应用数学和力学

1983 Vol. 4, No. 3

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Shear Modulus of Transversely Isotropic Materals

K. P. Cheng

1983, 4(3): 289-296.

Abstract(2608) PDF(551)

Abstract:
A new and simple method is presented to determine the independent shear modulus of transversely isotropic material. Mathematical formulation, derivation and solution are given, and test apparatus and results are presented.The method was tested on one of such materials——Green River Formation oil shale. Comparisons with other approximate results and acoustical methods are made. Confirmation of the test method with materials having known shear moduli is also presented.

Representation Theorem for Linear, lsotropic Tensor Functions of a Skew Argument

Guo Zhong-heng

1983, 4(3): 297-301.

Abstract(2144) PDF(635)

Abstract:
The present paper offers two proofs of the representation theorem for linear, isotropic tensor functions of a skew argument. The first proof is new. The second one is basically along the lines of reasoning exploited in [1], but more concise, and it corrects some errors committed in[1].

Hydrodynamic Coefficients for Vertical Plane Wave Motion Problems

Michael de St. Q. Isaacson, Wu Song-ren

1983, 4(3): 303-313.

Abstract(1853) PDF(392)

Abstract:
In this paper a numerical method for calculating the hydro-dynamic coefficients for vertical plane wave motion problems in deep water is described. This procedure is developed by using the wave source method based on Green's theorem. The applications of the method to the cases of semi-circular and rectangular section bodies subjected to linear waves are presented, here, and the computed results are compared with the earlier experimental data of Vugts.

On Crack Propagation in a Coupled Thermo-Mechanical System of Nonlinear Media

Ouyang Chang

1983, 4(3): 315-324.

Abstract(1796) PDF(469)

Abstract:
In some engineering problems, thermo-mechanical coupling is important and may not be ignored. This paper deals with the crack propagation problem in a coupled thermo-mechanical system of nonlinear media. Various nonlinear media, including nonlinear e-lastic and elastic-plastic cases, have been considered and the related path-independent integrals are given. To explain the physical meaning of these integrals, a notched specimen has been considered, and the dynamical crack extension force in a coupled thermo-mechanical system is shown to be equal to this integral. Thus, we could consider such integrals as some nonlinear criteria for coupled thermo-mechanical fracture dynamics.

On the Problems of Sandwich Shells Having the Form of a Surface of Revolution and Face Layers of Non-Equal Thicknesses

Li Shu-ming, Hsueh Dah-wei

1983, 4(3): 325-340.

Abstract(2053) PDF(430)

Abstract:
Fundamental eguations which govern the behavior of an elastic sandwich shell having the form of a surface of revolution and face layers of non-equal thicknesses are derived, with the solution of refs.[3] and [4] as special examples.The problems of the shell under the action of symmetrical loads are reduced to the solution of a displacement-function ψ_a, where ψ_a satisfies a differential equation of sixth order.

The Velocity of the Collective Motion of Sedimentation of Sand and Clay

Tsai Shu-tang

1983, 4(3): 341-346.

Abstract(2105) PDF(609)

Abstract:
In this article, we shall discuss the velocity of the collective motion of sedimentation when the concentration of clay particles is very high. We believe that the problem of the so-called velocity of the collective motion of sedimentation is not a real problem of sedimentation in physical nature, but it is a problem of filtration in the porous medium which is composed of colloidal clusters. That is to say, those clusters consist of water and clay particles.It is a problem of the water passing through the porous medium. Based upon this consideration, we put down the mathematical expression of the velocity of the collective motion of sedimentation. In comparing with the theoretical curves with the experimental data of the Institute of Hydraulic Research, of the Yellow River Conservancy Commission, we get congruous results.

Thermal Contact Stresses of Bi-Metal Strip Thermostat

Zhang Fu-fan

1983, 4(3): 347-360.

Abstract(1944) PDF(557)

Abstract:
The distribution of shearing and normal stresses on the contact surface of the two strips composing a thermostat is found in closed form. They are of local type and concentrated near the ends of the strip along a length almost equal to the thickness of the strip.

On Path-Independent Integrals in 3-Dimentional Nonlinear Fracture Dynamics

Lu Mei-zi

1983, 4(3): 361-368.

Abstract(2169) PDF(512)

Abstract:
This paper deals with the path-independent integrals in nonlinear three-dimensional fracture dynamics. Both the nonlinear elastic case and the elastic-plastic case are considered, and some path-independent integrals have been worked out.For explaining the physical meaning of these integrals, a specimen with plane notch is considered, and the relation between the integral and dynamical crack extension force is established. Thus, such integrals may serve as a fracture criterion in nonlinear fracture dynamics.

