应用数学和力学

2007 Vol. 28, No. 9

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Analysis of Delamination Growth for Composite Laminated Cylindrical Shells Under External Pressure

FU Yi-ming, YANG Jin-hua

2007, 28(9): 1009-1020.

Abstract(2915) PDF(689)

Abstract:
The delamination growth may occur in delaminated cylindrical shells under external pressure. This will cause structure failure. By using the variational principle of moving boundary and considering the contact effect between delamination regions, the delamination growth was investigated for cylindrical shells under the action of external pressure. At the same time, according to the Griffith criterion, the formulas of energy release rate along the delamination front were obtained. In the numerical calculation, the delamination growth of axisymmetrical laminated cylindrical shells was analyzed. And the effects of delamination sizes and depths, the geometrical parameters, the material properties and the laminate stacking sequences on delamination growth were discussed.

Coupled Viscoplasticity Damage Constitutive Model for Concrete Materials

LIU Chang-chun, LÜ He-xiang, GUAN Ping

2007, 28(9): 1021-1027.

Abstract(2974) PDF(890)

Abstract:
Coupled viscoplasticity damage constitutive model for concrete materials is developed within the framework of irreversible thermodynamics, and simultaneously the Helmholtz free energy function and a non-associated flow potential function are given, which include the internal variables of kinematic hardening, isotropic hardening and damage. Results from numerical simulation show that the model presented can describe the deformation properties of the concrete without the formal hypotheses of yield criterion and failure criteria, such as that volume dilatancy under compression; strain-rate sensitivity; stiffness degradation and stress-softening behavior beyond the peak stress which are brought by damages and fractures. Moreover, we could benefit from the application of finite element method based on this model under complex loading because of avoiding the choice of different constitutive model based on the deformation level.

Reflection and Transmission of Regular Waves at a Surface-Pitching Slotted Barrier

HUANG Zhen-hua, LIU Chun-rong

2007, 28(9): 1028-1036.

Abstract(2539) PDF(748)

Abstract:
The interactions between regular surface waves and a surface-pitching slotted barrier are investigated both analytically and experimentally. A quas-i linear theory was developed using the eigenfunction expansion method. The energy dissipation within the barriers was modeled by a quadratic friction factor, and an equivalent linear dissipation coefficient, which is depth-varying, wave-height dependent, was introduced to linearize the matching condition at the surface-pitching barrier. By comparison the theoretical results with laboratory experiments, it is shown that the present method can satisfactorily predict the variation of the reflection and transmission coefficients with wave height.

Combined Adaptive Meshing Technique and Characteristic Based Split Algorithm for Viscous Incompressible Flow Analysis

Suthee Traivivatana, Parinya Boonmarlet, Patcharee Theeraek, Sutthisak Phongthanapanich, Pramote Dechaumphai

2007, 28(9): 1037-1046.

Abstract(2829) PDF(617)

Abstract:
A combined chara cteristic-based splitalgorithm and anada ptive meshing technique foranalyzing two-dimensional viscous incompressible flow is presented. The method uses the three-node triangular element with equal-order interpolation functions forall variables of the velocity components and pressure. The main a dvantage of the combined method is toimprove solution a ccuracy by coupling an error estimation procedure to anada ptivemeshing technique that generates small elements in regions with largechange in solution gradients, and at the same time, larger elements in other regions. The performance of the combined procedure is evaluated by analyzing the three testcases of the flow past a cylinder, for their transient and steady-state flow behaviors.

Solution and Its Application of Transient Stream/Groundwater Model Subjected to Time-Dependent Vertical Seepage

TAO Yue-zan, YAO Mei, ZHANG Bing-feng

2007, 28(9): 1047-1053.

