应用数学和力学

1988 Vol. 9, No. 10

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Deformations and Stability of Spherical Caps under Centrally Distributed Pressures

Yeh Kai-yuan, Song Wei-ping

1988, 9(10): 857-864.

Abstract(1753) PDF(502)

Abstract:
In this paper the deformations and stability in large axisymmetric deflection of spherical caps under centrally distributed pressures are investigated. The Newton-spline method for solving the nonlinear equations governing large axisymmetric deflection of spherical caps is presented. The buckling behavior is studied for a cap with fixed geometry when the size of the loaded radius is allowed to vary, and for a fixed loaded radius when the shell geometry is allowed to vary. The influence of the buckling modes on the critical loads is analysed. Numerical results are given for v=0.3.

The Functional and Its Variational Principle in Coupled Thermo Elastoplasticity

Cheng He-ming, Wang Hong-gang

1988, 9(10): 865-870.

Abstract(1872) PDF(512)

Abstract:
In order to solve the coupled thermoelastoplastic problems by the finite element method, it is necessary to establish suitable functional. In this paper, based on the thermoelastoplastic constitutive relation proposed by K.N. Rysinko and E.I. Blinov^[1], the functional of coupled thermoelastoplasticity is derived by means of the nonlinear functional analysis theory.

A Generalized Conforming Isoparametric Element

Long Yu-qiu, Huang Min-feng

1988, 9(10): 871-877.

Abstract(1645) PDF(698)

Abstract:
Based on the generalized compatibility condition under constant and linear stress field, a quadrilateral generalized conforming isoparametric element, GC-Q6, for plane stress analysis, is developed. The element GC-Q6 can be regarded as an improved form of Wilson's non-conforming isoparametric element Q6. GC-Q6 can pass the patch test for arbitrary irregular mesh while Q6 can not. GC-Q6 degenerates to Q6 when it is a parallelogram. Numerical examples show that the GC-Q6 element gives more accurate stress solution than the existing non-conforming elements and is less sensitive to geometric distortion.

Applicability of Hamilton-Jacobi Method to Nonlinear Nonholonomic Systems

Q. K. Ckori, Naseer Ahmed

1988, 9(10): 879-892.

Abstract(1845) PDF(481)

Abstract:
This paper uses Poincare formalism to obtain a generalization of the Hamilton-Jacobi method of integrating dynamical systems moving with nonlinear nonholonomic constraints. Necessary and sufficient conditions are investigated for the applicability of this method to such systems. The method is illustrated by considering some concrete examples of nonholonomic systems.

The Fixed Point and Eigenelement of Sum and Product about Concave and Convex Operators

Yan Xin-li

1988, 9(10): 893-897.

Abstract(2464) PDF(476)

Abstract:
In this paper, we obtain the sufficient conditions under which there exists the fixed point of sum and product about α concave and-α convex operators in the positive cone of linear semi-order space, and the iterative procedure and error estimate can be given. The relation between eigenvalue and eigenelement will also be studied in this paper.

Polar Coordinate Transformation Approach for Treatment of Singular Integrals in Boundary Element Methods

Liu Yong-hui, Lu Xin-sen

1988, 9(10): 899-907.

Abstract(1842) PDF(674)

Abstract:
In boundary element methods the treatment of singular integrals, as one of the main numerical problems has been noticed seriously. In this paper, by using polar coordinate transformation for elements a new approach is proposed to remove the singularities in the integrals explicitly. The formulations for treatment of the singularities in quadrilateral boundary elements with four nodes, eight nodes and nine nodes are derived and it can be extended easily to other higher order boundary elements. Numerical examples are given. The results show the present approach is effective and efficient.

Instability of Solution for the Third Order Linear Differential Equation with Varied Coefficient

Liao Zong-huang, Lu De-yuan

1988, 9(10): 909-923.

Abstract(1717) PDF(440)

Abstract:
In reference [1] asymptotic stability of dynamic system with slowly changing coefficients for all characteristic roots which have negative real part has been proved by means of Liapunov's second method. In this paper, we give some sufficient conditions of the instability for the third order linear differential equation with varied coefficient, at least one of the characteristic roots of which has positive real part, by means of Liapunov's second method.

Study on the Complicated Dynamical Behaviors of Nonlinear Ecosystem (Ⅰ)

Zan Tin-quan

1988, 9(10): 925-931.

Abstract(1744) PDF(486)

Abstract:
This series of papers is prepared to develop systematically the complicated dynamical behaviors of nonlinear ecosystem and its internal mechanism. In this paper, we state briefly the increasing importance of ecology, describe and comment on the situations and reasons why ecology theory is behind practice. Then, we point out a procedure which modern ecology research should obey, and discuss the four basic characteristics of ecosystem in detail: level, opening, nonlinear and far from equilibrium. At last, we discuss systematically equilibrium and nonequilibrium, stable and unstable, environmental stochasticity and dynamical stochasticity, and conclude that there exists a bridge between deterministic behaviors and stochastic behaviors, which will result in a new model for ecological prediction.

A Bifurcation Theorem of Nongradient, Weakly Continuous Maps and Applications

Ma Tian, Yu Qing-yu

1988, 9(10): 933-938.

Abstract(1634) PDF(334)

Abstract:
In this paper, M. A. Krasnosels'kii's local bifurcation theorem for compactly continuous mappings is extended to weakly continuous mappings. So we can surmount the difficulty of lacking compactness in application. Lastly, we apply it to Dilichlet problem of quasilinear elliptic equation.

Global Structure of a Kind of Predator-Prey System

Ding Sun-hong

1988, 9(10): 939-943.

Abstract(1707) PDF(497)

Abstract:
In this paper we prove a theorem, theorem 2, on nonexistence of closed trajectory for a general predator-prey system.Then, using this theorem and another theorem on existence and uniqueness of limit cycle for predator-prey system^[1], we complete the investigation of a concrete model of predator-prey system^[2]

under the conditions of all kinds of parameters.

The Second Harmonic Resonance for the Shallow Water Surface-Wave in a Rectangular Trough

Huang Guo-xiang, Yan Jia-ren, Zou Feng-wu

1988, 9(10): 945-950.

Abstract(1791) PDF(410)

Abstract:
By using the perturbation method of multiple scales, this paper deals with the phenomenon of the second harmonic resonance for shallow water surface-wave in a rectangular trough. The results show that the envelope of the wave only depends on slow-variables of time. Eqs. of wave envelope are strictly solved and the results are discussed.