The Elastoplastic Constitutive Relation of Generalized Cap Model for Rock Medium

Tsien Shou-i, Chang Ken-ta

1983, 4(3): 369-377.

Abstract(1916) PDF(487)

Abstract:
In this paper, the rock behavior before yielding is analyzed by using the theory of continuum mechanics. The nonlinearly elastic constitutive equation of rock medium is derived and compared satisfactorily with the available experimental data. Moreover, the substitution of the linearly elastic hypothesis used in the conventional cap model with the nonlinearly elastic one leads to the development of a new nonlinearly elastic-hardening plastic cap model as presented herein.

The Construction of Large Elements in Finite Element Method

Liang Guo-ping, Fu Zi-zhi

1983, 4(3): 379-390.

Abstract(2028) PDF(451)

Abstract:
In the usual finite element method, the order of the interpolation in an element is kept unchanged, and the accuracy is raised by subdividing the grid denser and denser. Alternatively, in the large element method, the grid is kept unchanged, and the terms of approximate series in the element are increased to raise the accuracy.In this paper, a method for constructing large elements is presented. When using this method,two sets of variables, one set defined inside the element, and the other defined on the boundary of the element, are adopted. Then, these two sets of variables are combined by the hybrid-penalty function method.This method can be applied to any elliptic equations in a domain with arbitrary shape and arbitrary complex boundary condition.It is proved with strict mathematical method in this paper, that in general cases,the accuracy of this method is much higher than that of the usual element and the large element method presented in [7].Therefore,the degrees of freedom needed in this method are much fewer than those in the two methods if the same accuracy is preserved.

The Creep Effects on the Buckling of Shallow Shells

He Guang-qian, Wei Lian

1983, 4(3): 391-399.

Abstract(1874) PDF(405)

Abstract:
An analysis of the creep effects on the buckling of concrete shallow shells is presented in this paper.Based on the nonlinear theory of thin elastic shells, it is found that for those of the elliptical paraboloidal type, the upper critical load of the load-deflection curve will decrease while the lover limit will increase with time.As to the problem of local buckling of the shell, the critical load is dependent only upon the modulus of elasticity at the instant it occurs.

Narrow Gap Stability Theory of Blood Flow between Two Relatively Rotating Concentric Cones

Chu Yueh-rei

1983, 4(3): 401-410.

Abstract(1967) PDF(428)

Abstract:
The boundary perturbation solutions for blood flow between two relatively rotating concentric cones (one is them is stationary, the other is rotating with constant angle velocity ω) have been obtained^[1]. Then on basis of the solutions obtained, using theory of narrow gap stability, the stability of the density stratified blood flow between relatively rotating concentric cones with an axial flow is demonstrated.

The Derivation of J-lntegral Conservation Law from the Principle of Virtual Work

Chen Ying-tian

1983, 4(3): 411-413.

Abstract(2441) PDF(602)

Abstract:
The general form of J-integral conservation law in three dimensions has been derived from the principle of virtual work. The necessary conditions for J-integral conservation are also given.

Exact Solution to the Problem of Flow of Slightly Compressible Fluids in a Bounded Confined "Fracture-Pore" Medium and Its Application to Well Testing

Chen Zhong-xiang

1983, 4(3): 415-426.

Abstract(1822) PDF(471)

Abstract:
The problem of flow of slightly compressible fluids through a bounded confined "fracture-pore" medium is solved and studied thoroughly in this paper. Some essential natures of flow of elastic liquids through a medium with double porosity under the condition of neglecting the flow in matrix system were revealed and clarified further.The method of estimating all parameters commonly interested in a bounded confined "fracture-pore" medium reservoir through a series of flow tests in wells by use of the solution obtained is presented.

Solid Mechanics of Discrete Form and the Variational Principles of the Discontinuous Form

Niu Xiang-jun

1983, 4(3): 427-438.

Abstract(2052) PDF(510)

Abstract:
This paper discusses the fundamental assumptions, the differential equations, and the variational principles of discontinuous form belonging to a new developing branch of science-the solid mechanics of discrete form.The solid mechanics of discrete form belongs to the branch of science of discrete medium mechanics which is the developing direction of the mechanics for the present. Based on the solid system with discretization and separability, the unknown functions with discontinuity in defined regions and the defined regions with variable boundaries, the mechanics systems to solve the solid displacements,strains and stresses in various cases are called the solid mechanics of discrete form.When the unknown functions are sufficiently smooth functions in the whole defined region and the effects of the variable boundaries are disregarded,the solid mechanics of discrete form will degenerate into the classical solid mechanics belonging to continuum.mechanics: Its variational principles will degenerate into the classical variational principles with the same cases.