应用数学和力学

1997 Vol. 18, No. 1

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The First Order Approximation of Non-Kirchhoff-Love Theory for Elastic Circular Plate with Fixed Boundary under Uniform Surface Loading(Ⅰ)

Chien Weizang

1997, 18(1): 1-17.

Abstract(2218) PDF(568)

Abstract:
Based on the approximation theory adopting non-Kirchhoff-Love assumption forthree dimensional elaslic plates with arbitrary shapes, the author derives afunctional of generalized variation for three dimensional elastic circular plates, therebyobtains a set of differtial equations and the relate boundary conditions to establish afirst order approximation theory for elastic circular plate with fixed boundary andunder uniform loading on one of its surface. The analytical solution of this problem will present in another paper.

1997, 18(1): 18-18.

Abstract(1707) PDF(538)

Abstract:

Nonlnear Theory of Multilayer Sandwich Shells and Its Application(Ⅰ)-General Theory

Wu Jiancheng, Pan Lizhou

1997, 18(1): 19-27.

Abstract(2166) PDF(499)

Abstract:
In this paper, a nonlinear theory is given for multilayer sandwich shell sundergoing small strains and moderate rotations. Then a simplified theory for the shells undergoing moderate or moderate/small rotations are obtained.

Snap-Buckling of Dished Shallow Shells under Uniform Loads

Liu Dong, Chen Shanlin

1997, 18(1): 29-35.

Abstract(2115) PDF(571)

Abstract:
A theoretical analysis is presented for the snap-buckling behaviour of dished shallow shells under undorm loads. By means of the modified iteration method, the second approximate formula of elastic behaviour and a set of numerical solutions aregiven. And effects of parameters β and k on the snap-buckling behaviour are discussed.

A New Approach to Predicting Interfacial Crack Growth

Hu Hurang, Wu Chengping

1997, 18(1): 37-44.

Abstract(2030) PDF(613)

Abstract:
A new approach, called "β=0 approach" is presented for use in the prediction of interfacial crack growth. This approach is a kind of transformation. It transforms an oscillatory stress field to a nonoscillatory case by adjusting the elastic constants of the materials involved. The interface toughness locus is also changed according to the new material properties. It is shown that this approach will predict the exact same critical load as interfacial fracture mechanics does. Finally several examples are presented to show how to enforce β=0 while keeping the energy release rate unchanged.

New Points of View on the Nonlocal Field Theory and Their Applications to the Fracture Mechanics (Ⅰ)——Fundamental Theory

Huang Zaixin, Fan Weixun, Huang Weiyang

1997, 18(1): 45-54.

Abstract(2633) PDF(658)

Abstract:
In the linear nonlocal elasticity theory, the solution to the boundary-value problem of the crack with a constant stress boundary condition does not exist. This problem has been studied in this paper. The contents studicd contain of examining objectivity of the energy balance, deducing the constitutive equations of nonlocal thermoelastic bodies, and determining nonlocalforce and the linear nonlocal elasticity theory. Some new results are obtained. Among them, the stress boundary condition derived from the linear theory not only solves the problem mentioned at the beginning, but also contains the model of molecular cohesive stress on the shorp crack tip advanced by Barenblatt.

Stability of Motion for a Constrained Birkhoff’s System in Terms of Independent Variables

Mei Fengxiang

1997, 18(1): 55-60.

Abstract(2178) PDF(535)

Abstract:
This paper proposes firstly the pfaff-Birkhoff-D'Alembert's principle and obtains the equations of motion in terms of the independent variables for a constrained Birkhoff's system from the principle. Secondly, it establishes the equations of perturbation of the system. Finally, it obtains the stability criteria by using the Liaqpunov direct method and the firstly approximate method.

The Optimal Control Variational Principle and Finite Elements Analysis for Viscoplastic Dynamics

Ma Jinghuai

1997, 18(1): 61-66.

Abstract(2398) PDF(621)

Abstract:
This paper presents the optimal control variational principle for Perzyna model which is one of the main constitutive relation of viscoplasticity in dynamics. And it could also be transformed to solve the parametric quadratic programming problem.The FEM form of this problem and its implementation have also been discussed in the paper.

Unitive Analysis Schemes Problems of Multiple Moving Boundaries with 3-D Liquid-Solid Multiple Nonlinear Coupling for Uplift of Anchored Liquid Storage Tanks

Wen Dechao, Zheng Zhaochang

1997, 18(1): 67-75.

Abstract(1894) PDF(504)

Abstract:
In the paper, 3-D analysis method with unitive schemes is set up. which is used toresolve the uplift with multiple moving boundaries and multiple nonlinear coupling for anchored liquid storage tanks. In it, an algorithm of quasi-harmonious finite elements for arbitrary quadrilateral of thin plates and shells is built up to analyze the multiple coupling problems of general thin plates and shells structures with three dimensions,the complementary equations for analyzing uplifting moving boundary problems arededuced The axial symmetry and presumption of beam type mode are not used. In it,an algorithm is put forward for analyzing the Navier-Stokes problems of unsteady,three-dimensional, and viscous liquid with sloshing of moving boundary surfaces in large amplitude under ALE frame by scheme of time-split-steps to which linear potential theory is not applied. The algorithms can be used to analyze the solid liquidmultiple nonlinear coupling problems with 3-D moving boundary with friction in multiple places.

Three Dimensional Simulation of Unstable Immiscible Displacement in the Porous Medium

Tan Xiaoping, Pei Juemin, Chen Junkai

1997, 18(1): 77-84.

Abstract(1741) PDF(509)

Abstract:
In this study changes of uncontinuous potential functions at the interface wereused to simulate the immiscible displacement in porous media. The elliptic partial differential equation was changed to a seven-pomt molecule form algebraic equation inthree dimensions using the finite difference method. The Strongly implicit procedure was adopted to determine the potential functions at every time instant. Then the change of interface was determmed. The simulation was continued until the displacement changed to unstable state. The effect of capillary pressure, wetting properly, and nonuniformity of permeability were consthered.

Neural Network-Based Adaptive Control of a Class of Uncertain Nonlinear System

Mu Xiaowu, Zhang Huaizhou

1997, 18(1): 85-89.

Abstract(2081) PDF(467)

Abstract:
For a class of nonlinear systems which can be transformed into the canonical form, an adaptive control scheme based on Gaussian radial basis function networks was proposed in [9].In this paper,the idea in [5,10] which was combined to discuss has adaptive control of a more general class of uncertain nonlinear systems.

The Nonparametric Estimation of the Next Failure Time

Li Gang

1997, 18(1): 91-94.

Abstract(1636) PDF(500)

Abstract:
The nonparametric estimation of the next failure time is considered in this paper.The estimator given in the paper has a.s. convergence under some proper conditions.The asymptotic normality of the estimator is also discussed.