应用数学和力学

On a Class of Method for Solving Problems with Random Boundary Notches and/or Cracks——(Ⅲ) Computations for Boundary Cracks

Ouyang Chang, Zu Hang

1985, 6(8): 671-680.

Abstract(2003) PDF(651)

Abstract:
This paper continues the discussions to a class of method for solving problems with random boundary notches and/or cracks in refs. [1] and [2]. Using the method developed in [1],[2] with important modifications about inclusion of singularities in the formulation, we arrive at a very effective computational process for problems with random boundary orucks. Actual computations for boundary cracks with or without applied tractions in their surfaces. Show that the present method is quite workable for the problems considered within proper range of characteristic parameters. The results obtained here extend the contents of "Handbook of Stress Intensity Factors" given by G. C. Sih.

The Inlet Effect on the Drag Factor of a Sphere in a Tube

Wu Wang-yi, Richard Skalak

1985, 6(8): 681-698.

Abstract(2057) PDF(796)

Abstract:
The creeping motion oround a sphere situated axisymmetricnlly near the entrance of a semi-infinite circular cylindrical tube is analyzed using infinite series solutions for the velocity components, pressure and the stream function. Truncating the infinite series, the corresponding coefficients in the series are determined by a collocation technique. The drag factor and the stress distribution on the surface of the sphere are calculated for the sphere in motion in quiescent fluid and for the flow with uniform velocity at the entrance past a rigidly held sphere. The results indicate that a sphere near the entrance which has a uniform entrance velocity profile will suffer larger drag than that in an infinite tube. The convergence of the collocation technique is tested by numerical calculation. It is shown that the technique has good convergence properties.

Interlaminar Stresses of a Laminated Composite Bar under Bending(Ⅱ)

Zhang Fu-fan

1985, 6(8): 699-710.

Abstract(1687) PDF(572)

Abstract:
A laminated composite bar of rectangular cross section consists of a middle portion of one material as well as upper and lower identical cover plates of another material. Couples formed by linear bending stresses act in the middle portion at the ends of the bar to cause bending. Interlaminar stresses are to be found showing how the forces are transmitted through the glued surfaces to the cover plates.

The Relation of von Karman Equation for Elastic Large Deflection Problem and Schrodinger Equation for Quantum Eigenvalues Problem

Shen Hui-chuan

1985, 6(8): 711-723.

Abstract(1833) PDF(667)

Abstract:
In this paper the solutions of von Kármán for elastic large deflection problem are classified as the several solutions of Schrödinger equation for quantum eigenvalues problem, and we present the transform for elastic large deflection problem from non-linear equation into linear equation. Thus, we create favourable conditions of the adoption of converse scattering methnd and Bácklund transformation. We also discuss the large deflection problem of long and narrow plate.We can study the non-linear transition of elastic thin plate by furnished method from this paper.

Solution of Spline Function of Elastic Plates

Wang Lei

1985, 6(8): 725-734.

Abstract(1778) PDF(655)

Abstract:
In this paper, from four and three-order differential equations defined by cubic and quadratic splines of generaized beam. The beam functions with many boundary conditions and under various loads are reduced. The approximate solution of deformalion surface ami stress of elastic thin plate is very accurate.

Solution of Bending of Cantilever Rectangular Plates under Uniform Surface-Load by the Method of Two-Direction Trigonometric Series

Lin Xiao-song, Yuan Wen-bo

1985, 6(8): 735-744.

Abstract(1748) PDF(685)

Abstract:
The bending of a cantilever rectangular plate is a very complicated problem in the theory of plates. For a long time, there have been only approximate solutions for this problem by energy methods and numerical methods.since 1979. Prof. F. V. Chang of Tsing Hua University obtained, by the method of superposition, a series of analytic solutions for cantilever rectangular plates under uniform load and concentrated load.In this paper, the two-direction trigonometric series is used to obtain the solution for the bending of cantilever rectangular plates under uniform load. The obtained results are compared with the results by the method of superposition. The comparison shows that the results of these two methods are in good agreement, hence they are mutually confirmed to be correct.

Elastic-Plastic Analysis of Cylindrically Orthotropic Composite Lamina with a Circular Hole under Uniform Pressure

Zhou Ci-qing

1985, 6(8): 745-753.

Abstract(1677) PDF(550)

Abstract:
This paper presents the standard parametric representation of the Tsai-Hill yield criterion in a state of plane stress and the equations governing the stress distribution in a cylindrically orthotropic composite lamina with a circular hole under uniform pressure for the three cases:(a) elastic state,(b) limit state and(c) elastoplastic state. The formulas for the yield pressure and the limit pressure have been obtained.

An Analysis on Response of Structure to Random Earthquake Excitation

Yu Jia-sheng, Chang Jian-hao

1985, 6(8): 755-760.

Abstract(1783) PDF(537)

Abstract:
In this paper the response of elastic structure to random earth-quake excitation is analysed. For a frame-wall system, practical calculating formulas are derived and a program in FORTRAN language is made. The program is checked with a numerical example. The envelope of the lateral displacement of the system and the variation regularity of the internal forces are determined from given values of dynamic reliability(first excursion probability) based on the requirement of the operation of the structures.

Some Problems for Viscoelastic Rods

Zou Feng-wu, Liu Xun-ming

1985, 6(8): 761-768.

Abstract(1611) PDF(525)

Abstract:
Using an approach proposed in [3], we consider some linear and nonlinear problems for viscoelastic rods. Results in [1] for linear case are affirmed more elamentarily and simply here. We also treat linear problem with damping term and nonlinear problem with power nonlinearity pu³. Some new results are established.

1985 Vol. 6, No. 8