Bending of thick plates with a concentrated load

In this paper, according to the simplified theory of [1], the bending of rectangular plates with two opposite edges simply supported and other two opposite edges being arbitrary under the action of a concentrated load is treated by means of properties of two-variable-function and the method of series^[2]. The effect of transverse shearing forces on the bending of plates is considered. When the thickness h of plates is small, and the term, whose orders are more than order of h² are neglected, then the results agree with the solutions corresponding to the problem of thin plates^[3]. At the end, the solutions of the bending problem of plates with arbitrary linear distributed load are also obtained.     

HAMILTONIAN SYSTEM AND SIMPLETIC GEOMETRY IN MECHANICS OF COMPOSITE MATERIALS (Ⅱ)——PLANE STRESS PROBLEM

Fundamental theory presented in Part (I)^[8] is used to analyze anisotropic plane stress problems. First we construct the generalized variational principle to enter Hamiltonian system and get Hamiltonian differential operator matrix; then we solve eigen problem; finally, we present the process of obtaining analytical solutions and semi-analytical solutions for anisotropic plane stress problems on rectangular area.     

A free rectangular plate on the two-parameter elastic foundation

This paper provides a rigorous solution of a free rectangular plate on the V.Z. Vlazov two-parameter elastic foundation by the method of superposition[1]. In this paper we derive basic solutions under the various boundary conditions. To superpose these basic solutions the most generally rigorous solution of a free rectangular plate on the two-parameter elastic foundation can be obtained. The solution strictly satisfies the differential equation of a plate on the two-parameter elastic model foundation, the boundary conditions of the free edges and the free corner conditions. Some numerical examples are presented The calculated results show that when the plane dimension of plate is given and the ratio between the laver depth and the plate thick is equal to 15, the two-parameter elastic model is near the Winkler’s. It shows that the Winkler model can be applied to the thinner layer.     

The problems of nonlinear bending for orthotropic rectangular plate with four clamped edges

（黄家寅）（秦圣立）ＴＨＥＰＲＯＢＬＥＭＳＯＦＮＯＮＬＩＮＥＡＲＢＥＮＤＩＮＧＦＯＲＯＲＴＨＯＴＲＯＰＩＣＲＥＣＴＡＮＧＵＬＡＲＰＬＡＴＥＷＩＴＨＦＯＵＲＣＬＡＭＰＥＤＥＤＧＥＳ￥ＨｕａｎｇＪｉａｙｉｎ;ＱｉｎＳｈｅｎｇｌｉ（ＱｕｆｕＮｏｒｍａｌＵｎ...     

Existence and comparison results for solutions of random integral and differential equations

This paper is the continuation of [1]. In this paper, we give another criteria of the existence of solutions for nonlinear random Volterra integral. A comparison theorem and the existence of random extremal solutions are also obtained by using the notion of ordering with respect to a cone. Our theorems generalize the corresponding results of Vaughan^[2,3] and Lakshmikantham^[4,5].     

The method of matrices conjoint multiplication for the problem of circular arc corrugated diaphragm

The circular are corrugated diaphragins are taken in this paper and structures of several sections of the ring shells and a central cireular plale I matrices and link matrices are derived by using Prof. Chuen Hei-zang’s general the ring shell[1] and perturbation theory of the circular thin plates. Throngh the meined of matrices conjoint multiplication, the linear exact solution and nonlinear soluaen are obtained. The resutts agree with that of the experiments presented by W. A. Wildhack..     

Several exact solutions of the simplified Navier-Stokes equations (SNSE)

The Simplified Navier-Stokes equations (SNSE) and their exact solutions for the flow near a rotating disk and the flow in the vicinity of a stagnation point for both two- and three-dimensional flows are presented in this paper. The analysis shows that in the aforementioned cases the exact solutions of the inner-outer-layer-matched SNSE^[4] are completely consistent with those of the complete Navier-Stokes equations (CNSE) and that the exact velocity solutions of D-SNSE^[1,3] agree with those of CNSE, however, the exact pressure solutions of D-SNSE do not agree with those of CNSE. The maximum relative pressure errors between the exact solutions of D-SNSE and CNSE can be as high as a hundred per cent.     

On the torsion of a cylinder with several cracks

In this paper, based on paper [1], the analytic expression of the torsion function for a cylinder containing arbitrary oriented cracks is obtained. The problem is reduced to solve a system of singular integral equations for the unknown dislocation density functions. Using the numerical method of the singular integral equations^[2,7] the torsional rigidities and stress intensity factors are evaluated for several multicracked cylinders. Next, the creak-cutting method^[5] is firstly extended to lve the torsion problem for a rectangular prism. The numerical results show that the method presented here is successful. Projects Supported by the Science Fund of the Chinese Academy of Sciences.     

Further research on the bending of the cantilever rectangular plates under a concentrated load

In this paper we apply the reciprocal theorem^[1] to further research on the bending problem of the cantilever rectangular plate under a concentrated load acting at any of its points. This method is even simpler and more general.     

平面4节点广义等参单元

在文献[1]建立的广义平面矩形单元的基础上,建立了平面4节点广义等参单元,并进行了深入研究,包括分片试验、单元的变形模态以及形函数的影响等.通过典型算例,对单元的性能进行了检验,数值结果表明,常规情况下建立的广义等参单元较传统单元具有更高的计算精度.     

