应用数学和力学

1980 Vol. 1, No. 2

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A Two-shaft Balance System Analysis and a Slipper Balance Scheme for the Second Order Reciprocating Inertia Forces of Plane Crankshaft Eight cylinder V-type Internal Combustion Engines

Liu Hsien-chih

1980, 1(2): 139-152.

Abstract(2265) PDF(685)

Abstract:
By using "four shaft concept" a balance system for the second order reciprocating inertia forces of the plane crankshaft eigbt-cylinder V-type internal combustion enr,ines was worked out as reported in the paper[1].In paper[2] we have been able to acquire a "two shaft balance scheme" as a degeneracy of the"four shaft balance system" by pur suiting a far roundabout way.By the way as a mathematical by-product it has been met possibly a new curve which could be named,perhaps,as "The Degenerated hour-Leave.d Rose".which was intended to be discussed in detail with a special paper.

The Explicit Forms of Field Functions in Tetrahedron Element with 16 and 20 Degrees of Freedom

Chien Wei-chang

1980, 1(2): 153-158.

Abstract(1769) PDF(578)

Abstract:
In this paper,the explicit forms of field functions in tetrahedron elements with 16 and 20 degrees of freedom are given in tcrms of volume coordinates L¹,L,L³,L⁴,of tetrahedron.

On a Class of Methods for Solving Problems of Random Boundary Notches and/or Cracks

Ouyang Chang

1980, 1(2): 159-166.

Abstract(1618) PDF(547)

Abstract:
In engineering fracture analysis,random boundary imperfections as notches or cracks are common and important.In this paper,we have worked out a class of methods for solving two-dimensional problems of random boundary notches and/or cracks by an extension of Muskhelishvili's method.Through successive applications of analytic conti-nuation,Laurent series expansion and conformal mapping,we finally arrived at a set of linear algebraic equations governing the problem,Then standard com puting program of linear algebraic eq nations may he used to com plete the solution.It is noticed that the prescn method may give solutions for the cases in which there are certain smooth load distrihutmns on the notch surfaces.

The Difference Method for the Solution of Singular-Perturbation Problems for the Elliptic-Parabolic Partial Differential Equation

Su Yu-cheng, Wu Chi-kuang

1980, 1(2): 167-176.

Abstract(1921) PDF(807)

Abstract:
In this paper is discussed the difference method for the solution of singular perturbation problems for the elliptic equations,involving small parameter in the higher derivatives,As ε=0,the original equations are degenerated into the parabalic equations.Authors constructed special difference scheme by means of the boundary layer properties of the solutions of these problems and investigated the convergence of this scheme and asymptotic behaviour of the solutions,Finally,a numerical example is given.

Circular Shallow Spherical Shells with Circular Holes at the Center under Simultaneous Actions of Arbitrary Unsteady Temperature Field and Arbitrary Dynamic Normal Load

Ye Kai-yuan, Hsu Chin-yun

1980, 1(2): 177-199.

Abstract(1717) PDF(637)

Abstract:
In this paper,under assumption that temperature is linearly distributed along the thickness of the shell.we deal with problems as indicated in the title and obtain general solutions of them which are expressed in analytic form.In the first part,we investigate free vibration of circular shallo w spherical shells with circular holes at the center under usual arbitrary boundary conditions.As an example,we calculate fundamental natural frequency of a circular shallow spherical shell whose edge is fixed(m=0).Results we get are expressed in analytic form and check well with E,Reissner's[1].Method for calculating frequency equation is recently suggested by Chien Wei-zang and is to be introduced in appendix 3.In the second part,we investigate forced vibration of shells as indicated in the title under arbitrary harmonic temperature field and arbitrary harmonic dynamic normal load.In the third part,we investigate forced vibration of the above mentioned shells with initial conditions under arbitrary unsteady temperature field and arbitrary normal load.In appendix 1 and 2,we discuss how to express displacement boundary conditions witli stress function and boundary conditions in the case m=1.

On the Boundary Value Problems for a Class of Ordinary Differential Equations with Turning Points

Jiang Fu-ru

1980, 1(2): 201-213.

Abstract(1648) PDF(780)

Abstract:
In this paper we study the boundary value problems for a class of ordinary differential equations with turning points by the method of multiple scales.The paradox in[1] and the variational approach in [2] are avoided,The uniformly valid asymptotic approximations of solutions have been constructed.We also study the case which does not exhibit resonance.

A Brief Account of G.D.Birkhoff’s Problem in the Problem of Three Bodies

Tung Chinchu

1980, 1(2): 215-219.

Abstract(1808) PDF(477)

Abstract:
The present article gives a historical survey of G,D.Birkhoff's seventh problem whick is an inquiry about the topological structure of the set of definition of the reduced differential equations of motion,Recent advances in the problem and their meaning have been briefly indicated.

On the Reissner Theory of Bending of an Elastic Plate

Miao Tian-de, Cheng Chang-jun

1980, 1(2): 221-235.

Abstract(2312) PDF(827)

Abstract:
Reissner equations of elastic plate are derived on the bases of incomplete generalized variational principle of complementary energy.The stress function ψ is obtained from the variational calculation in the form of Lagrange multiplier.The structure of solution of Reissner equations is thus determined.On the bases of these discussions,we obtained a simplified theory,in which the equations of equilibrium involving the shearing influence can be reduced into a fourth order differential equation similar to those of classic plate theory.

Longitudinal Free Vibration of an Elastic Non-uniform Strut

Liu Hsien-chih

1980, 1(2): 237-245.

Abstract(1647) PDF(732)

Abstract:
The aim of this paper is to give a more or less general treatment of vibration of elastic non-uniform strut,such as composite wooden screw-propeller.In this paper,elastic modulus,cross-sectional area,and mass per unit length are considered to be of exponential functions of longitudinal coordinates,A general solution is obtained together with these three para meters,which are fou nd to be the main factors closely related to the frequencies of free vibration of such an elastic-non-uniform strut.

The Fundamental Equations in Finite-Element Method of Coupled Thermo-elastic Plane Problem

Wang Hong-gang

1980, 1(2): 247-259.

Abstract(1991) PDF(669)

Abstract:
The fundamental equations in finite element method for unsteady temperature field elastic plane proble m are derived on the bases of variational principle of coupled thermoelastic problems,In these derivations,elastic plane is divided into three nodes triangular elements,and time interval is divided into linear time elements,in which all the variables,including displacements and temperatures at various nodal points,are varied linearly with time,Two coupled sets of linear algebraic equations of all the unknown displacements and temperatures at every nodal point in every instant(i,e,the terminal values of time elements) are obtained.They are the fundamental equations of the said problem.

Elastic Behavior of Uniformly Loaded Circular Corrugated Plate with Sine-shaped Shallow Waves in Large Deflection

Chen Shan-lin

1980, 1(2): 261-272.

Abstract(1884) PDF(532)

Abstract:
By means of modified iteration method,this paper gives approximate solution of the large deflection equations of circular corrugated plate with sine-shaped shallow waves having a central platform under uniform lateral load.A formula of initial modification coefficient β is given,and an integral is obtained for the simplification of modified iteration calculations.The results of present paper shows better agreement with experi-mental data and larger applicable range than all other existing solutions of corrugated plates.