应用数学和力学

1989 Vol. 10, No. 7

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Buckling of Cooling Tower Shells with Ring-Stiffeners

Lu Wen-da, Gu Hao-zhong

1989, 10(7): 559-567.

Abstract(1645) PDF(571)

Abstract:
With the stability analysis of hyperbolic cooling tower shells with ring-stiffeners, our paper proposes the linear pre-buckling consistent theory. The numerical result shows that this linear analysis method is very effective and practical in engineering, for its precision of compulation is up to the level of the nonlinear analysis when it is used for the study of critical loads of the hyperbolic cooling tower which is mainly governed by wind pressure and for the study of the effect of some oilier factors concerned in design on the buckling of shells. Based on that, we have obtained a scries of conclusions which will greatly benefits the engineering design when discussing the effect on the critical windloading of the shell which is caused by the following factors such as the position of rings, the number of rings and the dead weight.

Representation Theorem and One-Iteration Theorem for Fredholm Integral Equation of the First Kind Ax=y

Yun Tian-quan

1989, 10(7): 569-574.

Abstract(1787) PDF(403)

Abstract:
In this paper, two theorems are presented. The representation theorem stales: if the Fredholm integral equation of the first kind Ax=y, with bounded L₂ kernel, has a uniquesolution , Then ,where .The one-iteration theorem states: can be achieved in one iteration by =x₀+g₀A^*(y-Ax₀)if one of the following conditions is satisfied:

The Dynamic Plastic Response Characteristics of Circular Beam

Wang Jian-jun, Liu Xiao-kun, Chen Bai-ping

1989, 10(7): 575-584.

Abstract(1594) PDF(454)

Abstract:
In this paper the problem of a circular beam subjected to radial impact by a rigid mass at its tip in its own plane is investigaleil on the basis of rigid-perfectly plastic assumption. The analytical solution of the particle velocities is obtained as the junction of travelling plastic hinge location. By analysing the solution, some special properties of circular beam problem are found.

A Mixed Variational Formulation for Large Deformation Analysis of Plates

S. Dost, B. Tabarrok

1989, 10(7): 585-595.

Abstract(1566) PDF(447)

Abstract:
A mixed vuriational formulation for large deformation analysis of plates is introduced. In this formulation the equilibrium and compatibility equations are satisfied identically by means of stress functions and displacement components, respectively, and the constitutive equations are satisfied in a least square sense. An example is solved and the results are compared with those available in the literature.Further, the functional is particularized for buckling analysis of plates and a simple example is solved to illustrate the theory.

An Analytical Method for Solving Internal Forces and Deformations of Bar-System Structure in Space

Yuan Fa-rong, Chen Xue-feng

1989, 10(7): 597-604.

Abstract(1655) PDF(450)

Abstract:
In this paper, based on the idea of finite element method, the initial parametric method in bending, problem of a beam is extended to analyse the bar-system structure by employing Dirac δ function and llcavisidc step function.Then a new method for analysing the internal forces and deformations of bar-system structure in space is suggested by improving the mixed method in statically indeterminate structure.The inferred process and obtained answer will be more succinct and accurate when the problem of internal forces and deformations of bar-system structure is analysed by using the new method provided in this paper.

Propagation Velocities of Elastic Waves in Saturated Soils

Wu Shi-ming, Chen Long-zhu

1989, 10(7): 605-612.

Abstract(1983) PDF(541)

Abstract:
Bused on the wave equations established by the authors, the characteristics of propagation velocities of elastic vaves in saturated soils arc analyzed and verified by ultrasonic test in laboratory and seismic survey in the field. The results provide theoretical basis for the determination of physical and mechanical parameters of saturated soils using propagation velocities of elastic waves, especially P-wave velocity.

Numerical Investigation of Three-Dimensional Viscous Incompressible Flows in Divergent Curved Channels and Turbulent Model Study

Jiao De-yong, Yang Hong-wei, Zhao Zhi-jun, Su Jie-xian, Feng Guo-tai

1989, 10(7): 613-620.

Abstract(1715) PDF(551)

Abstract:
In order to make the numerical calculation of viscous flows more convenient for the flows in channel with complicated profile governing equations expressed in the arbitrary curvilinear coordinates were derived by means of Favre density-weighted averaged method, and a turbulent model with effect of curvature modification was also derived. The numerical calculation of laminar and turbulent flown in divergent curved channels was carried out by means of parabolizeil computation method. The calculating results were used to analyze and investigate the aerodynamic performance of talor cascades in compressors preliminarily.

The Multigrid Method for Reservoir Simulation

Chen Tian-xiang, Lü Tao, Lin Ai-min

1989, 10(7): 621-628.

Abstract(1474) PDF(464)

Abstract:
This paper describes a way of solving the reservoir simulation pressure equation using mulligrid technique. The subroutine MG of four-grid method is presented. The result for 2-D two-phase problem is exactly the same as that of the SOR method and the CPU time is much less than that of the latter one.

On Uniform Convergence of Linear Operators on the Probabilistic Normed Space

Wei Yong

1989, 10(7): 629-635.

Abstract(1721) PDF(427)

Abstract:
In this paper, we introduced the notion of uniform convergence of the linear operators on the probabilistic nornied space, and the notion of probabilistic distance between the operators, which describes the above convergence completely. In terms of these notions, we obtained the essential features of the continuity of operators, and of the uniform convergence of operator sequences, and we also obtained the closure of continuity and complete continuity under the operation of the limit of uniform convergence.

Derivation of Some Special Stress Function from Beltrami-Schaefer Stress Function

Wang Min-zhong, Wang Lu-nan

1989, 10(7): 637-644.

Abstract(1661) PDF(526)

Abstract:
Using liellrami-Schaefer stress funtion in the theory of elasticity in this paper, we derive the stress functions of torsion, plane problem, axisymmetric deformation in solid of revolution and torsion on solid of revolution.

An Application of Ungar’s Differential Transform to Elastodynamics

Hu De-sui

1989, 10(7): 645-648.

Abstract(1465) PDF(414)

Abstract:
In recent years, a lot of writers have used Cagniard-de Hoop's method^[1][2] to solve some problems of elastic wave. But it is a difficult and complicated task to change the path of integration when we use this method. A differential transform by A.Ungar^[3,6] can obviate this difficulty. In this paper, weuse Ungar's differential transform to solve a case of Lamb's problem^[1][2].