Applied Mathematics and Mechanics (English Edition)

THEOREMS ON THE LIMIT ANALYSIS OF FINITE DEFORMATION

薛大为

1988, 9(3): 207-211.

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A generalized variational principle (theorem I) which is equivalent mathematically to the whole set of equations and conditions and must be satisfied by the limit analysis of finite deformation is proposed in this paper. It is also proved that the limit load deduced from theorem I will lie between the lower and upper bounds given by the bound theorems of finite deformation[1].

BASIC THEORY AND APPLICATIONS OF PROBABILISTIC METRIC SPACES (Ⅱ)

张石生

1988, 9(3): 213-225.

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This paper is a continuation of the author’s previous paper [1], in which the characterizations of various probabilistically bounded sets are presented, and the linear operator theory and fixed point theory on probabilistic metric spaces are given, too.

ON THE NONLINEAR STABILITY OF A TRUNCATED SHALLOW SPHERICAL SHELL UNDER A NIFORMLY DISTRIBUTED LOAD

刘人怀;李东

1988, 9(3): 227-240.

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A problem of practical interest for nonlinear axisymmetrical stability of a clamped truncated shallow spherical shell with a nondeformable rigid body under a uniformly distributed load is studied in this paper. By using modified iteration method, some important analytic results are obtained and the corresponding numerical results are given in figures.

THE USAGE OF HERMITE POLYNOMIAL IN THE CALCULATION OF STRUCTURAL DYNAMIC RESPONSES

张益松;徐尹格;高德平

1988, 9(3): 241-251.

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This paper employs the best approximation of part series sum of normal polynomials. and proposes a new method with the Fourier-Hermite polynomial expansion expressing structural dynamic responses. Analytic expressions of displacement and velocity responses of vibrational systems are e stablished in this paper, and stability condition of the step-by-step algorithm is discussed. Finally, a computational example is demonstrated, and the precision of its results is compared with conventional methods.

NONLINEAR ROSSBY WAVES FORCED BY TOPOGRAPHY

刘式适;谭本馗

1988, 9(3): 253-266.

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Using a barotropic semi-geostrophic model with topographic forcing the stability and solutions of the nonlinear Rossby waves are discussed. It is found that the effects of the W-E oriented topography and the N-S oriented topography on the stability and phase speed of the waves are quite different. It is also found that the nonlinear Rossby waves forced by the topography can be described by the well-known KdV equation.

A STUDY ON HEAT TRANSFER OF THE OPTIMIZATION IN CIRCULAR FINS OF PARABOLIC PROFILE WITH VARIABLE THERMAL PARAMETERS

杨翔翔

1988, 9(3): 267-278.

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Circular fins are used extensively in heat exchange devices to increase the heat transfer. For economic purposes, the traditional approach to the optimization of fins consists of minimizing the comsumption (investment) of fin material for the execution of a specified heat transfer task. The minimum weight cooling fin has optional profile to be a concave parabola. Therefore, the optimum geometric dimensions of circular fins of parabolic profile with variable thermal parameters are studied. The effect of the two pertinent physical parameters-thermal conductivity variation parameter a and the index of the heat transfer coefficient variation m upon the optimum geometric dimensions is aliso studied. The results presented can be used as the design guideline for engineering practice.

AN APPROXIMATE SOLUTION CONSIDERING FLOW INERTIA BETWEEN CONICAL SURFACES

刘震北;王成敏

1988, 9(3): 279-293.

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In this paper, analytical calculation expressions of the pressure distribution, velocity distribution and the rate of the flow between conical surfaces are found by using the method of iterative approximate solution when the inertia terms of the Navier-Stokes equations in conical coordinates are taken into account. Furthermore, we compare the centrifugal flow with the centripetal flow of axisymmetrical passing flow.

NONLINEAR BENDINGS OF SYMMETRICALLY LAYERED ANISOTROPIC RECTANGULAR PLATES

周次青

1988, 9(3): 295-309.

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This paper has studied the nonlinear bendings of symmetrically layered anisotropic rectangular plates under various supports. The uniformly valid N-order asymptotic solutions of the deflection and stress function are derived by the singular perturbation method offered in [1]. The analysis and calculations are given for simply and clamped supported, rectangular plates subjected to combined edge tensions and lateral loading in conjunction with the modified Galerkin procedure (a method of weighted residuals).

SOLITARY WAVE AND SIMILARITY SOLUTIONS OF THE COMBINED KdV EQUATION

潘秀德

1988, 9(3): 311-316.

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In this paper, we discuss a property of solitary wave solutions of the combined KdV equation. Meantime, we point out that the combined KdV equation can be reduced to the Painleve equation. Furthermore, utilizing special transformations of similarity variables, we derive a kind of new partial differential equations.

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