应用数学和力学

On Solving High-Order Solutions of Chien’s Perturbation Method to Study Convergence by Computer

Ye Kai-yuan, Zhou You-he

1986, 7(4): 285-293.

Abstract(1802) PDF(484)

Abstract:
In this paper,we have obtained the analytical formula of arbitrary n-th order perturbation solution which perturbation parameter is central deflection for circular thin plate under a concentrated load by means of its integral equation.All unkown constants of every perturbation solution can be determined by computer.Hence higher order perturbation solution is obtained.Based on the solution of higher order perturbation,asymptotical property and suitable interval of Chien's perturbation method are also discussed.

Buckling Analysis of Discretely Stiffened Composite Curved Panels under Compression and Shear

X. X. Tong, B. Geier, K. Rohwer

1986, 7(4): 295-305.

Abstract(2013) PDF(504)

Abstract:
An analytical method for the buckling discretely thin-wall stiffened composite curved panels under compression and shear is presented by use of finite strip-element method.In the report a simplified scheme for complex displacement functions is developed.It enables that computation to be performed in real number algebra easily.And a simple and easy way to satisify the boundary conditions is introduced.Numerical results are given and are in good agreement with available data.

Analytical Solution of Partial Differential Equations for Radial Transport of a Solute in Double Porous Media

Huang Jun-qi, Liu Ci-qun

1986, 7(4): 307-316.

Abstract(2046) PDF(714)

Abstract:
The mathematical model for radial transport of a solute is summed up in this paper.The action of non-equilibrium linear adsorption,the double property of porous media and the decay of solute are considered.With the first kind of boundary condition,one finds the analytical solution of these equations by Laplace transform and calculates the dimensionless solution by FORTRAN program with DJS-040.The distribution and change of solute are evaluated and the solution under various limit cases is given.By numerical analysis,one obtains some valuable conclusions.

General Digital Picture Processing and Texture Analysis for Photoelasticity

Ouyang Chang, Ye Ning

1986, 7(4): 317-323.

Abstract(1630) PDF(433)

Abstract:
In this paper,a general digital picture processing and texture analysis for photoelasticity is developed.Overcoming some defects of references [2] and [3],it presents an effective method to analyse fringe patterns of the photoelasticity.By means of the trigonometric function relationship between the light intensity land the image fringe order N,the equations of the fringe order N on brightness Z are deduced,and the mechanical parameters are thus obtained.We established a system of sigital picture processing and texture analysis for photoelasticity,which is called OYC-1 system.Finally,this system is checked with an example.It is found that the differences between measured results and the theoretical values are within 2.3 percent.

The Large Deflection on Problem of Circular Plate on Elastic Foundation and in Conjunction with Linear Elastic Structure

Chen Shan-lin, Zhang Li-ying

1986, 7(4): 325-333.

Abstract(1982) PDF(502)

Abstract:
This paper deals with the axisymmetrical deformation of the circular plate in large deflection,which is on elastic foundation and in conjunction with a certain linear elastic structure.The governing integral equations are established by the method of mixed boundary condition 1 and the simplified form is given.The pertrubation method is used to obtain the solutions and an example of the composite structure made up of a circular plate and a cylindrical shell is presented.

The Mathematical Principles of Vibration Redactor

Jin Jun, Lu Ting-he, Hang Yong-zhen

1986, 7(4): 335-342.

Abstract(1899) PDF(416)

Abstract:
In engineering and technology,it is often demanded that self-oscillation.be eliminated.50 that the equipment or machinery may not be damaged.In this paper,a mathematical model for reducing vibration is given by the following equations: We have discussed how to choose suitable parameters c₁,k₁,k₂ of equations(*),so as to make the zero solution to be of global stability.Several theorems on the global stability of the zero solution of equations(*)are also given.

Uniform Difference Scheme for Hyperbolic-Hyperbolic Singular Perturbation Mixed Problems

Yin Guang-yan

1986, 7(4): 343-352.

Abstract(1815) PDF(567)

Abstract:
A difference scheme is established in this paper for second-order hyperbolic-hyperbolic singular perturbation mixed problems.We give an energy inequality of the numerical solution and prove that the numerical solution converges to the solution of the singular perturbation problems uniformly with respect to a small parameter and in the sense of a discrete norm.

Principles of Minimum Transformed Energy and Minimum Principles for Dynamics of Plates

Li Jia-ren, Zhang Shen-xue

1986, 7(4): 353-364.

Abstract(1888) PDF(640)

Abstract:
In the present paper,we first by Laplace transform present a derivation of principle of transformed virtual work,three principles of minimum transformed energy with influence of rotatory enertiafor dynamics of anisotropic linear elastic plates with three generalized displacements.Moreover,the forms with the original in place-time domain corresponding these variational principles are presented.Then by the introduction of the set of admissible weight functions the three minimum principles for the original place-time domain are derived.In each of the preceding groups of the variational principles there are two which are the dynamic counterparts to the static principles of minimum potetial energy and minimum complementary energy;the other principles are formulated in terms of the internal force alone,but have no counterpart in elastostatics of plates.

The Theory of Functions of a Complex Variable under Dirac-Pauli Representation and Its Application in Fluid Dynamics(Ⅰ)

Shen Hui-chuan

1986, 7(4): 365-382.

Abstract(2860) PDF(799)

Abstract:
In this paper:(A)We cast aside the traditional quaternion theory and build up the theory of functions of a complex variable under Dirac-Pauli representation.Thus the multivariate and multidimensional problems become rather simple problems.(B)We simplify the Navier-Stokes equation of incompressible viscous fluid dynamics and the equations group ofisentropic aerodynamics by theory of functions of a complex variable under Dirac-Pauli representation.And the above-equations,as central problems of fluid dynamics,are classified as the nonlinear equation with only one complex unknown function.

1986 Vol. 7, No. 4