应用数学和力学

Variational Principles and Generalized Variational Principles for Nonlinear Elasticity with Finite Dispiacemant

Chien Wei-zhang

1988, 9(1): 1-11.

Abstract(1857) PDF(901)

Abstract:
In a previous paper(1979), the minimum potential energy principle and stationary complementary energy principle for nonlinear elasticity with finite displacement, together withvarious complete and incomplete generalized principlesIwere studied. However, the statements and proofs of these principles were not so clearly stated about their constraint conditions and their Euler equations. In somecases, the Euler equations have been mistaken as constraint conditions. For example, the stress displacement relation should be considered as Euler equation in complementary energy prindple,but have been mistaken as constraint conditions in variation. That is to say, in the above mentioned paper, the number of constraint conditions exceeds the necessary requirement. Furthermore, in all these variational principles, the stress-strain relation never participate in the variation process as constraints, i.e., they may act as a constraint in the sense that, after the set of Euler equations is solved, the stress-strain relation may be used to derive the stresses from known strains, or to derive the strainsfrom known stresses. This point was not clearly mentioned in the previous paper(1979). In this paper, the high order Lagrange multiplier method(1983) is used to construct the corresponding generalized variational principle in more general form. Throughout this paper, V.V. Novozhilov's results(1958) for nonlinear elasticity are used.

Optimal Design of Minimax Deflection of an Annular Plate

Yu Huan-ran, Ye Kai-yuan

1988, 9(1): 13-18.

Abstract(1680) PDF(490)

Abstract:
The optimal design ofminimax deflection of an annular plate is studied in this paper. The annular plate is subjected to an arbitrary axisymmetric loading. The problem can be posed as a standard nonlinear programming problem with equality constraints by means of the stepped reduction method. Some examples are also given to illustrate the method which has many advantages.

The Perturbation Finite Element Method for Solving the Plane Problem in Consideration of Linear Creep

Wu Rui-feng, Yang Hai-tian

1988, 9(1): 19-29.

Abstract(1768) PDF(492)

Abstract:
In this paper, a method(PFMC) for solving plane problem of linear creep is presented by using perturbation finite element. It can be used in plane problem in consideration of creep, such as reinforced concrete beam, presiressed concrete beam, reinforced concrete cylinder and reinforced concrete tunnel in elastic or visco-elastic medium, as well as underground building and so on.In the presented method, the assumption made in the general increment method that variables remain constant in a divided time interval is not taken. The accuracy is improved and the length of time step becomes larger. The computer storage can be reduced and the calculating efficiency can be increased.Perturbation finite element formulae for four-node quadrilateral isoparametric element including reinforcement are established and five numerical examples are given. As contrasted with the analytical solution, the accuracy is satisfactory.

Anisotropic Plastic Stress Fields at a Rapidly Propagating Crack-Tip

Lin Bai-song

1988, 9(1): 31-36.

Abstract(1780) PDF(505)

Abstract:
All the stress components at a rapidly propagating crack-tip in an elastic perfectly-plastic material are the functions of θ only. Making use of this condition and the equations of steady-state motion, stress-strain relations and Hill anisotropic yield condition, we obtain the general solutions in both the cases of anti-plane and in-plane strain. Applying these two general solutions to propagating Mode III and Mode I cracks, respectively, the anisotropic plastic stress fields at the rapidly propagating tips of Mode III and Mode I cracks are derived.

Dynamics of Multi-Deformable Bodies

Hong Shan-tao

1988, 9(1): 37-48.

Abstract(1818) PDF(682)

Abstract:
The Gibbs-Appell equations provide what is the powerful tool to formulate equations of motion not only for rigid-body, but also for deformable body. The application of the Gibbs-Appell equations in formulating equations of motion ofmulti-deformable hoodies is developed and exploited in this paper. The advantages of using Gibbs-Appell equation are shown herein. Equations of motion of multi-deformable bodies with explicit form have been obtained and their physical meaning is apparent. In addition, recently developed new ideas are also employed. These ideas include the use of Euler parameters, quasi-coordinates, and relative coordinates.

The Equations of Motion of a System under the Action of the Impulsive Constraints

Sun You-lie

1988, 9(1): 49-56.

Abstract(1863) PDF(607)

Abstract:
In order to solve the problem of motion for the system with n degrees of freedom under the action of p impulsive constraints, we must solve the simultaneous equations consisting of n+p equations. In this paper, it has been shown that the undetermined multipliers in the equations of impact can be cancelled for the cases of both the generalized coordinates and the quasi-coordinates. Thus there are only n-p equations of impact. Combining these equations with p impulsive constraint equations, we have simultaneous equations consisting ofn equations. Therefore, only n equations are necessary to solve the problem of impact for the system subjected to impulsive constraints. The method proposed in this paper is simpler than ordinary methods.

The New Solutions for Two Kinds of Axially Symmetrical Laminar Boundary Layer Equations

Wang Zhi-qing, Shang Er-bing

1988, 9(1): 57-62.

Abstract(2031) PDF(540)

Abstract:
The transformations, which are similar to Mangier's transformation, are given in this paper, and make the two kinds of entrance region flow of axially symmetrical laminar boundary layer in internal way into the flow of two-dimensional boundary layer, and simplify the proboems. The simplified equations can be solved by the 2-D boundary layer theory. Therefore, a new way is opened up to solve the axially symmetrical flow in the entrance region of internal way.

A New Approximate Analytical Solution of the ideal Potential Flow around a Circular Cylinder between Two Parallel Flat Plates

Yuan Yi-wu

1988, 9(1): 63-71.

Abstract(1834) PDF(555)

Abstract:
In ref. [1], Lin obtained an approximate analytical solution of the ideal potential flow around a circular cylinder between two parallel flat flates.In this paper, the author shows that one may obtain the result coinciding with that obtained in ref. [1] by making use of the Shvez's method^[2]. Morever, we can obtain a more accurate result than that obtained in ref. [1], if we make use of the improved Shvez's method^[2]. Some calculating examples are presented.

A Kind of Distortion of Mean Velocity Profile in Pipe Poiseuille Flow and Its Stability Behaviour

Zhou Zhe-wei

1988, 9(1): 73-82.

Abstract(1964) PDF(546)

Abstract:
This paper presents a kind of distortion of Hagen-Poiseuille velocity profile in pipe Poiseuilleflow. This distortion can be regarded as a general expression of the influence on the mean flow by nonlinear interaction of various components of axisymmetric perturbations. Through the investigation of the stability behaviour of this velocity profile, this paper obtains unstable result induced by axisymmetric perturbations for the first time, and thus presents a new possible approach which leads to instability of Hagen-Poiseuille flow.

On the Convergence of Elastopiastic Boundary Element Analysis

Li Wen-long, Zhang Xiang-lin

1988, 9(1): 83-89.

Abstract(1819) PDF(463)

Abstract:
Iterative process is a main componertt of boundary element method in plasticity. In this paper, the convergence of elastoplastic boundary element analysis has been discussed in detail and studied theoretically.

Boundary Value Problems for Second Order Singularly Perturbed Differential Equations

Zhou Qin-de, Miao Shu-mei

1988, 9(1): 91-94.

Abstract(1708) PDF(533)

Abstract:
In this paper the existence and uniqueness of solutions of boundary value problems εy"=f(t,y,e) L(y(0),y'(0,ε=0, R(y(1),y'(1),ε=0)(which contains the Robin's problem) is discussed by using the upper and lower solution. In addition,the asymptotic estimation of the solution is given as well.

1988 Vol. 9, No. 1