homogeneous static state, a cavity forms at the center of the sphere when the tensile load is larger than its critical value. It is proved that the evolution of cavity radius with time displays nonlinear periodic oscillations. The phase diagram for oscillation, the maximum amplitude, the approximate period and the critical load were all discussed.

Computation of Super-Convergent Nodal Stresses of Timoshenko Beam Elements by EEP Method

WANG Mei, YUAN Si

2004, 25(11): 1124-1134.

Abstract(2641) PDF(758)

Abstract:
The newly proposed element energy projection(EEP) method has been applied to the computation of super-convergent nodal stresses of Timoshenko beam elements. General formulas based on element projection theorem were derived and illustrative numerical examples using two typical elements were given. Both the analysis and examples show that EEP method also works very well for the problems with vector function solutions. The EEP method gives super-convergent nodal stresses, which are well comparable to the nodal displacements in terms of both convergence rate and error magnitude. And in addition, it can overcome the "shear locking" difficulty for stresses even when the displacements are badly affected. This research paves the way for application of the EEP method to general one-dimensional systems of ordinary differential equations.

Semi-Weight Function Method on Computation of Stress Intensity Factors in Dissimilar Materials

MA Kai-ping, LIU Chun-tu

2004, 25(11): 1135-1142.

Abstract(2568) PDF(814)

Abstract:
Semi-weight function method is developed to solve the plane problem of two bonded dissimilar materials containing a crack along the bond. From equilibrium equation, stress and strain relationship, conditions of continuity across interface and free crack surface, the stress and displacement fields were obtained. The eigenvalue of these fields is lambda. Semi-weight functions were obtained as virtual displacement and stress fields with eigenvalue-lambda. Integral expression of fracture parameters, K_Ⅰ and K_Ⅱ, were obtained from reciprocal work theorem with semi-weight functions and approximate displacement and stress values on any integral path around crack tip. The calculation results of applications show that the semi-weight function method is a simple, convenient and high precision calculation method.

Stress Analysis of Restrained Bending for Box Beam With Rectangular Cross-Section Filled by Honeycomb Core

ZHANG Ying-shi, ZHANG Xing

2004, 25(11): 1143-1149.

Abstract(2163) PDF(699)

Abstract:
On the basis about studying free bending for box beam with rectangular cross-section filled by honeycomb core, supplementary displacements and stresses of restrained bending for such beam were analyzed. The hypothesis for separated variables was adopted to solve displacement. According to this, three aspect equations of geometrical, physical and balance were obtained. With Galerkin's method, it is summed up as two-order ordinary differential equations with the attenuation character. Analysis makes clear that attenuation speed of stress is concerned with a big load or a small one, geometric dimensions of cross section of beam, and physical parameter of material.

Research on Abrasion of Debris Flow to High-Speed Drainage Structure

CHEN Hong-kai, TANG Hong-mei, WU Si-fei

2004, 25(11): 1150-1156.

Abstract(2611) PDF(714)

Abstract:
As one weak topic in research of debris flow, abrasion of debris flow shortens obviously application life of control structure composed of concrete. High-speed drainage structure, one of the most effective techniques to control giant debris flow disaster, has shortened one-third application life due to abrasion by debris flow. Based on velocity calculation method founded by two-phase theory, research of abrasion mechanism of debris flow to high-speed drainage structure was made. the mechanisms includes both abrasion mechanism of homogeneous sizing and shearing mechanism of particle of debris flow to high-speed drainage through structure. Further abrasion equations of both sizing and particle were established by Newton movement theory of debris flow. And abrasion amount formula of the high-speed drainage through structure is set up by dimensional analysis. Amount to calculating in the formula is consistent with testing data in-situ, which is valuable in design of high-speed drainage structure.

Semi-Analytical Finite Element Method for Fictitious Crack Model in Fracture Mechanics of Concrete

WANG Cheng-qiang, ZHENG Chang-liang

2004, 25(11): 1157-1162.

