应用数学和力学

1990 Vol. 11, No. 9

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Nonlinear Bending of Simply Supported Symmetric Laminated Cross-Ply Rectangular Plates

Liu Reu-huai, He Ling-hui

1990, 11(9): 753-759.

Abstract(2037) PDF(430)

Abstract:
Based on the von Kármán-type theory of plates, nonlinear bending problems of simply supported symmetric laminated cross-ply rectangular plates under the combined action of pressure and inplane load are investigated in this paper. The solution which satisfies the governing equations and boundary conditions is obtained by using the double Fourier series method.

A Potential-Hybrid/Mixed Finite Element Scheme for Analysis of Plates and Cylindrical Shells

Chen Da-peng, Pan Yi-su

1990, 11(9): 761-770.

Abstract(1766) PDF(459)

Abstract:
Based on the potential-hybrid/mixed finite element scheme, 4-node quadrilateral plate-bending elements MP4, MP4a and cylindrical shell element MCS4 are derived with, the inclusion of splitting rotations. All these elements demonstrate favorable convergence behavior over the existing counterparts, free from spurious kinematic modes and do not exhibit locking phenomenon in thin platef shell limit. Inter-connections between the existing modified variational functionals for the use of formulating C⁰-and C¹-continuous elements are also indicated. Important particularizations of the present scheme include Prathop's consistent field formulation, the RIT/SRIT-compatible displacement model and so on.

On the Existence of Solutions for Equations with Accretive Mappings in Probabilistic Metric Spaces

Zhang Shi-sheng, Chen Yu-qing

1990, 11(9): 771-778.

Abstract(1510) PDF(478)

Abstract:
The purpose of this paper is to expand the concept of accretive mapping to probabilistic normed space and to study the existence conditions of solutions for the accretive mapping equatians.

Isotropicalized Spline Integral Equation Method for the Analysis of Anisotropic Plates

Wang You-cheng, Wang Zuo-hui

1990, 11(9): 779-784.

Abstract(1536) PDF(553)

Abstract:
In the view of Reissner's and Kirchhoff's theories, respectively, we formulate the isotropicalized governing equations for the anisotropic plates, and give the proof of the equivalence relation between these two plate-models for the simply-supported rectangular orthotropic plates. The well-known fundamental solutions of the isotrqpic plates are utlized for the spline integral equation analysis of anisotropic plates.Even with sparse meshes the satisfactory results can be obtained. The analysis of plates on two-parameter elastic foundation is so simple as the common case that only a few terms should be added to the formulas of fictitious loads.

Space Time on the Poincare Diagrams

Lin Jin

1990, 11(9): 785-796.

Abstract(1798) PDF(497)

Abstract:
Relations between the experience of space technology and theory of space and time arefound in this paper.A nontraditional approach to the concepts of space and time isintroduced.The approach is based upon the the analysis of the detailed mechanism of radarmeasurement and nonlinear Doppler effects as measured by an astronaut.The Lorentz factor √1-v²/c² and four-dimensional interval t²-x²/c² may be interpreted fromthe point of view of a space technologist.A "geometrical mean" notion for computing timeinterval is introduced parallelly with the usual arithmetic mean formulas,giving resultscomparable with those of special relativity theory.Space time relationships aredemonstrated on the Poincare diagrams.

Plastic Limit Analysis of Incompatible Finite Element Method

Hua Bo-hao, Wu Chang-chun, Liu Xiao-ling, Mao Zhao-lin

1990, 11(9): 797-803.

Abstract(1522) PDF(440)

Abstract:
This paper describes an incompatible finite element model satisfying the consistency condition of energy to solve the numerical precision problem of finite element solution in perfectly plastic analysis. In this paper the reason and criterion of the application of the model to plastic limit analysis are discussed, and an algorithm of computing plastic limit load is given.

A Donnell Type Theory for Finite Deflection of Stiffened Thin Conical Shells Composed of Composite Materials

Wang Hu Wang, Tsun-kuei

1990, 11(9): 805-816.

Abstract(1778) PDF(875)

Abstract:
A Donnell type theory is developed for finite deflection of closely stiffened truncated laminated composite conical shells under arbitrary loads by using the variational calculus and smeared-stiffener theory. The most general bending-stretching coupling and the effect of eccentricity of stiffeners are considered. The equilibrium equations, boundary conditions and the equation of compatibility are derived. The new equations of the mixed-type of stiffened laminated composite conical shells are obtained in terms of the transverse deflection and stress function. The simplified equations are also given for some commonly encountered cases.

Thick Rectangular Plates with Free Edges on Elastic Foundations

Wang Ke-rang

1990, 11(9): 817-826.

Abstract(1818) PDF(496)

Abstract:
In this paper an accurate solution for the thick rectangular plate with free edges laid on elastic foundation is presented. The superposition method of trigonometric series is used. The method can solve this kind of plates directly and simply. Its results completely satisfy the boundary conditions of the four free edges and nicely agree with the solutions by Wang Ke-lin and Huang Yi.

On the Boundedness and the Stability Properties of Solution of Certain Fourth Order Differential Equations

Yu Yuan-hong, Cheng Wen-deng

1990, 11(9): 827-832.

Abstract(1854) PDF(498)

Abstract:
This paper investigates equation(1)in two cases:(i)P≡0,(ii)P≠0 satisfies|P(i,x,y,z,w)<(A+|y|+|z|+|w|)q(t). where q(t) is a nonnegative function of t. For case(i)the asymptotic stability in the large of the trivial solution x=0 is investigated and for case(ii) the boundedness result is obtained for solutions of equation(1). These results improve and include several well-known results.

Application of Sub region Function Method for Solving Beam-Board Structure

Sua Zong-guang

1990, 11(9): 833-836.

Abstract(1669) PDF(474)

Abstract:
In this paper, the solution to the structure consisting of a bead and a board is given as a result of the application of the subregion function method which was suggested in ref. [1]. The same problem is also computed with finite element method. The comparison between the two results shows that the application of the subregion function in the method of weighted residuals is practical and effective, especially for solving compound structures.

Momental Solution of Spherical Shells with Variably Nonlinear Section under Normal Pressure

Jia Nai-wen

1990, 11(9): 837-842.

Abstract(2013) PDF(417)

Abstract:
In this paper, spherical shell with variably nonlinear section that is widely used in eingineering and its equation of the section, δ=δ₀(1+βφ)² analysed to momental problem. The Euler solutions of internal forces are obtained under normal pressure.