应用数学和力学

1992 Vol. 13, No. 11

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Finite Layer Analysis for Semi-Infinite Soils(Ⅱ)——Special Cases and Numerical Examples

Loo wen-da, Yang Zheng-wen

1992, 13(11): 945-950.

Abstract(2342) PDF(451)

Abstract:
In the present paper reductions of the finite layer mathod once studied in detail by the authors for the elastodvnamics of transverse isotropic bodies are given to several special cases.Two-dimensional problems,axisymmetric problems and static problems are discussed,respectively,and this finite layer method is also generalized to the problems in which materials possess viscous properties.Two numerical examples have been presented for the axisymmetric case.From these two examples it can be concluded that the finite layer method can be used to analyse semi-infinite layered soils and to deal with the problem of the interaction between soils and structures.

General Solution for Large Deflection Problems of Nonhomogeneous Circular Plates on Elastic Foundation

Ji Zhen-yi, Yeh Kai-yuan

1992, 13(11): 951-962.

Abstract(2142) PDF(562)

Abstract:
In this paper,a new method is presented based on [1].It can be used to solve the arbitrary nonlinear system of differential equations with variable coefficients.By this method,the general solution for large deformation of nonhomogeneous circular plates resting on an elastic foundation is derived.The convergence of the solution is proved.Finally,it is only necessary to solve a set of nonlinear algebraic equations with three unknowns.The solution obtained by the present method has large convergence range and the computation is simpler and more rapid than other numerical methods.Numerical examples given at the end of this paper indicate that satisfactory results of stress resultants and displacements can be obtained by the present method.The correctness of the theory in this paper is confirmed.

A Coupling Difference Scheme for the Numerical Solution of a Singular Perturbation Problem

Sun Xiao-di, Wu Qi-guang

1992, 13(11): 963-970.

Abstract(2487) PDF(466)

Abstract:
In this paper,we consider a singularly perturbed problem without turning points.On a special discretization mesh,a coupling difference scheme,resulting from central difference scheme and Abrahamsson-Keller-Kreiss box scheme,is proposed and the second order convergence,uniform in the small parameter,is proved.Finally,numerical results are provided.

Hamiltonian System and Simpletic Geometry in Mechanics of Composite Materials(Ⅰ)——Fundamental Theory

Zhong Wan-xie, Ouyang Hua-jiang

1992, 13(11): 971-975.

Abstract(3018) PDF(672)

Abstract:
For the first time,Hamiltonian systemused in dynamics is introduced to formulate statics and Hamiltonian equation is derived corresponding to the original governing equation,which enables separation of variables to work and eigen function to be obtained for the boundary problem.Consequently,analytical and semi-analytical solutions can be got.The method is especially suitable to solve rectangular plane problem and spatial prism in elastic mechanics.The paper presents a new idea to solve partially differential equation in solid mechanics.The flexural problem and plane stress problem of laminated plate are studied in detail.

Subspace Variational Principle of Rods and Shells

Zheng Quan-shui, Yang De-pin, Song Gu-quan

1992, 13(11): 977-983.

Abstract(2657) PDF(551)

Abstract:
This paper builds the general forms of subspace variational principles of rods and shells which are taken as the controlled equations of the constitutive theories developed front the three-dimensional(non-polar) continuum mechanics.And the constitutive equations of rods and shells using the principles are satisfactory.

Theory of Elasticity of an Anisotropic Body for the Bending of Beams

Luo Jian-hui, Li Li-juan

1992, 13(11): 985-991.

Abstract(2933) PDF(560)

Abstract:
A theory of elasticity for the bending of orthogonal anisotropic beams has been developed by analogy with the special case,which can be obtained by applying the theory of elasticity for bending of transversely isotropic plates to the problems of two deminsions.In this paper,we present a method to solve the problems of bending of orthogonal anisotropic beams and a new theory of the deep-beam whose ratio of depth to length is larger.It is pointed out that Reissner's theory to account for the effect of transverse shear deformation is not very approximate in the components of stress.

The Solution for Two-Phase Flow by Split Flux Vector Method

Weng Rong-zhou

1992, 13(11): 993-1000.

Abstract(2187) PDF(570)

Abstract:
In this paper the transient two-phase flow equations and their eigenvalues are first introduced.The flux vector is then split into subvectors which just contain a specially signed eigenvalue.Using one-sided spatial difference operators finite difference equations and their solutions are obtained.Finally comparison with experiment shows the predicted results produce good agreement with experimental data.

The New Criteria of Elastic and Fatigue Failure in the Component of Complex Stress States

Hu Zhu-hua

1992, 13(11): 1001-1007.

Abstract(2211) PDF(596)

Abstract:
In this paper,a total criterion on elastic and fatigue failure in complex stress,that is.octahedral stress strength theory on dynamic and static states on the basis of studying modern and classic strength theories.At the same time,an analysis of an independent and fairly comprehensive theoretical system is set up.It gives generalized failure factor by 36 materials and computative theory of the 11 states of complex stresses on a point,and derives the operator equation on generalized allowable strength and a computative method for a total equation can be applied to dynamic and static states.It is illustrated that the method has a good exactness through computation of eight examples of engineering.Therefore,the author suggests applying it to engineering widely.

Theory of Thick-Walled Shells and Its Application in Cylindrical Shell

Fang Ying-guang, Pan Ji-hao, Chen wei-xin

1992, 13(11): 1009-1019.

Abstract(2925) PDF(883)

Abstract:
In this paper,a theory of thick-walled shells is established by means of Hellinger-Reissner's variational principle,with displacement and stress assumptions.The displacements are expanded into power series of the thickness coordinate.Only the first four and the first three terms are used for the displacements parallel and normal to the middle surface respectively.The normal extruding and transverse shear stresses are assumed to be cubic polynomials and to satisfy the boundary stress conditions on the outer and inner surfaces of the shell.The governing equations and boundary conditions are derived by means of variational principle.As an example,a thick-walled cylindrical shell is disscussed with the theory proposed.Furthermore,a photoelastic experiment has been carried out,and the results are in fair agreement with the computations.

The Traction Problem in Elastodynamics

Gu An-hai

1992, 13(11): 1021-1029.

Abstract(2264) PDF(448)

Abstract:
In continuum mechanics.Cauchy's six equations

are incomplete[1] and the famous Cauchy's laws of motion

where ,ρb,T and divT are continuous are also incomplete^[2].The first six equations are incomplete because the geometrical representation of deformation at a given point is as yet incomplete^[3],and the last two laws are incomplete because b,T and divT are frame-indifferent,but is not,and T is a symmetric,as Cauchy interpreted himself.Therefore,we say,the last two laws can't accommodate to the asymmetric tensor.The purpose of this paper is to complete Cauchy's laws of motion by postulating an asymmetric tensor for the underlying traction field of 3-dimensional space on a general framing.