An application of Ungar's differential transform to elastodynamics

In recent years, a lot of writers have used Cagniard-de Hoop’s method^[1][2] to solve some problems of elastic wave. But it is a difficult and complicated task to change the path of integration when we use this method. A differential transform by A.Ungar^[3,6] can obviate this difficulty. In this paper, weuse Ungar’s differential transform to solve a case of Lamb’s problem^[1][2].     

The application of compatible stress iterative method in dynamic finite element analysis of high velocity impact

There is a common difficulty in elastic-plastic impact codes such as EPIC ^[2,3].NONSAP ^[4],etc. Most of these codes use the simple linear functions usually taken from static problem to represent the displacement components. In such finite element formulation, the stress components are constant in each element and they are discontinuous in any two neighboring elements. Therefore, the bases of using the virtual work principle in such elements are unreliable. In this paper, we introduce a new method, namely, the compatible stress iterative method, to eliminate the above-said difficulty. The calculated examples show that the calculation using the new method in dynamic finite element analysis of high velocity impact is valid and stable, and the element stiffness can be somewhat reduced.This is a part of the author's Ph. D dissertation under the supervision of Professor Chien Wei-zang.     

A new approximate analytical solution of the ideal potential flow around a circular cylinder between two parallel flat plates

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.     

On the torsion of a cylinder with several cracks

In this paper, based on paper [1], the analytic expression of the torsion function for a cylinder containing arbitrary oriented cracks is obtained. The problem is reduced to solve a system of singular integral equations for the unknown dislocation density functions. Using the numerical method of the singular integral equations^[2,7] the torsional rigidities and stress intensity factors are evaluated for several multicracked cylinders. Next, the creak-cutting method^[5] is firstly extended to lve the torsion problem for a rectangular prism. The numerical results show that the method presented here is successful. Projects Supported by the Science Fund of the Chinese Academy of Sciences.     

The calculation of bending and stability of a thin rectangular plate for variable rigidity

The subject discussed in this paper is the rectangular plate. Its wwo opposite edges are simply supported, while the other two are arbitrary, and the rigidity of the plate is variable along the direction parallel to the simply supported edges. In order to solve the problem, the author adopts the finite plate-strip element method^[1], which is different from the usual finite element method or the finite strip method. The steps of the above method is no longer to establish a rigidity matrix for elements or strips and gather them into a total matrix for solution. Now the relation of transfer between the strain and inner force of every plate-strip is shown. Finally a practical example is given and this method is found to be easier and more effective.     

Completely exponentially finite difference methods for problems of turning point

In this paper we construct a completely exponentially fitted finite difference scheme for the boundary value problem of differential equation with turning points, extending Miller’s method^[1] and simplifying the method of the proof We prove the first order uniform convergence of the scheme. The numerical results show that it is better than Hin’s^[2] scheme.     

Asymptotic solution to a nonlinear diffusion process by Chien-Latta's method

In this paper, by using Chien Wei-zang — Latta's composite expansion method^[5], we have obtained the first-order asymptotic solution to a system of equations for a nonlinear diffusion process, thus simplifying and improving the previous work^[4] considerably. Moreover, a kind of complete analytical solution has been given for a special case, and the periodic solution at the bifurcation point has been discussed, the related results being in agreement with the experiments.     

A new method for obtaining the exact solutions of the Navier-Stokes (NS) equations and its applications

In this paper we propose a new method for obtaining the exact solutions of the Mavier-Stokes (NS) equations for incompressible viscous fluid in the light of the theory of simplified Navier-Stokes (SNS) equations developed by the first author^[1,2], Using the present method we can find some new exact solutions as well as the well-known exact solutions of the NS equations. In illustration of its applications, we give a variety of exact solutions of incompressible viscous fluid flows for which NS equations of fluid motion are written in Cartesian coordinates, or in cylindrical polar coordinates, or in spherical coordinates. The project supported by National Natural Science Foundation of China.     

Calculation of stresses and deformations of bellows by initial parameter method of numerical integration

By reducing the boundary value problem in stress analysis of bellows into initial value problem, this paper presents a numerical solution of stress distribution in semi-circular arc type bellows based upon the toroidal shell equation of V. V. Novozelov^[8]. Throughout the computation, S. Gill’s method^[1O] of extrapolation is used. The stresses and deformations of bellows under axial load and internal pressure are c-alculated, the results of which agree completely with those derived from the general solution of Prof. Chien Wei-zang^[1-4]. The extrapolation formula presented in this paper greatly promotes the accuracy of discrete calculation.The computer program in BASIC language of Wang 2200 VS computer is included in the appendix.     

A field method for solving the equations of motion of nonholonomic systems

In this paper, the field method^[1] for solving the equations of motion of holonomic nonconservative systems is extended to nonholonomic systems with constant mass and with variable mass. Two examples are given to illustrate its application. The project supported by the National Natural Science Foundation of China.     

