应用数学和力学

Analytical, Numerical and Experimental Investigations of Architectural Sandwich Panels

K. P. Chong, Y. K. Cheung, L. G. Tham

1987, 8(2): 95-118.

Abstract(1931) PDF(472)

Abstract:
Architectural sandwich panels with thin-walled cold-formed steel facings and rigid foamed insulating core are becoming more and more popular as enclosures for system buildings. In this paper, the structural behavior, including flexural stresses/deflections, flexural wrinkling, axial stability, thermal stresses and vibration, is presented, summarizing more than a decade of research. Methods used are analytical (boundary-valued approaches), numerical (finite-strip, finite-layer, finite prism approaches) and experimental (full-scale testings). Key equations are formulated, and results by different methods are compared.

The Stokes Flow of the Rotating Double Spheres and Multiple Spheres

Wu Wang-yi, He Xiao-yi

1987, 8(2): 119-132.

Abstract(1789) PDF(499)

Abstract:
In this paper the expressions for a kind of new rotlets in Stokes flow are derived. By means of superposition of this new rotlets, the drag moment for rotating double spheres and multiple spheres along the smae axis are presented. It has been demonstrated that drag moment for each sphere is the linear function of its angular velocity.

Complex Variable Function Method for Hole Shape Optimization in an Elastic Plane

Sun Huan-chun, Zhang Ju-yong, Yan Guo-mei, Zhang Ji-zhu

1987, 8(2): 133-142.

Abstract(1951) PDF(661)

Abstract:
In this paper, a complex variable function method for solving the hole, shape optimization problem in an elastic plane is presented. In this method, the stresses in hole problems are analysed by taking advantage of the efficiency of the complex variable Junction method. To optimize the hole shape, the coeffecients in conformal mapping functions are taken as design variables, and the sensitivity analysis and gradient methods are used to reduce the largest circumferential stress in absolute value and at the same time to make the second largest circumferential stress in absolute value not to exceed the largest one (in fact, these two stresses are the stationary values of the circumferential stresses). The coefficients in conformal mapping function are revised by iteration step by step until the largest circumferential stress in absolute value is reduced to the second largest stress. This method guarantees the continuity, differentiability and accuracy of the stress solution along the boundary, and it is evident that this method is better than either the difference method or the finite element method.

Perturbation Solution of the Weak-Nonlinear Partial Differential Equation with δ-Function

Xu Zhen-yuan, Liu Zheng-rong

1987, 8(2): 143-150.

Abstract(1663) PDF(480)

Abstract:
In this paper we extend the method which Liu Zheng-rong provided to the weak-nonlinear partial equation with δ-function.

Progressing Step by Step and Integrating Calculation of Overcritical Deformation of Spherical Shallow Shells

Jia Nai-wen

1987, 8(2): 151-162.

Abstract(1810) PDF(513)

Abstract:
In this paper, the problem of second buckling of the spherical shallow shell is calculated by use of the method of progressing step by step and integrating. The result is more exact than that of first approximate analysis for over-critical deformation of spherical shallow shell. It has been solved that the solution of second approximate analysis in this problem can't be found. The calculating example in this paper shows that the solution of progressing step by step and integrating converges to second approximate solution.

Pansystems Studies in Stability, Bifurcation and Chaos

Gao Long-ying

1987, 8(2): 163-168.

Abstract(1707) PDF(461)

Abstract:
This paper divides fixed subsets into three kinds, mainly discusses the existence of II-type fixed subset, connects the investigations in fixed subsets with the studies in non-linear problems, such as stability, bifurcation, chaos, etc., and proposes a kind of discrete simulation to Liapunov stability and his second method.

The Equations of Motion for a Nonholonomic System under the Action of.lmpulsive Forces

Sun You-lie

1987, 8(2): 169-176.

Abstract(1724) PDF(458)

Abstract:
The equations of impact for a nonholonomic system described with generalized coordinated have been discussed in detail in the general references of classical dynamics. But these equations contain undetermined multipliers which made the problem complicated.Through the appropriate treatment of mathematics, using the 8 -function and expression of matrix in this paper, the author derived equations of impact for a nonholonomic system without undetermined multipliers. Therefore, the problem can be solved more simply.

The Application of Dirac Matrices and Pauli Matrices for the Theory of Plasticity

Shen Hui-chuan

1987, 8(2): 177-183.

Abstract(2021) PDF(476)

Abstract:
We are primarily concerned in this paper with the problem of plasticity. The solution of the problem of stress-increment for plasticity can be put into extremely compact form by famous Dirac matrices and Pauli matrices of quantum electrodynamics.

On the New Forms of the Differential Equations of the Systems with Higher-Order Non-Holonomic Constraints

Shen Ze-chun, Mei Feng-xiang

1987, 8(2): 186-192.

Abstract(1644) PDF(514)

Abstract:
In this paper, the new forms of the differential equations of motion of the systems with higher-order non-holonomic constraints are obtained at first, and then the equivalence between these equations and the known equations is demonstrated. Finally an example is given to illustrate the application of our new equations.

1987 Vol. 8, No. 2