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1981年 第2卷 第1期    刊出日期：1981-01-18

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论文

The Bending of Elastic Circular Ring of Non-homogeneous and Variable Cross Section under the Actions of Arbitrary Loads

叶开沅;汤任基;甄继庆

1981, 2(1):  1-14. 

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On the basis of the stepped reduction method suggested in [1], we investigate the problem of the bending of elastic circular ring of non-homogeneous and variable cross section under the actions of arbitrary loads. The general solution of this problem is obtained so that it can be used for the calculations of strength and rigidity of practical problems such as arch, tunnel etc. In order to examine results of this paper and explain the application of this new method, an example is brought out at the end of this paper.Circular ring and arch are commonly used structures in engineering. Timo-shenko, S.^[2], Barber, J. R.^[3], Tsumura Rimitsuul et al. have studied these problems of bending, but, so far as we know, it has been solely restricted to the general solution of homogeneous uniform cross section ring. The only known solution for the problems with variable cross section ones has been solely restricted to the solution of special case of flexural rigidity in linear function of coordinates. On account of fundamental equations of the non-homogeneous variable cross section problem being variable coefficients, it is very difficult to solve them. In this paper, we use the stepped reduction method suggested in[1] to transiorm the variable coefficient differential equation into equivalent constant coefficient one. After introducing virtual internal forces, we obtain general solution of an elastic circular ring with non-homogeneity and variable cross section under the actions of arbitrary loads.

The Solution of Elastostatic Problems and the Principles of Minimum Potential Energy, Minimum Complementary Work, under Fuzzy Boundary Conditions

云天铨

1981, 2(1):  15-24. 

摘要 ( 507 )   PDF (523KB) ( 613 )  

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A Solution of elastostatic problem is defined on the basis of set theory and extended to the cases with fuzzy boundary conditions. Extension is also given for the principles of minimum potential energy and minimum complementary work with fuzzy boundary conditions. A quasisolution of an elastostatic problem is defined as an approximate solution with boundary conditions most close to the original. And the existance of quasisolution of an elastostatic problem can be proved on the basis of certain assumptions and the theorem of minimum elementary potential energy.

On the Dirichlet Problem for Quasi-linear Elliptic Equation with a Small Parameter

江福汝

1981, 2(1):  25-50. 

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In this paper we deal with the Dirichlet problem for quasilinear elliptic equation with a small parameter at highest derivatives. In case the characteristics of the degenerated equation are curvilinear and the domain, where the problem is defined, is a bounded convex domain, we offer a method to construct the uniformly valid asymptotic solution of this problem, and prove that the solution of this problem really exists, and being uniquely determined as the small parameter is sufficiently small.

Investigation of the Stability Problems of Elastic Bodies Using the Method of Mathematical Theory of Elasticity

王震鸣

1981, 2(1):  51-78. 

摘要 ( 393 )   PDF (1223KB) ( 548 )  

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In this paper, using the equilibrium equations and boundary conditions of elastic stability problem of and the method of mathematical theory of elasticity, we solve some elastic stability problems, which were studied by Ишлынский^[2] and Войцеховская^[3,4],and obtained more reasonable results than theirs.

Doubly Curved Shallow Shells with the Rectangular Base Elastically Supported by Edge Arched Beams and Tie-Rods (Ⅱ)

卢文达

1981, 2(1):  79-102. 

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In order to study the boundary conditions of integrated form(91a,d),firstlywe make use of trigonometrical series to express N_ξη(0,η),Q_ξ^*(0,η)of(97C,D).Suppose

The Calculation of Semi-circular Corrugated Tube——An Application of the General Solution of Ring Shell

钱伟长;郑思梁

1981, 2(1):  103-116. 

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In this paper, the deformation and stress distribution in semi-circular corrugated tube under axial force are calculated by means of the general solutions of circular ring shell given in previous paper [1].

The Solution for Axisymmetrical Shells with Abrupt Curvature Change (Corrugated Shells) by the Finite Element Method

谢志成;傅承诵;郑思梁

1981, 2(1):  117-136. 

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It has been noted in the present paper that the finite element method using linear elements for solving axisymmetrical shells cannot be applied to the analysis of axisymmetrical shells with abrupt curvature change, owing to the fact that the influence of the curvature upon the angular displacements has been neglected. The present paper provides a finite element method using linear elements in which the influence of curvature is considered and the angular displacements are treated as continuous parameters. This method has been applied to the calculation of corrugated shells of the type C, and compared with the experimental results obtained by Turner-Ford as well as with the analytical solution given by Prof. Chien Wei-zang. The comparisons have been proved that this theory is correct.

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

陈山林;光积昌

1981, 2(1):  137-154. 

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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.