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(2270) 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 computing efforts.Cylindrical and conical frusium composite elemenls are proposed lo suit different problems, and examples are presenled to demonsirate the accuraey of the method.

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

Wu Wang-yi, Richard Skalak

1985, 6(1): 9-23.

Abstract(2307) 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 velocity profile from the Poiseuille one becomes equal to or less than 1%.The inlet length in this case is considerably shorter than Dagan's finite circular cylinder one. In the half-space outside the cylinder pore the region, strongly affected by the tube wzll, is restricted within a narrow limit no more than one radius of the tube from the orifice. Beyond this region the solutions match almost exactly the Sampson's one for a flow through an orifice of Zero thickness, The relationship between the pressure drop and the volumetric flow rate is also considered in this paper.

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

Chien Wei-zhang

1985, 6(1): 25-40.

Abstract(2233) 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 transformations are also introduced in order to reduce the order of differentiations for the variables in the variation. Funhermore, these involutory transformations become infacl the additional constraints in the varialion, and additional Lagrange multipliers may be used in order to remove these additional constraints. Thus, various multi-variable variational principles are obtained for the plate bending problems. However, it is observed that, not all the constrainls of variaticn can be removed simply by the ordinary method of linear Lagrange multipliers. In such cases, the method of high-order Lagrange multipliers are used to remove those constrainls left over by ordinary linear multiplier method. And consequently, some functionals of more general forms are oblained for the generaleed variational principles of plate bending problems.

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(2239) 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(2191) 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 employed for the analysis of piles and other geotechnical engineering problems.

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

Huang Zhu-ping

1985, 6(1): 61-66.

Abstract(1962) 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 interface moves from the plastic region into the rigid region, the rate of deformation is continuous too. These conclusions can also be applied to structures such as beams, pletes and shells in which the shear deformation and rotatory inertia are considered.

Fixed Point Theorem in Probabilistic Inner Product Spaces

Zhang Shi-sheng

1985, 6(1): 67-74.

Abstract(1992) 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 uniqueness of solution of Urysons integral equation in [4].

The Plane Piston Problem in a Weak Gravitational Field

Hu Wen-rui

1985, 6(1): 75-85.

Abstract(2026) 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 applied gravity.If we expand the quantities as a series of a small parameter, which is the ratio of a typical escape velocity to the plasma velocity, the basic stale gives a uniform flow, as shown by the case of gasdynamical theory without gravity. The first-order relationships show the influence of the applied gravity on the flow fields, that is, the strength of the shock wave changes slightly, the internat energy of the gas exhausts. For the cases of strong shock wave and near the piston, an analytical solution may be approximately olitained and has the similar features.Because of the importance of the applied gravity in the astrophysical and atmospheric physical processes, these results may shed light on the mechanics of transient process in the stellar and planetary atmosphere.

On the Assumption of Saint-Venant’s Problem

Wang Min-zhong

1985, 6(1): 87-92.

Abstract(2074) 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(2314) 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 complex structural systems with nonlinear characteristics of each subslructure. At the end of this paper, an example shows the defendable accuracy of the results and high efficiency of this process.