应用数学和力学

1984 Vol. 5, No. 6

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Analysis of Thin Parallelogram Plates’ Bending by Spline-Finite-Strip Method

M. J. Chen L. G. Tham, Y. K. Cheung

1984, 5(6): 755-764.

Abstract(1860) PDF(656)

Abstract:
Spline finite strip has bees successfully applied in solving right plates and shells by Chenag et al in 1982. In this paper, the method is eateaded to the analysis of paralle-logram plate, This ezteasioa still retains the beaded aatare of the spline finite strip and only small amount of eztra computing effort is required. Furthermore, the discretisation error of the above method is established theoretically as a general case for the spline finite strip method.

Classification of Variational Principles in Elasticity

Chien Wei-zang

1984, 5(6): 765-770.

Abstract(1671) PDF(522)

Abstract:
In this paper, variational principles in elasticity are classified accordiag to the differences is the constraints used in these principles, It is shown in a previous paper^[4] that the stress-strain relations are the constraint conditions in all these variational principles, and can not be removed by the method of liaear Lagrange multiplier.The other possible constraats are four of them:(1)equations of equilibrium,(2)Strain-displacement relations,(3)boundary conditions of given external forces and boundary conditions of given boundary displacements. In variational principles of elasticity, some of them have only one kind of such constraints, some have two kinds or three kinds of constraints and at the most four kinds of constraints. Thus, we have altogether 15 kinds of possible variational principles, However, for every possible variatioaal prineiple, either the strain energy density,or the complementary energy density may be used, Hence, there are altogether 3p classes of functionals of variational principles in elasticity. In this paper, all these functionals are tabulated in detail.

On Characterizations of Structural Stability

Liao Shan-tao

1984, 5(6): 771-775.

Abstract(1846) PDF(579)

Abstract:
This aote takes a sketch of a proof of a characterization theorem for diffeomor-Phisms on a compact 3-dimensional smooth maaifold to be structurally stable.

New Theory for Equations of Non-Fuchsian Type——Representation Theorem of Tree Series Solution(Ⅱ)

Dong Ming-de

1984, 5(6): 777-792.

Abstract(1715) PDF(553)

Abstract:
Our main result consists in proving the representation theorem, Irregular integral is a new type of analytic functions.represented by a compound Taylor-Fourier tree series, in whick each coefficient of the Fourier series is a Taylor series, while the Taylor coefficients are tree series in terms of equations parameters, higher order correctibn terms to each coefficient having tree structure with inesaustalile proliferation.The solution obtained is proved to be convergent absolutely and uniformly in the region defined by coefficient functions of the original equation, provided the structure parameter is less than unity. Direct substitution shows that our tree series solution satisfies the equation ezulicitlv eeneration by eeneration.As compared with classical theory our method not only furnishes explicit expression of irregular integral, leading to the solution of Poincaré problem, but also provides possibility of extending the scope of investigation for analytic theory to equations with various kinds of singularities in a unifying way.Enact explicit analytic expression for irregular integrals can be obtained by means of correspondence principle.It is not difficult to prove the convergence of the tree series solution obtained. Direct subsitution shows it satisfies the equation.The tree series is automorphic, which agrees completely with Poincaré's conjecture.

The Linear Approximation of the Line Continuous Distribution Method of Singularities in Creeping Motion

Wu Wang-yi, He Qing

1984, 5(6): 793-800.

Abstract(1873) PDF(497)

Abstract:
The linear approximation of the line continuous distribution method of singularities is proposed to treat the creeping motion of the arbitrary prolate axisymmetrical body. The analytic expressions in closed form for the flow ffield are obtained. The numerical results for the prolate spheroid and Cassini oval demonstrate that the convergence and the accuracy of the proposed method are better than the constant density approximation. Fnthermore, it can be applied to greater slender ratio, In this paper the ezample is yielded to show that the linear approximation of the singularities for the density on the partitioned segments can be utilized to consider the creeping motion of the arbitrated prolate asisymmetrical body.

The Backlund Transformation and Nonlinear Superposition Formula of Solutions for the Liouville’s Equation in Higher Dimensions

Huang Xun-cheng

1984, 5(6): 801-807.

