应用数学和力学

2005 Vol. 26, No. 12

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New Boundary Element Method for Torsion Problems of a Cylinder With Curvilinear Cracks

WANG Yin-bang, LU Zi-zi

2005, 26(12): 1387-1393.

Abstract(2793) PDF(643)

Abstract:
The Saint-Venant torsion problems of a cylinder with curvilinear cracks were considered and reduced to solving the boundary integral equations only on cracks.Using the interpolation models for both singular crack tip elements and other crack linear elements,the boundary element formulas of the torsion rigidity and stress intensity factors were given.Some typical torsion problems of a cylinder involving a straight,kinked or curvilinear crack were calculated.The obtained results for the case of straight crack agree well with those given by using the Gauss-Chebyshev integration formulas,which demonstrates the validity and applicability of the present boundary element method.

Interfacial Crack Analysis in Three-Dimensional Transversely Isotropic Bi-Materials by Boundary Integral Equation Method

ZHAO Ming-hao, LI Dong-xia, SHEN Ya-peng

2005, 26(12): 1394-1400.

Abstract(3006) PDF(654)

Abstract:
The integr al-differential equations for three-dimensional planar interfacial cracks of arbitrary shape in transversely isotropic bimaterials were derived by virtue of the Somigliana identity and the fundamental solutions,in which the displacement discontinuities across the crack faces are the unknowns to be determined.The interface is parallel to both the planes of isotropy.The singular behaviors of displacement and stress near the crack border were analyzed and the stress singularity indexes were obtained by integral equation method.The stress intensity factors were expressed in terms of the displaceme nt discontinuities.In the non-oscillatory case,the hyper-singular bo undary integral-differential equations werere duced to hyper-singular boundary integral equations similar to those of homogeneously isotropic materials.

System of Coincidence Theorems in Product Topological Spaces and Applications(Ⅰ)

DING Xie-ping

2005, 26(12): 1401-1408.

Abstract(2970) PDF(917)

Abstract:
A new notion of finite continuous topological space (in short,FC-space) without convexity structure was introduced.A new continuous selection theorem was established in FC-spaces.By applying the continuous selection theorem,some new coincidence theorems for two families of set-valued mappings defined on product space of noncompact FC-spaces are proved under much weak assumptions.These results generalize many known results in recent literature.Some applications will be given in a follow-up paper.

System of Coincidence Theorems in Product Topological Spaces and Applications(Ⅱ)

DING Xie-ping

2005, 26(12): 1409-1416.

Abstract(2563) PDF(685)

Abstract:
By applying coincidence the orems in ( ) for two families of set-valued mappings defined on product space of noncompact FC-spaces in prece ding paper,some new existence theorems for system of vector equilibrium problems,system of inequalities and system of minimax the orems weree stablished in FC-spaces.These results generalize some known results in recent literature.

Dual Reciprocity Boundary Element Method for Flexural Waves in Thin Plate With Cutout

GAO Suo-wen, WANG Yue-sheng. ZHANG Zi-mao, MA Xing-rui

2005, 26(12): 1417-1424.

Abstract(3174) PDF(475)

Abstract:
The theoretical analysis and numerical calculation of scattering of elastic waves and dynamic stress concentrations in the thin plate with the cutout was studied usingdual reciprocity boundary element method (DRM).Based on the work equivalent law,the dual reciprocity boundary integral equations for flexural waves in the thin plate were established using static fundamental solution.As illustration,numerical results for the dynamic stress concentration factors in the thin plate with a circular hole are given.The results obtained demonstrate good agreement with other reported results and show high accuracy.

Adaptive Finite Element Method for Analysis of Pollutant Dispersion in Shallow WaterSomboon Otarawanna,Pramote Dechaumphai

LIU You-wen, FANG Qi-hong

2005, 26(12): 1425-1435.

Abstract(2669) PDF(460)

Abstract:
A finite element method for analysis of pollutant dispersion in shallow water is presented.The analysis is divided into two parts:1) computation of the velo city flow field and water surface elevation,and 2) computation of the pollutant concentr ation field from the dispersion model.The method was combined with an adaptive meshing technique to increase the solution a ccuracy,as well as to reduce the computational time and computer memory.The finite element formulation and the computer programs werev alidated by several examples that have known solutions.In addition,the capability of the combined method was demonstrated by analyzing pollutant dispersion in Chao Phraya River near the gulf of Thailand.

Plane Elastic Problem on the Rigid Lines Along a Circular Inclusion

LIU You-wen, FANG Qi-hong

2005, 26(12): 1436-1444.

