Applied Mathematics and Mechanics (English Edition)

A SEMI-ANALYTICAL METHOD FOR STRUCTURE-INTERNAL LIQUID INTERACTION PROBLEMS

曹志远;张佑启

1985, 6(1): 1-8.

摘要 ( 474 )

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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 lo 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 INTO SEMI-INFINITE CIRCULAR CYLINDER

吴望一;Richard Skalak

1985, 6(1): 9-23.

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The infinile-series solulions fur the ereeping motion of a viscous incompressible fluid front half-space into semi-infinile circular cylinder are presented The resalts show that inside the cylinder beyond a distance equal to 0.5 times the radius af the tube from the pore opening, the deviation of the velocity profile from Poiseuille flow is less than 1%. The intel lenglh in this case is comparable In that computed for a finite circular crlinder pure br Dagan et al. [1]. In the half-space outside the cylinder pore region, the flow is strongly affected by the wall. Beyond one radius of the tube from the orifice. the solutions match almost exactly the flow through an orifice of zero thickness given by Sampson[2]. The relationship between the pressure drop and the volumetric flow rate is also computed in the present paper for the semi-infinite tube.

INVOLUTORY TRANSFORMATIONS AND VARIATIONAL PRINCIPLES WITH MULTI-VAROABLES IN THIN PLATE BENDING PROBLEMS

钱伟长

1985, 6(1): 25-39.

摘要 ( 416 )

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In this paper, the generalizd variational principles of plate bending, froblems 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. nol all the constrainls ofva’iaticn can be removed simply by the ordinary method of linear Lagrange multipliers. In such cases, the method of high-order Lagrange multipliers are usedto remove iliose constrainls left over by ordinary linear multiplier method. And consequently. some funct ionals 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

张鸿庆;王鸣

1985, 6(1): 41-52.

摘要 ( 447 )

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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

云天铨

1985, 6(1): 53-59.

摘要 ( 391 )

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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

黄筑平

1985, 6(1): 61-66.

摘要 ( 458 )

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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 u) 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 THEOREMS IN PROBABILISTIC INNER PRODUCT SPACES

张石生

1985, 6(1): 67-74.

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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 Uryson’s integral equation in IV.

THE PLANE PISTON PROBLEM IN A WEAK GRAVITATIONAL FIELD

胡文瑞

1985, 6(1): 75-85.

摘要 ( 444 )

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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

王敏中

1985, 6(1): 87-92.

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In this paper we obtain uniquely the solution of Saint- Venant’s problem under theassumption of ∂^m/∂z^mσ_z=0(m≥2) for noncircular prismatic bars.

NUMERICAL METHOD IN DYNAMIC RESPONSE OF NONLINEAR SYSTEMS

郑兆昌;谭明一

1985, 6(1): 93-101.

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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.

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