Abstract(2061) PDF(703)

Abstract:
Based on the Hamiltonian governing equations of plane elasticity for sectorial domain, the variable separation and eigenfunction expansion techniques were employed to develop a novel analytical finite element for the fictitious crack model in fracture mechanics of concrete. The new analytical element can be implemented into FEM program systems to solve fictitious crack propagation problems for concrete cracked plates with arbitrary shapes and loads. Numerical results indicate that the method is more efficient and accurate than ordinary finite element method.

Pendulum With Linear Damping and Variable Length

CAI Jian-ping, YANG Cui-hong, LI Yi-ping

2004, 25(11): 1163-1168.

Abstract(2633) PDF(538)

Abstract:
The methods of multiple scales and approximate potential are used to study pendulums with linear damping and variable length. According to the order of the coefficient of friction compared with that of the slowly varying parameter of length, three different cases were discussed in details. Asymptotic analytical expressions of amplitude, frequency and solution were obtained. The method of approximate potential makes the results effective for large oscillations. A modified multiple scales method is used to get more accurate leading order approximations when the coefficient friction is not small. Comparisons are also made with numerical results to show the efficiency of the present method.

Stability and Bifurcation of a Human Respiratory System Model With Time Delay

SHEN Qi-hong, WEI Jun-jie

2004, 25(11): 1169-1181.

Abstract(2776) PDF(772)

Abstract:
The stability and bifurcation of the trivial solution in the two-dimensional differental equation of a model describing human respiratory system with time delay were investigated. Formulas about the stability of bifurcating periodic solution and the direction of Hopf bifurcation were exhibited by applying the normal form theory and the center manifold theorem. Furthermore, numerical simulation was carried out.

Kantorovich Theorem for Variational Inequalities

WANG Zheng-yu, SHEN Zu-he

2004, 25(11): 1182-1188.

Abstract(2792) PDF(732)

Abstract:
Kantorovich theorem was extended to variational inequalities by which the convergence of Newton iteration, the existence and uniqueness of the solution of the problem can be tested via computational conditions at the initial point.

Stress Analysis for an Infinite Strip Weakned by Periodic Cracks

CHEN Yi-zhou

2004, 25(11): 1189-1194.

Abstract(2023) PDF(608)

Abstract:
Stress analysis for an infinite strip weakened by periodic cracks is studied. The cracks were assumed in a horizontal position, and the strip is applied by tension "p" in y-direction. The boundary value problem can be reduced into a complex mixed one. It is found that the EEVM (eigen-function expansion variational method) is efficient to solve the problem. The stress intensity factor at the crack tip and the T-stress were evaluated. From the deformation response under tension the cracked strip can be equivalent to an orthotropic strip without cracks. The elastic properties in the equivalent orthotropic strip were also investigated. Finally, numerical examples and results were given.

Analysis on Transverse Impact Response of an Unrestrained Timoshenko Beam

CHEN Rong, ZHENG Hai-tao, XUE Song-tao, TANG He-sheng, WANG Yuan-gong

2004, 25(11): 1195-1202.

Abstract(2747) PDF(598)

Abstract:
A moving rigid-body and an unrestrained Timoshenko beam, which is subjected to the transverse impact of the rigid-body, are treated as a contact-impact system. The generalized Fourier-series method was used to derive the characteristic equation and the characteristic function of the system. The analytical solutions of the impact responses for the system were presented. The responses can be divided into two parts: elastic responses and rigid responses. The momentum sum of elastic responses of the contact-impact system is demonstrated to be zero, which makes the rigid responses of the system easy to evaluate according to the principle of momentum conservation.

A New Satic Mechanics Model to Solve Contact Problems in Mechanical Systems

LU Zhi-hua, YE Qing-tai

2004, 25(11): 1203-1210.

Abstract(2207) PDF(810)

Abstract:
The coupling of the local contact problems between the components and the deformation of the components in the mechanical system were discovered. A series of coordinate systems have been founded to describe the mechanical system with the contact problems. The method of isolating the boundary of contact body from others has been used to describe the constraint between the contacting points. A more generalized static mechanics model of the mechanical system with the contact problems has been founded through the principle of virtual work. As an application, the model was used to study the multi-teeth engagement problems in the inner meshed planet gear systems. The stress distribution of contact gears was got. A test has verified that the static contact model and the computational method are right.