Large deflection problem of a clamped elliptical plate subjected to uniform pressure

In this paper, the perturbation solution of large deflection problem of clamped elliptical plate subjected to uniform pressure is given on the basis of the perturbation solution of large deflection problem of similar clamped circular plate (1948), (1954). The analytical solution of this problem was obtained in 1957. However, due to social difficulties, these results have never been published. Nash and Cooley (1959) published a brief note of similar nature, in which only the case λ=a/b=2 is given. In this paper, the analytical solution is given in detail up to the 2nd approximation. The numerical solutions are given for various Poisson ratios v=0.25, 0.30, 0.35 and for various eccentricities λ=1, 2, 3, 4, 5, which can be used in the calculation of engineering designs.     

Random directional contractors and their applications

In this paper, as the generalizations of Altman’s directional contractors[4,5] and Lee and Padgett’s random contractors[1,2] we introduce the concept of random directional contractors for set-valued random operators. Using the new concept and transfinite induction, we show several existence theorems to solutions of nonlinear set-valued random operator equations. Our theorems improve and generalize the corresponding results in [1,2,4,5,11]. Next, some applications of our results to nonlinear random integral and differential equations are given.     

The stokes flow from half-space into semi-infinite circular cylinder

The infinite-series solutions for the creeping motion of a viscous incompressible fluid from half-space into semi-infinite circular cylinder are presented. The results show that inside the cylinder beyond a distance equal to 0.5 times the radius of the tube from the pore opening, the deviation of the velocity profile from Poiseuille flow is less than 1%. The inlet length in this case is comparable to that computed for a finite circular cylinder pore by 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.     

A uniformly valid asymptotic solution of the Navier-Stokes equations

ＡＵＮＩＦＯＲＭＬＹＶＡＬＩＤＡＳＹＭＰＴＯＴＩＣＳＯＬＵＴＩＯＮＯＦＴＨＥＮＡＶＩＥＲ－ＳＴＯＫＥＳＥＱＵＡＴＩＯＮＳＱｉｎＳｈｅｎｇ－ｌｉ（秦圣立）ＺｈａｎｇＡｉ－ｓｈｕ（张爱淑）（Ｄｅｐｔ．ＯｆＰｈｙｓｉｃｓ,ＱｕｆｕＴｅａｃｈｅｒｓＵｎｉｖｅ...     

The bending of a thick rectangular plate with three clamped edges and one free edge

The exact solution of the bending of a thick rectangular plate with three clamped edges and one free edge under a uniform transverse load is obtained by means of the concept of generalized simply-supported boundary^[1] in Reissner’s theory of thick plates. The effect of the thickness h of a plate on the bending is studied and the applicable range of Kirchhoffs theory for bending of thin plates is considered.     

The wedge subjected to general tractions: A paradox resolved

A wedge subjected to tractions in proportion tor ⁿ (n≥0), is considered. The stresses in the solutions of the classical theory of elasticity become infinite when the angle of the wedge is ρ or 2ρ. The paradox has been resolved by Dempsey^[4] and T.C.T. Ting^[5] whenn=0. The purpose of this paper is to resolve the paradox whenn>0.     

Problems on collinear cracks between bonded dissimilar materials under concentrated loads

Following Ref. [6], this paper deals with the problem on collinear cracks between bonded dissimilar materials under a concentrated force and moment at an arbitrary point. Several typical solutions of complex stress functions in closed form are formulated and the stress intensity factors are given. These solutions include a series of results of previous researchers, and redress some errors in the researches of problems containing semi-infinite cracks^[3],[4].     

THE PROBLEMS OF THE NONLINEAR UNSYMMETRICAL BENDING FOR CYLINDRICALLY ORTHOTROPIC CIRCULA RPLATE（I）

ＴＨＥＰＲＯＢＬＥＭＳＯＦＴＨＥＮＯＮＬＩＮＥＡＲＵＮＳＹＭＭＥＴＲＩＣＡＬＢＥＮＤＩＮＧＦＯＲＣＹＬＩＮＤＲＩＣＡＬＬＹＯＲＴＨＯＴＲＯＰＩＣＣＩＲＣＵＬＡＲＰＬＡＴＥ（Ｉ）ＱｉｎＳｈｅｎｇ－Ｉｉ（秦圣立）ＨｕａｎｇＪｉａ－ｙｉｎ（黄家寅）（Ｑｕｆ...     

The first-order approximation of non-Kirchhoff-Love theory for elastic circular plate with fixed boundary under uniform surface loading (III)—Numerical results

Based upon the differential equations and their related boundary conditions given in the previous papers^{[1, 2]}, using a global interpolation method, this paper presents a numerical solution to the axisymmetric bending problem of non-Kirchhoff-Love theory for circular plate with fixed boundary under uniform surface loading. All the numerical results obtained in this paper are compared with that of Kirchhoff-Love classical theory^[3] and E. Reissner's modified theory^[4].     

The numerical solution of the unsteady natural convection flow in a square cavity at high Rayleigh number using SADI method

The unsteady natural convection flow in a square cavity at high Rayleigh number Ra=10 ⁷ and 2×10 ⁷ has been computed using cubic spline integration. The required solutions to the two dimensional Navier-Stokes and energy equations have been obtained using two alternate numerical formulations on non-uniform grids. The main features of the transient flow have been briefly discussed. The results obtained by using the present method are in good agreement with the theoretical predictions ^[1,2].The steady state results have been compared with accurate solutions presented recently for Ra=10 ⁷.