Abstract(2913) PDF(497)

Abstract:
The plane elastic problem of circular-arcrigid line inclusions is considered.The model is subjected to remote general loads and concentrated force which is applied at an arbitrary point inside either the matrix or the circular inclusion.Based on complex variable method,the general solutions of the problem were derived.The closed form expressions of the sectionally holomorphic complex potentials and the stress fields were derived for the case of the interface with a single rigid line.The exact expressions of the singular stress fields at the rigid line tips were calculated which show that they possess a pronounced oscillatory character similar to that for the corresponding crack problem under plane loads.The influence of the rigid line geometry,loading conditions and material mismatch on the stress singularity coefficients is evaluated and discussed for the case of remote uniform load.

Numerical Simulation Study on Rock Breaking Mechanism and Process Under High Pressure Water Jet

NI Hong-jian, WANG Rui-he, ZHANG Yan-qing

2005, 26(12): 1445-1452.

Abstract(2782) PDF(1000)

Abstract:
The numerical simulation method to study rock breaking process and mechanism under high pressure water jet was developed with the continuous mechanics and the FEM theory.The rock damage model and the damage-coupling model suited to analyze the whole process of water jet breaking rock were established with continuum damage mechanics and micro damage mechanics.The numerical results show the dynamic response of rock under water jet and the evolvement of hydrodynamic characteristic of jet during rock breaking is close to reality,and indicates that the body of rock damage and breakage under the general continual jet occurs within several imlliseconds,the main damage form is tensile damage caused by rock unload and jet impact,and the evolvement of rock damage shows a step-change trend.On the whole,the numerical results can agree with experimental conclusions,which manifest that the analytical method is feasible and can be applied to guide the research and application of jet breaking rock theory.

Way to Determine the Stiffness Function of Structure

WANG De-ming, GAI Bing-zheng

2005, 26(12): 1453-1458.

Abstract(2741) PDF(654)

Abstract:
For calculating the stiffness function of a structure,the differential equation of the vibration of the structure was divided into the differential equation on the original stiffness function that was known,and Fredholm integral equation of the first kind on the undetermined stiffness function that was unknown.And the stable solutions of the integral equation,when the smooth factor was equal to zero,was solved by the extrapolation with psmooth factors.So the stiffness function of the structure is obtained.Applied examples show that the method is feasible and effective.

Moving Screw Dislocation in Cubic Quasicrystal

ZHOU Wang-min, SONG Yu-hai

2005, 26(12): 1459-1462.

Abstract(2968) PDF(681)

Abstract:
The elasticity theory of the dislocation of cubic quasicrystals is developed.The governing equations of anti-plane elasticity dynamics problem of the quasicrystals were reduced to a solution of wave equations by introducing displacement functions,and the analytical expressions of displacements,stresses and energies induced by a moving screw dislocation in the cubic quasicrystalline and the velocity limit of the dislocation were obtained.These provide important information for studying the plastic deformation of the new solid material.

Plane Strain Problem of Piezoelectric Solid With an Elliptic Inclusion

DAI Long-chao, GUO Wan-lin, SHE Chong-min

2005, 26(12): 1463-1469.

Abstract(2939) PDF(762)

Abstract:
By using the complex variables function theory,a plane strain electro-elastic analysis was perfor medona transversely isotropic piezoelectric material containing an elliptic elastic inclusion,which is subje cted to a unifor mstress field and a uniform electric displacement loads at infinity.Based on the present finite elementresults and somerelated the oretical solutions,an acceptable conjecture was found that the stress field is constant inside the elastic inclusion.The stress field solutions in the piezoele ctric matrix and the elastic inclusion were obtained in the form of complex potentials based on the impermeable electric bo undary conditions.

Slippage Solution of Gas Pressure Distribution in the Process of Landfill Gas Seepage

XUE Qiang, FENG Xia-ting, LIANG Bing

2005, 26(12): 1470-1478.

Abstract(2944) PDF(625)

Abstract:
A mathematical model of landfill gas migration was established under presumption of the effect of gas slippage.The slippage solutions to the nonlinear mathematical model were accomplished by the perturbation and integral transformation method.The distribution law of gas pressure in landfill site was presented under the conditions of considering and neglecting slippage effect.Sensitivity of the model input parameters was analyzed.The model solutions were compared to observation values.Results show that gas slippage effect has a large impact on gas pressure distribution.Landfill gas pressure and pressure gradient considering slippage effect is lower than that neglecting slippage effect,with reasonable agreement between model solution and measured data.It makes clear that the difference between considering and neglecting slippage effect is obvious and the effects of coupling cannot be ignored.The theoretical basis is provided for engineering design of security control and decision making of gas exploitation in landfill site.The solutions give scientific foundation to analyzing well test data in the process of low-permeabilityoil gas reservoir exploitation.