Abstract(2605) PDF(775)

Abstract:
Based on the first linearized Boussinesq equation, analytical solution of the transient groundwater model, which is used for describing phreatic flow in a semi-infinite aquifer bounded by a linear stream and subjected to time-dependent vertical seepage, is derived out by Laplace transform and the convolution integral. According to the mathematical characteristics of the solution, different methods for estimating aquifer parameters are constructed to satisfy different hydrological conditions. Then, the equation for estimating water exchange between stream and aquifer is proposed. And a recursion equation or estimating the intensity of phreatic evaporation is proposed too. A phreatic aquifer stream system located in Huaibei Plain, Anhui Province, China, is taken as an example to demonstrate the estimation process of the methods stated above.

Multi-Symplectic Methods for Membrane Free Vibration Equation

HU Wei-peng, DENG Zi-chen, LI Wen-cheng

2007, 28(9): 1054-1062.

Abstract(2623) PDF(715)

Abstract:
The multi-symplectic formulations of the membrane free vibration equation with periodic boundary conditions in Hamilton space were considered. The complex method was introduced and a semi-implicit twenty-seven-point scheme with certain discrete conservation lawsa multi-symplectic conservation law (CLS), an energy conservation law (ECL) as well as a momentum conservation law (MCL)is constructed to discrete the PDEs that are derived from the membrane free vibration equation. The results of the numerical experiments show that the multi-symplectic scheme has excellent long-time numerical behavior.

Two Dimensional Non-Selfsimilar Initial Value Problem for Adhesion Particle Dynamics

SUN Wen-hua, SHENG Wan-cheng

2007, 28(9): 1063-1070.

Abstract(2774) PDF(631)

Abstract:
Two dimensional non-selfsimilar initial value problem for adhesion particle dynamics with two pieces constant states separated by a circular is considered. By using the generalized characteristic method and the generalized Rankine-Hugoniot relation which is a system of ordinary equations, unique solution which includes delta-shock waves and vacuum is constructed.

Vertical Vibrations of Elastic Foundation Resting on Saturated Half-Space

WANG Guo-cai, WANG Zhe, MENG Fan-li

2007, 28(9): 1071-1078.

Abstract(2776) PDF(740)

Abstract:
The dynamic response of an elastic foundation of finite height bonded to the surface of a saturated halfspace is mainly concerned with. The foundation is subjected to time-harmonic vertical loadings. First, the transform solutions for the governing equations of the saturated media were obtained. Then, based on the assumption that the contact between the foundation and the halfspace was fully relaxed and the half-space was completely pervious or impervious, this dynamic mixed boundary-value problem can lead to dual integral equations, which can be further reduced to the Fredholm integral equations of the second kind and solved by numerical procedures. In the numerical examples, the dynamic compliances, displacements and pore pressure are developed for a wide range of frequencies and material/geometrical properties of the saturated soilfoundation system. In most cases, the dynamic behavior of an elastic foundation resting on the saturated media significantly differs from that of a rigid disc on the saturated half-space. The solutions obtained can be used to study a variety of wave propagation problems and dynamic soil-structure interactions.

Wave Equations With Several Nonlinear Source Terms

LIU Ya-cheng, XU Run-zhang, YU Tao

2007, 28(9): 1079-1086.

Abstract(3172) PDF(866)

Abstract:
The initial boundary value problem of nonlinear wave equations with several nonlinear source terms in a bounded domain is studied by potential well method. The structure of potential wells and some properties of depth function of potential well are given. The invariance of some sets under the flow of these problems and the vacuum isolating of solutions are obtained by introducing a family of potential wells, which indicates that if initial value of the problem belongs to potential well or its outside, all the solutions for the problem are in the same potential well or its outside respectively in any time. At the same time, there exists a region, in which there are no any solutions. Then the threshold result of global existence and nonexistence of solutions are given. Finally the problems with critical initial conditions are discussed.

Solvability of 2n-Order m-Point Boundary Value Problem at Resonance

JIANG Wei-hua, GUO Yan-ping, QIU Ji-qing

2007, 28(9): 1087-1094.

