应用数学和力学

1981 Vol. 2, No. 1

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Bending of Non-homogeneous Variable Thickness Elastic Circular Ring under Arbitrarily Distributed Loads

Yeh Kai-yuan, Tang Ren-ji, Zhen Ji-qing

1981, 2(1): 1-12.

Abstract(2215) PDF(920)

Abstract:
On the foundation of the initial parameter formulae of elastic circular ring with constant flexural rigidity,using the stepped reduction method, suggested in[2],we investigate the bending problem of non-homogeneous variable thickness elastic circular ring under arbitrarily distributed loads and obtain the general solution of this problem which is also suitable for the corresponding problem of non-homogeneous variable thickness cylindrical arch.In the end, an example is carried out to examine the gained formulae and assure the exactness of this method.

The Solution of the Problems in Elastostatics and the Principles of Least-Potential Energy and Least-Complementary Energy with Fuzzy Boundary Conditions

Yun Tian-quan

1981, 2(1): 13-20.

Abstract(2133) PDF(623)

Abstract:
In this paper, the solution of the problems in elastostatics is defined on "Set Theory" and extended to fuzzy boundary conditions. Both of the principles of least-potential energy and least-complementary energy are also extended to fuzzy boundary conditions. A theorem of the existence and uniqueness of the solution of minimum elemental potential energy is given and thus the existence of a quasisolution of the problems in elastostatics is proved.

On the Dirichlet Problem for a Quasilinear Elliptic Equation with a Small Parameter

Jiang Fu-ru

1981, 2(1): 21-47.

Abstract(1925) PDF(541)

Abstract:
The method of "boundary layer corrections" is developed to study the Dirichlet problem for a quasilinear elliptic equation in a bounded domain, when the degenerate equation has characteristics tangent to the boundary. The existence and uniqueness of solution have been proved. The uniformly valid asymptotic expansion of solution has been constructed.

A Study of Elastic Stability Problems Based on Mathematical Theory of Elasticity

Wang Zhen-ming

1981, 2(1): 49-74.

Abstract(1875) PDF(621)

Abstract:
It is important but difficult to study the stability problems of elastic bodies based on mathematical theory of elasticity.In[1],B.B.Hовожилов had obtained the equilibrium eq uations and bouadary conditions, but he did not give any practical solution.

Doubly Curved Shallow Shells with the Rectangular Bases Elasticaily Supported by Edge Arch Beams and Tie-Rods (Ⅱ)

Loo Wen-da

1981, 2(1): 75-95.

Abstract(1951) PDF(734)

Abstract:
This paper gives the results of numerical calculation based upon the method of double trigonometrical seiies on the problems of spherical shallow shells with square bases elastically supported by arch beams.The corners are pinned supported or simply supporred. The calculated results for λ=11.5936 show that the trigonometrical series converges rapidly. The effect of elastic deformation in the arch beams to the components of membrane tension, moment's and deflections of the shell are given.

Calculations for Semi-Circular Arc Type Corrugated Tube——Applications of General Solutions of Ring Shell Eguation

Chien Wei-zang, Zheng Si-liang

1981, 2(1): 97-111.

Abstract(2354) PDF(637)

Abstract:
In this paper, the deformation and stress distribution of semi-circular are type corrugated tube under the actions of axial compression are calculated by means of the general solutions of riag shell theory given in a previous paper^[1].The results of calculation fit fairly well with eaperimeatal data gives by C.E.Turner-H.Ford(1957).

Finite Element Method of Axial Symmetrical Shell with Abrupt Change of Curvature (Corrugated Tubes)

Shieh Chih-cheng, Fu Cheng-sung, Zheng Si-liang

1981, 2(1): 113-130.

Abstract(2127) PDF(561)

Abstract:
It is shown in this paper that due to the neglecting of curvature effect in the calculation of deformation of slope, the ordinary straight line finite elements are not suitable for the calculation of axile symmetrical shells with abrupt change of curvature.A new straight line finite element is proposed by considering the curvature effect on the deformation of slope, and regarding the deformation of slope as a continuously varied parameter. This new straight-line element is used for the calculation of semi-circular arc type corrugated tubes. The computed results are compared with Turner-Ford Experiments and also with computed results by analytical solution of slender ring theory given by Prof, Chien Wei-zang (1979).

The Perturbation Parameter in the Problem of Large Deflection of Clamped Circular Plates

Chen Shan-lin, Kuang Ji-chang

1981, 2(1): 131-144.

Abstract(2066) PDF(756)

Abstract:
In the problems of large deflection of clamped circular plates under uniformly distributed loads, various perturbation parameters relating to load, deflection, slope of deflection, membrane force, etc, are studied. For a general perturbation parameter, the variational principle is used for the solution of such a problem. The applicable range of these perturbation parameters are studied in detail. In the case of uniformly loaded plate, perturbation parameter relating to central deflection seems to be the best among all others. The method of determination of perturbation solution by means of variational principle can be used to treat a variety of problems, including the large deflection problems under combine loads.