应用数学和力学

Rethinking to Finite Difference Time-Step Integrations

Zhong Wanxie, Zhu Jianping

1995, 16(8): 663-668.

Abstract(2662) PDF(813)

Abstract:
The numerical time step integrations of PDEs are mainly carried out by the finite difference method to date. However,when the time step becomes longer, it causes the problem of numerical instability,. The explicit integration schemes derived by the singlepoint precise integration method given in this paper are proved unconditionally stable.Comparisons between the schemes derived by the finite difference method and the schemes by the method employed in the present paper are made for diffusion and convective-diffusion equations. Nunierical examples show the superiority of the singlepoint integration method.

Plastic PostBucking of a Simply Supported Column with a Solid Rectangular Cross Section

Cheng Yaoshun, Lu Wenda, Fang Hong

1995, 16(8): 669-676.

Abstract(2212) PDF(509)

Abstract:
The plastic post-buckling of a simply supported column with a solid rectangular cross section is analysed by a new approach. High order terms in the asymptotic post-buckling expansions are carried out. In some aspects, the method proposed in this paper is similar io Hutchinson's. However, the computation is simple since the introduction is avoided of stretched coordinates. The method can be used to analyse initial post-bifurcation of plates and shells in the plastic range.

1995, 16(8): 677-691.

Abstract(2007) PDF(651)

Abstract:

Remarks on the Structure of Evolution Equations

J. Badur, Sun Bohua

1995, 16(8): 699-707.

Abstract(1835) PDF(476)

Abstract:
In the paper the evolution equations are discussed so as to enable a phenomenological description of microstruchtral behaviour e.g. partially reversible flow of Maxwellian gas, recovery structural relaxation and other experimental results coming from light scattering and molecular dynamics.The result deals with the revaluation of Zaremba's ansatz.It leads to resolution of problems with substantial and available nonlinearities in the transport equation.

Generalized Probabilistic Perturbation Method for Static Analysis

Zhang Yimin, Chen Suhuan, Zhou Zhenping, Liu Tieqiang

1995, 16(8): 709-714.

Abstract(2396) PDF(852)

Abstract:
This paper studies the static response and reliability of uncertain structures with vector-valued and matrix-valued functions.The finite element analysis method of uncertain structures is based on matrix calculus,Kronecker algebra and pertrubation theory,Random variables and system derivatives are conveniently arranged into 2D matrices and generalized mathematical formulae for perturbatc perturbatcion are obtained.

The Existence and Uniqueness of the Decaying Positive Entire Solutions for a Class of Semilinear Elliptic Equations

Tian Genbao

1995, 16(8): 715-726.

Abstract(2504) PDF(610)

Abstract:
This paper first proves the following equations △u-m²u+f(x,u)=0,x∈Rⁿ,n≥3,m>0 existence of decaying positive entire solution, then emphatically, proves this solution's uniqueness.

Stress-Strain Field near Crack Tip and Calculation of Critical Stress of Crack Propagation in a Pure Bending Beam of Rectangular Section with One-Sided Mode I Crack

Liu Hanchi

1995, 16(8): 727-736.

Abstract(2301) PDF(583)

Abstract:
This paper studies the stress-sirain field near crack tip in a pure bending beam of rectangular section with one-sided mode I crack by the analytic method of Ref [1],then it gives the stress and strain components at the crack tip when the crack propagates and further it obtains the formulas of calculating the elastic deformed area width, the deformed intensity, area width and the equation groups of calculating the critical stress of crack propagation, last the equation group of calculating critical stress of crack propagation is verified by calculating instance. The maximum error is 0.18%.

Shakedown Analysis of Elasto-Plastic Structures Subjected to External Loading and Temperature Variation

Du Sentian, Liu Hanbing, Chen Suhuan, Lian Jianshe

1995, 16(8): 737-744.

Abstract(2263) PDF(771)

Abstract:
A new kinematical shakedown theorem is presented under the consideration that external load and temperature change slowly. Anincremental collapse criterion, which is simple and applicable, is also derived based on the theorem. In the end of this paper,its application is illustrated by an example.

Endochronic Analysis for Compressive Buckling of Thin- Walled Cylinders in Yield Reglon

Peng Xianghe, Chen Yuanqiang, Zeng Xiangguo

1995, 16(8): 745-755.

Abstract(2214) PDF(576)

Abstract:
The longitudinal compressive buckling of long and thin-walled cylinders in yield region is analyzed with the incremental and finite forms of the endochronic constitutive equation, respectively. The relations between the critical stress σ_crversus the ratio of R (the radius) versus h (the thickness of the wall) are derived. The critical stress of the thin-walled cylinders made of abuminum alloys AMГ and Д1T are analyzed and compared with the experimental data and the analytical results based on traditional theory of plasticity. It is seen that. except that the σ_cr of the cylinders made of Д1T predicted by the finite form of the endochronic theory seems a little more conservative than that by traditional deformation theory of plasticity, in most cases, both forms of the endochornic constitutive equation provide more satisfactory results.

1995 Vol. 16, No. 8