Abstract(2622) PDF(757)

Abstract:
The higher order multiple point boundary value problem at resonance is studied. Firstly, a Fredholm operator L with index zero and a projector operator P are defined in the subset of X and in X, respectively, such that L is invertible in the intersection of the domain of L and the kernel of P, where X is the space of functions whose (2n-1) th order derivatives are continuous. Secondly, a projector operator Q is defined in the Lebesgue integrable functions. space Y such that the composition of the inverse operator of L, I-Q and the nonlinear term f is compact, where I is the identity mapping in Y. Finally, imposing growth conditions on f, the existence of at least one solution for the 2n-order m-point boundary value problem at resonance is obtained by using coincidence degree theory of Mawhin. An example is given to demonstrate the result. The interest is that the nonlinear term f may be noncontinuous.

Propagation of Slip Pulse Along a Frictionless Contact Interface With Local Separation Between Two Piezoelectric Solids

BAI Yu-zhu, WANG Yue-sheng, YU Gui-lan

2007, 28(9): 1095-1101.

Abstract(2883) PDF(715)

Abstract:
The Stroh formalism of piezoelectric materials, Fourier analysis and singular integral equation technique were used to investigate the existence of a pulse at the frictionless interface in presence of local separation between two contact piezoelectric solids. The two solids were pressed together by uniaxial tractions and laid in the electric field. The problem was cast into a set of Cauchy singular integral equations of which the closedform solutions were derived. The numerical discussion on the existence of such a slip pulse was presented. The results show that such a slip pulse, which has squareroot singularities at both ends of the local separation zone, can propagate in most material combinations. And the existence of such a slip pulse will not be affected by the applied mechanical and electric fields in some special material combinations.

Bifurcation and Patterns Formation in a Coupled Higher Autocatalator Reaction Diffusion System

ZHANG Li, LIU Sang-yang

2007, 28(9): 1102-1114.

Abstract(2476) PDF(769)

Abstract:
Spatiotemporal structures arising in two identical cells, which are governed by higher autocatalator kinetics and coupled via diffusive interchange of autocatalyst, are discussed. The stability of the unique homogeneous steady state is obtained by the linearized theory. A necessary condition for bifurcations to spatially nonuniform solutions in uncoupled and coupled systems is given. Further information about Turing pattern solutions near bifurcation points is obtained by weakly nonlinear theory. Finally, the stability of equilibrium points of the amplitude equation is discussed by weakly nonlinear theory, with the bifurcation branches of the weakly coupled system.

Basis-Free Expressions for the Derivatives of a Subclass of Nonsymmetric Isotropic Tensor Functions

WANG Zhi-qiao, DUI Guan-suo

2007, 28(9): 1115-1122.

Abstract(2773) PDF(977)

Abstract:
The method for solving the derivatives of symmetric isotropic tensor-valued functions proposed by Dui and Chen was generalized to a sub-class of nonsymmetric tensor functions satisfying the commutative condition. This subclass of tensor functions is more general than those investigated by the existing methods. In the case of three distinct eigenvalues, the commutativity makes it possible to introduce two scalar functions, which will be used to construct the general nonsymmetric tensor functions and their derivatives. In the cases of repeated eigenvalues, the results are acquired by taking limits.

Global Dynamics Behaviors for a New Delay SEIR Epidemic Disease Model With Vertical Transmission and Pulse Vaccination

MENG Xin-zhu, CHEN Lan-sun, SONG Zhi-tao

2007, 28(9): 1123-1134.

Abstract(2714) PDF(1542)

Abstract:
A robust SEIR epidemic disease model with a profitless delay and vertical transmission was formulated, and the dynamics behaviors of the model under pulse vaccination were analyzed. By use of the discrete dynamical system determined by the stroboscopic map, an infection-free. periodic solution was obtained. Further, it is shown that the infection-free. periodic solution is globally attractive when some parameters of the model are under appropriate conditions. Using the theory on delay functional and impulsive differential equation, sufficient condition with time delay for the permanence of the system was obtained. And it was proved, that time delays, pulse vaccination and vertical transmission can bring obvious effects on the dynamics behaviors of the model. The results indicate that the delay is "profitless".