Abstract(1985) PDF(465)

Abstract:
In this paper, we show that Backlund transformation derived by Leibbraadt et al for the Liouvilles equation in three spatial dimeasions,∇²a=expa∇²=∂_x²+∂_y²+∂_z² can be decomposed into several Backlund transformations for the same equation in two spatial dimensions, moreover, the superposition formula which is derived from this transformation is actually invalid, thus the discussions based on that formula is incorrect as well. We also considered some results about the Liouville's equation in N spatial dimensions.

Interpolation with Boundary Condition Using Bivariate Quadric Splines Connected with Triangular Partition

Lee Zhi-xian

1984, 5(6): 809-816.

Abstract(1983) PDF(490)

Abstract:
In this paper, we study the relations between the esistaace uniqueness of iaterpolation with boundary condition using bivariate quadric splines connected with triangular partition and positions of interpolating points. After proving the ezistence uniqueness of interpolation. Problems at center, vertez and partial center, we give the constructioa methods for these three interpolating fnactioas.

The Solution of Deflection of Elastic Thin Plate by the Joint Action of Dynamical Lateral Pressure Force in Central Surface and External Field on the Elastic Base

Shen Hui-chuan

1984, 5(6): 817-827.

Abstract(1805) PDF(667)

Abstract:
In this paper the Euler equation of the deflection of elastic thin plate is reduced to the equation with Schrödinger form by the principle of quantum electro-dynamics. Then we can obtain the general solution of deflection of elastic thin bending plate by the jointaction of dynamical lateral pressure, force mcentral surface and eternal, field on the elastic base.

One-Dimensional Piston Process in Strong Gravitational Field

Tang Ze-mei

1984, 5(6): 829-836.

Abstract(1831) PDF(471)

Abstract:
In this paper, the dynamic process driven by one-dimensional piston in stroag gravitational field was studied on the Cartesian, cylinderical and spherical coordinates. The gasdynamic equations were numerically solved by the characteristic method. The solution which satisfies the velocity condition at piston aad the boundary conditions nect the flow region and,the quiet region is btained. The present paper analyses especially the influence of coordinate systems on the field of compressible flow, uniform flow ana raretacuon mow region, the shock velocity and the temperature distnuution at the piston.

Decomposition of Symmetric Tensor and Its Application

Wang Min-zhong

1984, 5(6): 837-840.

Abstract(2112) PDF(638)

Abstract:
In this paper any symmetric tensor is decomposed into the sum of two tensors.One of them is a "type of stress",and another is a "type of strain" tensor. The inner product space of symmetric tensor is decomposed into the sum of two orthogonal subspaces. The geometric meaning of several principles in the theory of elasticity is given.

Variational Principles of Elastic-Viscous Dynamics in Laplace Transformation Form, F. E. M. Formulation and Numerical Method

Jin Wen-lu

1984, 5(6): 841-848.

Abstract(1497) PDF(619)

Abstract:
The authbr gives variatioaal principles of elastic-viscous damics is spectral resolving formula, it will be eatended to Laplace traasformetioa forte is this paper, mined variational principle of shell dynamics and variational principle of dynamics of dynamics of elastic-viscous-porous media are concerned,for the.later F., E. M. formulation is worked out.Variatioaal principles is Laplace transformation force have concise forms, for the sake of utilizing F, E. M. conveniently, it is necessary.to find out the values of preliminary time function at some instants, when values,of Laplace transformation at some points are known, but there are no efficient methods till now. In this paper, a aumerival method for finding discrete values of preliauaary function is presented, from numerical wzgmnles, we see such a method is efficient.By corubiaiag. both methods,stated above, variatioaal principles is Laplace transformatioa form and:numerical method,quite wide district of solid, dynamic problems can be solved by the aid of digital computers.

The Circumferential Stress-Strain Product Criterion of Mixed Mode Brittle Fracture

Lin Bai-song

1984, 5(6): 849-853.

Abstract(1684) PDF(460)

Abstract:
This paper presents a new criterion of mized mode brittle fracture, i, e, the circunmferential stress-strain product criterion. This criterion is shows to be is good agreemeaf with known espenmeatal data.

