应用数学和力学

An Exact Analytic Method Applied to Nonhomogeneous Ring-and Stringer Stiffened Cylindrical Shells

Yeh Kai-yuan, Ji Zhen-yi

1989, 10(9): 747-757.

Abstract(1700) PDF(453)

Abstract:
In this paper, the nonlinear axial symmetric deformation problem of nonhomogeneous ring-and stringer-stiffened shells is first solved by the exact analytic method.An analytic expression of displacements and stress resultants is obtained and its convergence is proved.Displacements and stress resultants converge to exact solution uniformly.Finally, it is only necessary to solve a system of linear algebraic equations with two unknowns.Four numerical examples are given at the end of the paper which indicate that satisfactory results can be obtained by the exact analytic method.

Asymmetric Dynamic Instability of Axisymmetric Polar Dimpling of Thin Shallow Spherical Shells

Yun Tian-quan

1989, 10(9): 759-766.

Abstract(1694) PDF(377)

Abstract:
If the parameter ε², which measures the thickness-to-rise of the sliell, is small, the axismnnetrie polar dimpling of shallow spherical shell due to quadratic pressure distribution is dynamic instability, i.e., a small perturbation can change it to an asymmetric polar dimple mode.In two cases, the problem can be reduced to an eigenvalue problem Tw_n=c_n+w_n, where T can approximately be reduced to a Sturm-Liouvi/le operator if ε²<<1. The existence of at least one real eigenvalue of T, which means that the axisyntmetric polar dimpling is dynamically unstable, is proved by spectral theorem or Hilbert theorem.Furthermore, an eigenfunction, which represents one of the asymmetric modes of the unstable dimple shell, belonging to an eigenvalue of T, is found.

Inf-Dif-Stability of Oblique Perturbation

Chen Song-qiang, Chou Kuan-wen

1989, 10(9): 767-772.

Abstract(1754) PDF(506)

Abstract:
Lanrem and Rockafellar have studied certain problems of perturbation and of stability in convex minimization problems.Laurent has discussed inf-dif-stability conditions respectively for horizontal perturbation and for vertical perturbation.In this paper, we generalize some results of Laurent^[1] by giving several inf-dif-slability conditions of oblique perturbation.

The Elasto-PIastic Strain Analysis of Notched Plate under Cyclic Loading——An Application of Plastic Anisotropic Hardening Theory

Jin Yong-jie, Li Ru-feng, Zhou Chun-tian, Gou Qiu-jing

1989, 10(9): 773-777.

Abstract(1793) PDF(1021)

Abstract:
In order to predict the life of engineering structures, it is necessary to investigate the strain distribution in notched members.In gineral, the Uauschinger Effect of materials under cyclic loading is not negligible, and so the anisolropic hardening model has been suggested.From the comparison between the calculated and experimental results in this paper, we can see that even the linear kinematic hardening model is quite suitable for strain analysis under cyclic loading.

Large Deflection Problem of Circular Plates with Variable Thickness under the Action of Combined Loads

Wang Xin-zhi, Xu Jian, Wang Lin-xiang

1989, 10(9): 779-788.

Abstract(1638) PDF(617)

Abstract:
By using the modified iteration method of large deflection theory of plates with variable thichness^[1], we solve the problem of circular plates with variable thickness subjected to combined loads under the boundary conditions of the clamped edges and get comparatively more accurate second-order approximate analytical solution.If the results of this paper are degraded into the special cases, the results coinciding with those of papers [1,2] can be obtained.In this paper, the characteristic curves are plotted and some comparisons are made.The results of this paper are satisfactory.

The Motion of a Spherical Particle in the Stokes Flow Outside a Circular Orifice

Shan Hui-xian, Yan Zong-yi

1989, 10(9): 789-800.

Abstract(1759) PDF(501)

Abstract:
For any study ofa suspension entering a pore, the knowledge of the force and moment exerted on a solute particle in an arbitrary position outside the pore is essential, This paper for the first lime presents approximate analytical expressions (in closed form) of all the twelve force and moment coefficienis for a sphere outsied a circular orifice, on the basis of a number of discrete data computed by Yan et al(1987).These coefficients are then applied to calculate the trajectory and angular velocity of a spherical particle approaching the pore at zero Reynolds number.The trajectory is in excellent agreement with the available experimental results.An analysis of the relative importance of the coefficients shows that the rotation effect cannot be neglected near the pore opening or near the wall, and that the lateral force effect must be taken into account in the neighborhood of the edge of the pore opening.It is due to neglecting these factors that previous theoretical results deviate from the experimental ones near the pore opening.The effects of the ratio of the particle to pore radii as well as the influences of the graritytbuoyance on the particle trajectory, velocity distribution and rotation are discnssed in detail.It is pointed out that in the experiments of neutrally-buoyant suspensions, the restriction on the density of the particle is most demanding for a large particle size.The expressions of forces and moments presenled herein are complete, relatively accurate and convenient, thus providing a good prerequisite for further studies of any problems involving the entrance of particles to a pare.

The Fourier Pseudo-Spectral Method for the SRLW Equation

Zheng Jia-dong, Zhang Ru-fen, Guo Ben-yu

1989, 10(9): 801-810.

Abstract(2161) PDF(1086)

Abstract:
In this paper we present a Fourier pseudo-spectral method with a restraint operator for the SRLW equation.We prove the stability of the schemes and give optimum error estimates.

Clifford Algebra, Theory of Its Function and Their Application to Mechanics

Huang Si-xun

1989, 10(9): 811-824.

Abstract(1954) PDF(503)

Abstract:
As is well known, in both elastic mechanics andfluid mechanics, the plane problems are more convenient than space problems.One of the causes is that there has been a complete theory about the complex Junction and the analytic junction, hut in space problems, the case is quite different.We have no effective method to deal with these problems.In this paper, we first introduces general theories of Clifford algebra.Then we emphatically explain Clifford algebra in three dimensions and establish theories of regular Junction in three dimensions analogically to analytic function in plane.Thus we extend some results of plane problem to three dimensions or high dimensions.Obviously, it is very important for elastic and fluid mechanics.But because Clifford algebra is not a commutative algebra, we can't simply extend the results of two dimensions to high dimensions.The left problems are yet to be found out.

Analytical Solution of Flow in Infinite Stratified Oil Reservoir and Its Application

Dai Rong-qing, Kong Xiang-yan, Zhong Zhao-xin

1989, 10(9): 825-832.

Abstract(1677) PDF(548)

Abstract:
This paper presents an analytical solution for the production function and pressure distribution function of flow in infinite stratified oil reservoir with crosflow under the condition of constant wellbore pressure (CWP condition) by Weber's integral transformation.The calculation results are shown in the form of curves and these results can be used to analyse unsteady flow test of production with CWP condition.

Fixed Pansystems Theorems and Eigen-Fuzzy Sets

Wang Shu-ji

1989, 10(9): 833-839.

Abstract(1702) PDF(392)

Abstract:
In this paper, we apply fixed pansystems theorems to study when a fuzzy transformation has a nonzero eigen-fuzzy set.Many necessary conditions and sufficient conditions are obtained.Furthermore, the properties of nonzero eigen-fuzzy sets are investigated, and the results presented in Ref.[4] are extended.

1989 Vol. 10, No. 9