应用数学和力学

2003 Vol. 24, No. 12

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Renewal of Basic Laws and Principles for Polar Continuum Theories(Ⅵ)——Conservation Laws of Mass and Inertia

DAI Tian-min

2003, 24(12): 1211-1216.

Abstract(2493) PDF(754)

Abstract:
The purpose is to reestablish the coupled conservation laws, the local conservation equations and the jump conditions of mass and inertia for polar continuum theories. In this connection the new material derivatives of the deformation gradient, the line element, the surface element and the volume el...

Renewal of Basic Laws and Principles for Polar Continuum Theories(Ⅶ)——Incremental Rate Type

DAI Tian-min

2003, 24(12): 1217-1222.

Abstract(2538) PDF(745)

Abstract:
The purpose is to establish the rather complete equations of motion, boundary conditions and equation of energy rate of incremental rate type for micropolar continua. To this end the rather complete definitions for rates of deformation gradient and its inverse are made. The new relations between var...

Nonlinear Vibration of Thin Shallow Conic Shells Under Combined Action of Peripheral Moment and Transverse Loads

ZHAO Yong-gang, WANG Xin-zhi, YEH Kai-yuan

2003, 24(12): 1223-1230.

Abstract(2537) PDF(629)

Abstract:
Based on the variation and harmonic equations and by taking the maximum amplitude of the shell center as the perturbation parameter, nonlinear vibration of thin shallow conic shells under combined action of peripheral moment and transverse loads was solved. The linear natural frequency can be got by...

Equivalent Boundary Integral Equations With Indirect Variables for Plane Elasticity Problems

ZHANG Yao-ming, WEN Wei-dong, ZHANG Zuo-quan, SUN Huan-chun, LÜ He-xiang

2003, 24(12): 1231-1237.

Abstract(2848) PDF(704)

Abstract:
The exact form of the exterior problem for plane elasticity problems was produced and fully proved by the variational principle. Based on this, the equivalent boundary integral equations(EBIE) with direct variables, which are equivalent to the original boundary value problem, were deduced rigorously...

Analysis of Transient Thermal Stress in Cylindrically Orthotropic Tubes

LING Dao-sheng

2003, 24(12): 1238-1242.

Abstract(2462) PDF(837)

Abstract:
The incorrect deduction of equations in the research works devoted to the studies of transient stress in cylindrically orthotropic tubes and done by Kardomateas(Journal of Applied Mechanics, 1989, 1990) leads to the wrong results. The errata(1991) correct the deduction error, but do not give the rig...

Objectivity Requirement for Fluid Dynamics

ZOU Wen-nan

2003, 24(12): 1243-1248.

Abstract(2404) PDF(728)

Abstract:
A new flow theory is established through the objectivity requirement on the fluid dynamics. It was known that inhomogeneous fluid motion gave rise to viscous force while the selection of observers on different space-time points would change such an inhomogeneous character. Therefore, when the viscou...

Internal Resonant Interactions of Three Free Surface-Waves in a Circular Cylindrical Basin

MA Chen-ming

2003, 24(12): 1249-1257.

Abstract(2923) PDF(769)

Abstract:
The basic equations of free capillary-gravity surface-waves in a circular cylindrical basin were derived from Luke's principle. Taking Galerkin's expansion of the velocity potential and the free surface elevation, two-order perturbation equations were derived by use of expansion of multiple scale. T...

Iterative Approximation of Fixed Points for Almost Asymptotically Nonexpansive Type Mappings in Banach Spaces

ZENG Lu-chuan

2003, 24(12): 1258-1266.

Abstract(2325) PDF(678)

Abstract:
A new class of almost asymptotically nonexpansive type mappings in Banach spaces is introduced, which includes a number of known classes of nonlinear Lipschitzian mappings and non-Lipschitzian mappings in Banach spaces as special cases; for example, the known classes of nonexpansive mappings, asympt...

Multiple Reciprocity Method With Two Series of Sequences of High-Order Fundamental Solution for Thin Plate Bending

DING Fang-yun, DING Rui, LI Bing-jie

2003, 24(12): 1267-1275.

Abstract(2678) PDF(760)

Abstract:
The boundary value problem of plate bending problem on two-parameter foundation was discussed. Using two series of the high-order fundamental solution sequences, namely the fundamental solution sequences for the multi-harmonic operator and Laplace operator, applying the multiple reciprocity method(M...

Singularly Perturbed Nonlinear Boundary Value Problem for a Kind of Volterra Type Functional Differential Equation

LU Shi-ping

2003, 24(12): 1276-1284.

Abstract(2990) PDF(623)

Abstract:
By employing the theory of differential inequality and some analysis methods, a nonlinear boundary value problem subject to a general kind of second order Volterra functional differential equation was considered first. Then, by constructing the right-side layer function and the outer solution, a non...

Singularly Perturbed Boundary Value Problems for Semi-Linear Retarded Differential Equations With Nonlinear Boundary Conditions

REN Jing-li, GE Wei-gao

2003, 24(12): 1285-1290.

Abstract(2520) PDF(730)

Abstract:
A boundary value problems for functional differenatial equations, with nonlinear boundary condition, is studied by the theorem of differential inequality. Using new method to construct the upper solution and lower solution, sufficient conditions for the existence of the problems. solution are establ...

Coarse-Mesh-Accuracy Improvement of Bilinear Q₄-Plane Element by the Combined Hybrid Finite Element Method

XIE Xiao-ping, ZHOU Tian-xiao

2003, 24(12): 1291-1300.

Abstract(2584) PDF(619)

Abstract:
The combined hybrid finite element method is of an intrinsic mechanism of enhancing coarse-mesh-accuracy of lower order displacement schemes. It was confirmed that the combined hybrid scheme without energy error leads to enhancement of accuracy at coarse meshes, and that the combination parameter pl...

Lower Bound Limit Analysis of Three-Dimensional Elastoplastic Structures by Boundary Element Method

LIU Ying-hua, ZHANG Xiao-feng, CEN Zhang-zhi

2003, 24(12): 1301-1308.

Abstract(2906) PDF(653)

Abstract:
Based on the lower bound theorem of limit analysis, a solution procedure for limit analysis of three-dimensional elastoplastic structures was established using conventional boundary element method(BEM). The elastic stress field for lower bound limit analysis was computed directly by three-dimensiona...

Fluid-Solid Coupling Mathematical Model of Contaminant Transport in Unsaturated Zone and Its Asymptotical Solution

XUE Qiang, LIANG Bing, LIU Xiao-li, LI Hong-yan

2003, 24(12): 1309-1318.

Abstract(3314) PDF(739)

Abstract:
The process of contaminant transport is a problem of multicomponent and multiphase flow in unsaturated zone. Under the presupposition that gas existence affects water transport, a coupled mathematical model of contaminant transport in unsaturated zone has been established based on fluid- solid inter...