Analysis of Postbuckling Strength of Stringer Stiffened Cylindrical Shells under Axial Compression

Shao Wen-jiao

1984, 5(6): 855-872.

Abstract(1752) PDF(539)

Abstract:
An analysis of the postbuckliag strength of stringer stiffened cylindrical shells,subject to axial compression is described, The method used is this paper is based on plastic analysis extending Murray's method which was used to analyse postbuckliag behaviour of stiffened plates loaded axially and in beading. The mechanism tripping of stringer and crumpling of shell plates is described based on how the test specimens are deformed after buckling.Finally the theoretical analyses are compared with the experimental results of steel specimens. The theoretical results coincide quite well with the ezperimeatal data. It should therefore be possible to use the method described here to analyse postbuckliag strength of stringer stiffened cylindrical shells and to estimate energy absorbtion capsbilities is relation to collison studies.

The Temperature Fields Around the Tip of a Fast Running Crack

Wang Mao-hua

1984, 5(6): 873-878.

Abstract(1671) PDF(433)

Abstract:
When a crack is running, the temperature rise is a quite important actual problem,which not only depends on soaze material constants, but also on the propagation velocity and the distribution of the heat resource density. In this paper, ou the shape of plastic zone around the crack tip and the density of heat resouroe have been discussed and the model of the temperature fields has been proposed. The numerical results with PMMA have been given and compared with other theories atcd experimental results.

Spline Sectorial Elements

Yuan Si

1984, 5(6): 879-886.

Abstract(1831) PDF(550)

Abstract:
In this paper, the quadratic and cubic spline local interpolations on a sectorial elemeat in polar coordinates is discussed and a class of spline sectorial elements for analyses of plane and thin plate problems are presented. A reasonable treatment of the assumed displacement fields for elements with nodes at the origin(r=0) is made so that the elemeats can not only characterize the geometrical properties at the origin but also remove the siagularitp of strains and stresses there.Some numerical examples are given to show the efficiency of the proposed elemeats.

The Description of the Characteristics of the Structure and the Quantity in Fixed Pansystems Theorems

Li Gui-hua

1984, 5(6): 887-893.

Abstract(1604) PDF(470)

Abstract:
Paaspmmetrp is the abstract of spmmetrp, stability and other concepts in phpsics and so on. Fined panspstems theorems portray a typical panspmmetry of systemic structure, The present paper complements and extends the work in[1]~[3] concerned in fixed pansystems theorems. It gives is finite case the structural character of fined subsets, the criterion of existence of the least fixed subset, and the numbering formula of fined subsets and minimal fined subsets.

Note on the Critical Variational State in Elasticity Theory

Liu Cheng-qun

1984, 5(6): 895-901.

Abstract(1828) PDF(442)

Abstract:
Recently Prof, Chien Wei-zang^[1] pointed out that certain cases, by means of ordinary Lagrange multiplier method, some of undetermined Lagrange multipliers may turn out to be zero during variation.This is a critical state of variation.In this critical state, the corresponding variational constraint can not be eliminated by means of simple Lagrange multiplier method. This is indeed the case when one tries to eliminate the constraint condition of stress-strain relation in variational principle of minimum complementary energy by the method of Lagrange multiplier. By means of Lagrange multiplier method, one can only derive, from minimum complementary energy principle, the Hellinger-Reissner principle^[2,3], in which only two types of independent variables, stresses and displacements, exist in the new functional.Hence Prof, Chien Wei-zang introduced the high-order Laaranae multiplier method by addine the quadratic terms
A_ifk1(e_ij-b_iimnσmn)(e_ki-b_k1pqσ_pq)
to the original functionals.The purpose of this paper is to show that by adding the quadratic terms
A_ifk1(e_ij-b_iimnσ_mn)(e_ki-1/2u_k2-1/2u_1:k)
to original functionals one can also eliminate the constraint condition of strain-stress by the high-order Lagrange multiplier method. With this method, we find more general form of generalized variational principle ever known to us from Helliager-Reissner principle, In particular, this more general form of functional can be, reduced into all known functionals of eaisting generalized variational principles in elasticity. Similarly, we can also find snore general form of functional by Hu-Washizu principle^[4,5].