应用数学和力学

1982 Vol. 3, No. 4

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Basic Formulation of Static and Dynamic Behaviours of Soil and Other Porous Media

0. C. Zienkiewicz

1982, 3(4): 417-428.

Abstract(1570) PDF(475)

Abstract:
This paper treats the soil and rock or concrete as a two-phase medium composed of a solid skeleton and an interstitial fluid. Under the unsaturated condition of interstitial fluid, the third phase is taken into consideration. In this paper, we consider the constitutive relation, dynamic and kinematic relations, and also various approximations with their limits of validity, including those of most practical engineering situations such as the consolidation problem and the undrained behaviour. The finite element discretization and the time dependent solution of various classes of soil problem are also discussed.

Diagonalized Consistant Mass Matrix and the Dynamical Finite Element Analysis of Elastic-Plastic Impact in Axisymmetrical Problems

Chien Wei-zhang

1982, 3(4): 429-448.

Abstract(1814) PDF(412)

Abstract:
In this paper, the diagonalized consistent mass matrix is found for the triangular ring element in axisymmetrical problems. The results of this work eliminate the feeling of uncertainty and arbitrariness of lumped mass method on the one hand and the difficulty of computation due to non-diagonalized character of consistent mass method on the other. This paper gives also the foundations of the finite element analysis of elastic-plastic axisymmetrical impact problems.

Lagrangian Description of Transport Equations for Shock Waves in Three-Dimensional Elastic Solids

Li Yong-chi, T. C. T. Ting

1982, 3(4): 449-462.

Abstract(1589) PDF(440)

Abstract:
A set of transport equations for the growth or decay of the amplitudes of shock waves along an arbitrary propagation direction in three-dimensional nonlinear elastic solids is derived using the Lagrangian coordinates. The transport equations obtained show that the time derivative of the amplitude of a shock wave along any propagation ray depends on(i) an unknown quantity immediately behind the shock wave,(ii) the two principal curvatures of the shock surface,(iii) the gradient taken on the shock surface of the normal shock wave speed and(iv) the inhomogeneous term,which is related to the motion ahead of the shock surface, vanishes when the motion ahead of the shock surface is uniform. Several choices of the propagation vector are given for which the transport equations can be simplified. Some universal relations, which relate the time derivatives of various jump quantities to each other but which do not depend on the constitutive equations of the material, are also presented.

On the Restricted Torsion of Narrow Rectangular Cross Section by Kirchhoff’s Thin Plate Theory

Chang Fo-van

1982, 3(4): 463-476.

Abstract(2564) PDF(651)

Abstract:
Kirchhoff's thin plate theory is used to solve the restricted torsion of narrow rectangular cross section as this problem is equivalent to the bending of a rectangular cantilever plate by a twisting moment at the free end. The results obtained not only prove the angle of twist obtained by Prof. Timoshenko using the energy method put give us stresses.

Discussion on the SIF for Points on Border of Elliptical Flat Crack inside Infinite Solid under Uniform Tension

Cai Zeng-shen

1982, 3(4): 477-482.

Abstract(1550) PDF(586)

Abstract:
Using the results of crack surface displacement field in Green-Sneddon's solution[1] and coordinate transformation, this paper has derived an expression K₁(x₁,z₁,a) for SIF at any point and at any orientation on the border of elliptical flat crack inside infinite solid under uniform tension. As a complement of Irwin's work^[3], it is shown that for any pointed point on the elliptical border the SIF defined on normal plane takes the maximum value. And it should be pointed out that in some works some idea concerning Irvin's contents is open to question. An expression K₁ in terms of polar angle which is more intuitional than centrifugal angle is proposed for SIF at any point on the elliptical border.

Bending of Rectangular Flat Slabs Supported by Four Columns

Li Ding-kun

1982, 3(4): 483-496.

Abstract(1604) PDF(567)

Abstract:
In this paper an analytical solution is proposed for the bending of uniformly loaded rectangular plates supported only by four intermediate columns, the edges and corners of which are all free. For several particular cases, the numerical results, which contain the column reaction and the values for the deflection and the bending moments at several points of the plate, are given.Calculations indicate that the method proposed in this paper is valid.

The Boundedness and Asymptotic Behavior of Solutions of Differential System of Second-Order with Variable Coefficients

Li Li

1982, 3(4): 497-504.