Free vibration of nonlinear deformation ring-and stringer-stiffened nonuniform cylindrical shell

Cylindrical shells stiffened with rings and stringers are used in many structural applications such as pipes conveying fluids or gases and acrospace. In this paper, the general solution is obtained for free vibration of nonlinear deformation ring-and stringer-stiffened cylindrical shell with arbitrary boundary condition by step reduction method^[1]. Finally, it is only necessary to solve a nonlinear algebraic equation. This equation is expressed as an analytic form. Its convergence is proved. Three numerical examples are given at the end of the paper which indicate that satisfactory results can be obtained by step reduction method. Project Supported by the Science and Technic Fund of the National Education Committee.     

Exact analytic method for solving variable coefficient differential equation

Many engineering problems can be reduced to the solution of a variable coefficient differential equation. In this paper, the exact analytic method is suggested to solve variable coefficient differential equations under arbitrary boundary condition. By this method, the general computation format is obtained. Its convergence is proved. We can get analytic expressions which converge to exact solution and its higher order derivatives unifornuy. Four numerical examples are given, which indicate that satisfactory results can be obtained by this method.     

THE NONLINEAR CHARACTERISTICS OF U-SHAPED BELLOWS——CALCULATIONS BY THE METHOD OF PERTURBATION

In this paper,the linear exact solution and nonlinear solutionfor U-shaped bellows have been obtained by using the general so-lution of circular ring shell and the method of perturbation.     

The method of matrices conjoint multiplication for the problem of circular arc corrugated diaphragm

The circular are corrugated diaphragins are taken in this paper and structures of several sections of the ring shells and a central cireular plale I matrices and link matrices are derived by using Prof. Chuen Hei-zang’s general the ring shell[1] and perturbation theory of the circular thin plates. Throngh the meined of matrices conjoint multiplication, the linear exact solution and nonlinear soluaen are obtained. The resutts agree with that of the experiments presented by W. A. Wildhack..     

Exact Relations for Effective Tensors of Polycrystals. I. Necessary Conditions

The set of all effective moduli of a polycrystal usually has a nonempty interior. When it does not, we say that there is an exact relation for effective moduli. This can indeed happen as evidenced by recent results [4, 10, 12] on polycrystals. In this paper we describe a general method for finding such relations for effective moduli of laminates. The method is applicable to any physical setting that can be put into the Hilbert space framework developed by Milton[13]. The idea is to use the W-function of Milton[13] that transforms a lamination formula into a convex combination. The method reduces the problem of finding exact relations to a problem from representation theory of SO(d)(d= 2 or 3) corresponding to a particular physical setting. When this last problem is solved, there is a finite amount of calculation required to be done in order to answer the question completely. At present, each candidate relation has to be examined separately in order to confirm the stability under homogenization. We apply our general theory to the settings of conductivity and two‐dimensional elasticity. (Accepted April 4, 1997)     

Bending problem of rectangular plates of unidirectional nonhomogeneity and variable thickness with two opposite edges simply supported under arbitrary distributed loads

Using the step reduction method^[1,2] suggested by the first author of this paper, we investigate the problem indicated in the title and obtain the stepped approximate solutions. As an example, the case of a square plate of linearly varying thickness with four edges simply supported under linearly distributed loads is calculated. The obtained results agree well with those given in [3] and thus the exactness of the new method is verified.Projects Suppotred by the Science and Technic Fund of the National Education Committee of the People's Republic of China.Although this paper has published in Journal of Lanzhou University, Special Number of Mechanics, No. 1, (1979) (in Chinese), it republishes here in order to correct some mistakes due to calculation.     

An exact analytic method applied to nonhomogeneous ring- and stringer-stiffened cylindrical shells

In this paper, the nonlinear axial symmetric deformation problem of nonhomogeneous ring- and stringer-stiffened shells is first solved by the exact analytic method. An analytic expression of displacements and stress resultants is obtained and its convergence is proved. Displacements and stress resultants converge to exact solution uniformly. Finally, it is only necessary to solve a system of linear algebraic equations with two unknowns. Four numerical examples are given at the end of the paper which indicate that satisfactory results can be obtained by the exact analytic method.     

Several exact solutions of the simplified Navier-Stokes equations (SNSE)

The Simplified Navier-Stokes equations (SNSE) and their exact solutions for the flow near a rotating disk and the flow in the vicinity of a stagnation point for both two- and three-dimensional flows are presented in this paper. The analysis shows that in the aforementioned cases the exact solutions of the inner-outer-layer-matched SNSE^[4] are completely consistent with those of the complete Navier-Stokes equations (CNSE) and that the exact velocity solutions of D-SNSE^[1,3] agree with those of CNSE, however, the exact pressure solutions of D-SNSE do not agree with those of CNSE. The maximum relative pressure errors between the exact solutions of D-SNSE and CNSE can be as high as a hundred per cent.     

The application of the finite element method to solving Biot's consolidation equation

Biot's theory of consolidation of saturated soil, regards the consolidation process as a coupling problem between stress of elastic body and flow of fluid existing in pores^[1]. It can more precisely reflect the mechanism of consolidation than Terzhigi's theory^[2]. In this article, we obtain the general Biot's finite element equations of consolidation with classical variational principles. The equations have clear physical meaning and have been applied to analysing the consolidation of Bajiazui earth dam. The computational results are in accord with engineering practice.