Motion and Deformation of a Viscous Drop in Stokes Flow Near a Rigid Wall

LU Hua-jian, ZHANG Hui-sheng

2005, 26(12): 1479-1486.

Abstract(2782) PDF(472)

Abstract:
A boundary integral method was developed for simulating the motion and deformation of a viscous drop in an axisymmetric ambient Stokes flow near a rigid wall and for direct calculating the stress on the wall.Numerical experiments by the method were performed for different initial stand-off distances of the drop to the wall,viscosity ratios,combined surface tension and buoyancy parameters and ambient flow parameters.Numerical results show that due to the action of ambient flow and buoyancy the drop is compressed and stretched respectively in axial and radial directions when time goes.When the ambient flow action is weaker than that of the buoyancy the drop raises and bends upward and the stress on the wall induced by drop motion decreases when time advances.When the ambient flow action is stronger than that of the buoyancy the drop descends and becomes flatter and flatter as time goes.In this case when the initial stand-off distance is large the stress on the wall increases as the drop evolutes but when the stand-off distance is small the stress on the wall decreases as a result of combined effects of ambient flow,buoyancy and the stronger wall action to the flow.The action of the stress on the wall induced by drop motion is restricted in an area near the symmetric axis,which increases when the initial stand-off distance increases.When the initial stand-off distance increases the stress induced by drop motion decreases substantially.The surface tension effects resist the deformation and smooth the profile of the drop surfaces.The drop viscosity will reduce the deformation and migration of the drop.

Asymptotic Non-Stability and Blow-up at the Boundary for the Solutions of a Filtration Equation

CAO Zhen-chao, CHEN Peng-nian

2005, 26(12): 1487-1492.

Abstract(2652) PDF(628)

Abstract:
For a class of nonlinear Filtration equation with nonlinear second-third boundary value condition,it is shown that a priori boundary of the solution can be estimated and controlled by initial data and integral on the boundary of the region.The priori estimate of the solutions was established by iterative method.By using this estimate the solutions may blow-upon the boundary of the region and thus it may have a symptotic non-stability.

Exact Augmented Lagrangian Function for Nonlinear Programming Problems With Inequality Constraints

DU Xue-wu, ZHANG Lian-sheng, SHANG You-lin, LI Ming-ming

2005, 26(12): 1493-1499.

Abstract(3114) PDF(1057)

Abstract:
An exact augmented Lagrangian function for the nonlinear nonconvex programming problems with inequality constraints was discussed.Under suitable hypotheses,the relationship was established between the local unconstrained minimizers of the augmented Lagrangian function on the space of problem variables and the local minimizers of the original constrained problem.Furthermore,under some assumptions,the relationship was also established between the global solutions of the augmented Lagrangian function on some compact subset of the space of problem variables and the global solutions of the constrained problem.Therefore,from the theoretical point of view,a solution of the inequality constrained problem and the corresponding values of the Lagrange multipliers can be found by the well known method of multipliers which resort to the unconstrained minimization of the augmented Lagrangian function presented.

Continuity of Generalized Inverses of Linear Operators in Banach Spaces and Its Applications

HUANG Qiang-lian, MA Ji-pu

2005, 26(12): 1500-1506.

Abstract(2840) PDF(768)

Abstract:
The perturbation problem of generalized inverse is studied.And somenewsta bility characteristics of generalize dinverses were prese nted.It was also proved that the stability characteristics of gener alized inverses were independent of the choice of the generalize dinver se.Based on this result,two sufficient and necessary conditions for the lower semi-continuity of gener alized inverses as the set-valued mappings are given.

A Class of Nonlinear Nonlocal Singularly Perturbed Problems for Reaction Diffusion Equations With Boundary Perturbation

MO Jia-qi, WANG Hui, LIN Wan-tao

2005, 26(12): 1507-1511.

Abstract(2944) PDF(718)

Abstract:
A class of nonlinear nonlocal for singularly perturbed Robin initial boundary value problems for reaction diffusion equations with boundary perturbation is considered.Under suitable conditions,first,the outer solution of the original problem was obtained.Secondly,using the stretched variable,the composing expansion method and the expanding theory of power series the initial layer was constructed.Finally,using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems was studied,and educing some relational inequalities the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation were discussed.