Abstract(1813) PDF(464)

Abstract:
In this paper, the differential system of second-order with variable coefficients is studied, and some criteria of the boundedness and asymptotic behavior for solutions are given.Consider a system of differential equations (0.1) Now we study the boundedness and asymptotic behavior of its solutions. In the case of P_if(t) being periodic functions, it was investigated by Burdina; in the case of P_if(t) being arbitrary functions, it has not been investigated yet. Besides, the method used by Burdina is only appropriate for the former but not for the latter case. In this paper we shall give a method which is appropriate for both cases.

The Nonlinear Strain Components of Thin Shells

Tao Qi-kun

1982, 3(4): 505-512.

Abstract(1766) PDF(464)

Abstract:
The nonlinear strain components of thin shells are the foundations of nonlinear shell mechanics. They are needed in the investigation of various thin shell stability and large displacement problems. Due to the geometrical variety of thin shells we have not seen in existing literatures a complete set of general formulae expressing nonlinearity of shell strain components. In this paper we have derived six of them expressed in Lame coefficients and orthogonal curvilinear coordinates, including both linear and nonlinear parts, three of them are tensile strain components,the other three are shear strain components.

Chien’s Solution and Its Asymptotic Behavior in Large Deflection of Circular Plates

Chen Shan-Tin

1982, 3(4): 513-518.

Abstract(1754) PDF(605)

Abstract:
A general treatment and residual values of Chien's solution for large deflection of circular plates are given. By means of the above results, the asymptotic behavior of Chien's solution is studied. Two examples of uniform load and concentrated load are discussed respectively.

The Linearization of Certain Class of Nonlinear Simultaneous Equation Set Containing Amplitude and Phase Frequency Characteristics and Application

Hu Xi-heng

1982, 3(4): 519-527.

Abstract(1974) PDF(728)

Abstract:
A class of complex function of rational fraction type G(jω)=1+a₁jω+a₂(jω)²+…+a_m(jω)ⁿ/b₀+b₁jω+b₂jω+…+b_n(jω)ⁿ is frequently used to describe the dyna-mical properties of systems. It is however quite difficult to establish a mathematical model of this type on the basis of amplitude and phase frequency data collected from experiments conducted on the related physical system. Since the erection of mathematical model G(;o) would involve the solution of a set of nonlinear simultaneous equations and bis(i=0, 1,…,m,…,n)in. Up to now, these nonlinear equa-tiorjs have been considered to be very difficult to solve directly. In spite of the fact there are special computer programmes in certain software packages available to tackle this problem, it is by no means an easy task due to the complex procedures involved in picking up a set of initial values that should be close enough to the exact solutions. This paper proposes a simplified method of linearizing these nonlinear equations set so that direct solution is possible. The method can also be applied to systems with factors of(jω) and e^-jωra in G(jω). An illustration by a workable example is furnished at the end of this paper to show its versatility.

The Exact Solutions of von Mises Yielding Criterion for Ideally Plastic Body under Uniform Pressure in Case of Plane Strain

Fan Ja-shen

1982, 3(4): 529-535.

Abstract(1445) PDF(440)

Abstract:
This problem is solved by dividing the quadratic yielding criterion into two linear partial differential equations. With the help of Cauchy's integral, these two linear equations can be easily solved. An example is given to show the calculation of the stress components in the plastic domain and the determination of equation of the boundary line between the plastic and elastic domains.

Free Bending Vibration of Circular Column Partially Submerged in Water

Zhang Xi-de

1982, 3(4): 537-546.

Abstract(1844) PDF(606)

Abstract:
In this paper, the author studied the bending vibration of circular column partially submerged in water.An equation of frequency and an exact solution of corresponding function of viirational modes are given. It points out that the effect of water is equivalent to an attached distributive mass. Therefore the frequency with water is lower than that without water.

A Study on Deformation Characteristic of Ultra High Strength Steel and Its Fracture

Han Fu-yi

1982, 3(4): 547-553.

Abstract(1686) PDF(486)

Abstract:
A new shape on the load and elongation curve of ultra high strength structural steel in tension is measured by means of the advanced physical methods. A method of calculating true stress-true strain is found in accordance with the whole load-elongation curve. The calculation results show that during the period of deformation, whether prior to or after the maximum load, all are staged power hardening. The method of calculating hardening in dex is finally studied for discussion.

A Study on Deformation Characteristic of Ultra High Strength Steel and Its Fracture

Luo Shi-yu

1982, 3(4): 555-561.

Abstract(1796) PDF(700)

Abstract:
The v₂=1/2 resonance was analyzed approximately, by using stability of Mathieu equation's solutions and the method of transfer matrix, and gradient amplitude of a critical perturbed field was derived.

Tai Tien-min

1982, 3(4): 562-562.

Abstract(1542) PDF(459)

Abstract: