应用数学和力学

1985 Vol. 6, No. 1

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A Semi-Analytical Method for Structure-Internal Liquid Interaction Problems

Cao Zhi-yuan, Y. K. Cheung

1985, 6(1): 1-8.

Abstract(2096) PDF(583)

Abstract:
A composite structure-internal liquid element is proposed in this paper. Through the use of analytical functions in two orthogonal directions. the three-dimensional problem of coupled structure-internal liquid vibration is reduced to a one-dimensional one, resulting in a drastic reduction in computi...

The Stokes Flow from Half-Space to Semi-Infinite Circular Cylinder

Wu Wang-yi, Richard Skalak

1985, 6(1): 9-23.

Abstract(2126) PDF(500)

Abstract:
The infinite-series solutions for the creeping motion of a viscous imcomperssible fluid from half-space to semi-infinite circular cylinder are presented. The results show that inside the cylinder beyond a distance equal to 0.5 times the radius of tube from the pore opening, the deviation of the velo...

Involutory Transformations and Variational Principles with Multi-Variables in Thin Plate Bending Problems

Chien Wei-zhang

1985, 6(1): 25-40.

Abstract(2073) PDF(798)

Abstract:
In this paper, the generalizd variational principles of plate bending, problems are established from their minimum potential energy principle and minimum complementary energy principle through the elimination of their constraints by means of the method of Lagrange multipliers. The involutory transfo...

Finite Element Approximations with Multiple Sets of Functions and Quasi-Conforming Elements for Plate Bending Problems

Zhang Hong-qing, Wang Ming

1985, 6(1): 41-52.

Abstract(2052) PDF(436)

Abstract:
Continuing refs. [1],[2]. we try toestablish here the mathematical foundation of quasi-conforming elements suggesied by Prof. Tang Limin and his colleagues for plate bending problems ^[3,4]. The main theme used in this paper is the finite element approximations with multiple sets of functions.

Formulae of Force at a Point in the Interior of a Half-Space with Shear Modulus Linearly Varied with Depth

Yun Tian-quan

1985, 6(1): 53-59.

Abstract(2041) PDF(453)

Abstract:
According to a lemma and an assumption, this paper prexenis formulae of force at a point in the interior of a half space with Poisson's ratio v=constant and shear modulus G linearly varied with depth. These formulae can be used as an approximate basic solution when the integral equation method is em...

Two Theorems Concerning Discontinuities in Dynamics of Rigid-Perfectly Plastic Continua under Finite Deformation

Huang Zhu-ping

1985, 6(1): 61-66.

Abstract(1811) PDF(596)

Abstract:
In this paper the results of ref [1] are gentralized. Two theorems concerning discontimsities in dynemics of rigid-perfectly plastic continua under finite deformation are proved, namely: i) the traction on the interface between the rigid and the plastic regions is contineous and ii) when the interfa...

Fixed Point Theorem in Probabilistic Inner Product Spaces

Zhang Shi-sheng

1985, 6(1): 67-74.

Abstract(1816) PDF(619)

Abstract:
The purpose of this paper is to introduce a new maditying detinition for probabilistie inner product space, and to establish seveeral new fixed point theorems for mappings on such kind of spaces. As an example of applications, we utilize the results of this paper to study the existence and uniquenes...

The Plane Piston Problem in a Weak Gravitational Field

Hu Wen-rui

1985, 6(1): 75-85.

Abstract(1844) PDF(539)

Abstract:
We analyze a gasdynamical process in the stellar atmosphere that is driven by a "piston" moving with constant velocity in a weak gravitalional field. Ahead of the piston, the gas is compressed, and this compressed gas uses part of its internal energy and somewhere its kinetic energy to overcome the ...

On the Assumption of Saint-Venant’s Problem

Wang Min-zhong

1985, 6(1): 87-92.

Abstract(1935) PDF(388)

Abstract:
In this paper, it is proved that Saint-Venant's solutions can be uniquely obtained from the following assumption: ∂^mσ_z/∂z^m=0(m≥2) where m(≥2) is an arbitrary integer, if some part of the side face of a cylinder is not the circular cylinder surface.

Numerical Method in Dynamic Respones of Nonlinear Systems

Zheng Zhao-chang, Tan Ming-yi

1985, 6(1): 93-101.

Abstract(2089) PDF(473)

Abstract:
A kind of modal synthesis lechniques, which is applicable to vibration analysis for linear substructures wilh nonlinear coupling altachments, has been exlended to nonlinear dynamic analysis of large complex structural systems. In this paper, a process is suggestcd to dynamic analysis of large comple...