应用数学和力学

1995 Vol. 16, No. 11

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An Exact Solution on the Stress Analysis of Fillet Welds

Xue Dawei

1995, 16(11): 849-854.

Abstract(2129) PDF(686)

Abstract:
An exact solution on the stress distribution of fillet welds is obtained in this paper This solution can be used not only for estimating the accuracy of the present design method of fillet welds but also for establishing a new design method.

Elasticity solutions of Spherically Isotropic Cones under Concentrated Loads at Apex

Ding Haojiang, Zou Daoqin, Ren Yongjian

1995, 16(11): 956-966.

Abstract(2250) PDF(497)

Abstract:
Based on the Ref.[9].the displacement and stress distributions in a spherically isotropic cone subjected to concentrated loads at apex are studied The displacementand stresses are given explicitly for the cone in compression torsion and bending cases respectively based on the situation of the concentrated forces and moments Finally.the hollow cone problems are discussed.

Element-by-element Matrix decomposition and Step-by-Step Integration Method for Transient Dynamic Problems

Wang Huaizhong

1995, 16(11): 967-972.

Abstract(1928) PDF(484)

Abstract:
In this paper a general matrix decomposition scheme as well as an element-by-element relaxation algorithm combined with step-by-step integration method is presented for transient dynamic problems thus the finite element method can be free form forming global stiffness matrix global mass matrix as well as solyin large scale sparse equations Theory analysis and numerical results show that the presented matrix decomposition scheme is the optimal one The presented algoithm has else physicalmeaning and can be busily applied to finite element codes.

Stability Analysis of Slowly Divergent Swirling Flow(Ⅰ)——Theory

Xia Nan, Yin Xieyuan

1995, 16(11): 973-979.

Abstract(2078) PDF(517)

Abstract:
The stability of inviscid incompressible swirling flow with slowly divergence is investigated.A multiple scale expansion is used to develop a linear stability study of slowly divergent swirling flow with non-axisymmetric disturbances.The differental equations of zero-order and first-order disturbance module and governing equation of amplitude variation due to slowly divergent flow are derved.The plaschko s equation for slowly divergent swirl-free jet has been extended to slowly divergent flow with swirlin the present study.

The Integration Methods of Vacco Dynamics Equation of Nonlinear Nonholonomic Systems

Luo Shaokai

1995, 16(11): 981-989.

Abstract(2129) PDF(539)

Abstract:
This paper presents the integration methods for vacco dynmmies equations of nonlinear nonholononic system,First vacco dynamies equations are written in the canonical form and the field form.second,the gradient methods the single-componentmethods and the field method are used to integrate the dynamics equations of the corresponding holonomic system respectively.And considering the restriction of nonholonomic construint to the initial conditions the solutions of Vacco dynamics cquations of nonlinear nonholonomic system are obtained.

The Analytic Resolutions and Applications of the Non-LInear Seepage Flow Equations of Coal Infusion

Zhang Yansong

1995, 16(11): 991-996.

Abstract(1831) PDF(515)

Abstract:
In this paper.the author uses the theory of fluid mechanics.dynamics of fluids in porous media,gas seepage flow in coal seams and combines the tests in the laboratory with the actual coal infusion to have an investigating and study from the theory to the mechanism of coal infusion to wet coal seams.Through the analysis to the process of coal infusion the author builds up the mathematical models and has a detailed discussion to the boundary conditions of coal infusion.Because the equation sets to describe coal infusion are non-linear.we have made a simplification to them to use the dimension analysis theory by leading into the non-dimensions of water pressure of coal infusion,seepage flow rate.increment of coal seam moisture and so on Besides the analytic and approximate solutions have also been discussed.At last.we use the scientific research item of the actual coal infusion to illustrate the effects and importance of the theory to direct actual coal infusion and its designs.

On the Existence and Stability of Solutions for Seml-Homogeneous Boundary Value Problems

Dong Qinxi, Huang Xiankai

1995, 16(11): 997-1001.

Abstract(1819) PDF(420)

Abstract:
In this paper.we discuss the existence and stability of solution for two semi-homogeneous boundary value problems.The relative theorems in [1-2] are extended.meanwhile,we obtain some new results.

The Problems of the Nonlinear Unsymmetrical Bending for Cylindrically Orthotropic Circular Plate(Ⅱ)

Huang Jiayin, Qin Shengli, Xia Yunjie, Xu Xiaoping, Kong Xianghe

1995, 16(11): 1003-1016.

Abstract(1776) PDF(664)

Abstract:
In this Paper we study the recursive equations under the recursive boundary conditions for W_nm,nm,v_nm and ψ_nm(n=0.1.2...N:m=1.2...M.which derivedby the two-variable method ^[3] in the preceding paper^[1].We then solve these problems by using the method of regular perturbation^[2].and the uniformly valid asymptotic solution is obtained.Lastly we consider a particular example i.e the bending problems of the axisymmetrical circular plate by using the mixed perurbation method and compare our results with the exact solution found in Ret[5].They are similarly coincided.

On Mechanical Property of Constraint

Wei Yang, Liang Lifu, Liang Zhongwei

1995, 16(11): 1017-1024.

Abstract(1952) PDF(423)

Abstract:
In this paper,the mechanical properties of holonomic systems and mon-holonomicsystems are strdied.This is an important and urgent problem.

A Supplemtary Study of Anisotropic Plastic Fields at a Rapidly Propagating Plane-Stress Crack-Tip(I)

Lin Baisong

1995, 16(11): 1025-1035.

Abstract(2092) PDF(478)

Abstract:
The results in Ref.[1] are not suitable for the cases of β≥2.For this reason,byusing the methods in Ref [1] and Ref [2],we derive the general expressions ofamsotropic plastic fields at a rapidly propagating plane-stress crack-tip for both thecases of β=2 and β>2.

Obic Dmain Decomposition for Artificial Compressible Equation

Lin Mingsen, Huan Lanjie

1995, 16(11): 1037-1041.

Abstract(1734) PDF(471)

Abstract:
This paper is a continuation of the domain decomposition method according to thephysics scale proposed in [1] and [2].Starting from systems of ordinary differentialequattons,a solution is decomposed into an outer solution(0)and its boundary layercorrections(BLC)mainly on the fixed boundary.For efficient numerical solution,different equations,different numerical methods and different grids can be suitablychosen for the different scales.This paper also gives the characteristic nature and well-posed boundary condition about artificial compressible equations.Numericalexperiments show that the computational method and the couple process presented inthe paper are effective.