应用数学和力学

1986 Vol. 7, No. 8

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A Perturbation-Variational Solution of the Large Deflection of Rectangular Plates under Uniform Load

Pan Li-zhou, Wang Shu

1986, 7(8): 675-688.

Abstract(1810) PDF(670)

Abstract:
In this paper, von Kármán's set of nonlinear equation for large deflection of rectangular plates is at first converted into several sets of linear equations by taking central dimensionless deflection as perturbation parameter, and then, the sets of linear equations for plates with various ratios of length to width are solved with application of variational method, The analytical expressions for displacements and stresses as well as formulas for numerical calculation are worked out, The figures of maximum deflection-load and maximum stress with ratio R of length to width as a parameter are given in this paper, Through comparison, it is found that the results of this paper are quite in accord with experiments.

FEM Analysis on Mixed-Mode Fracture of CSM-GRP

Zhang Shuang-yin, C. M. Leech

1986, 7(8): 689-702.

Abstract(2045) PDF(741)

Abstract:
An FEM analysis for studying mized-mode fracture problem of chopped strand mat glass fibre reinforced polyester laminate was presented, The analysis was formulated on the basis of 8-node quadrilateral isoparametric element, The collapsed triangular quarter-point singular elements were used for calculating stress intensity factors K_Ⅰ and K_Ⅱ. The crank propagation process was computed by implementing constraint release technique, Three different approaches to the solution of stress intensity factors K_Ⅰ and K_Ⅱ were compared, The effect of constraint condition imposed upon the displacement of the three collapsed nodes of the crack tip elements on the K_Ⅰ and K_Ⅱ results was evaluated, The mixed-mode critical stiress intensity factors K_ⅠC and K_ⅡC were estimated for CSM-GRP through the consideration of K_Ⅰ and K_Ⅱ calculated and the measured failure load and critical crack length in the experiment.

Chaplygin Equation in Three-Dimensional Non-Constant Isentropic Flow——The Theory of Functions of a Complex Variable under Dirac-Pauli Represen tation and Its Application in Fluid Dynamics(Ⅲ)

Shen Hui-chuan

1986, 7(8): 703-712.

Abstract(2670) PDF(622)

Abstract:
This work is the continuation of the discussion of ref, [1], In this paper we resolve the equations of isentropic gas dynamics into two problems: the three-dimensional non-constant irrotational flow (thus the isentropic flow, too), and the three-dimensional non-constant indivergent flow(i.e, the incompressible isentropic flow).We apply the theory of functions of a complez variable under Dirac-Pauli representation and the Legendre transformation,transform these equations of two problems from physical space into velocity space,and obtain two general Chaplygin equations in this paper, The general Chaplygin equation is a linear difference equation,and its general solution can be expressed at most by the hypergeometric functions, Thus we can obtain the general solution of general problems for the three-dimensional non-constant isentropic flow of gas dynamics.

On the Problem of Preventing Blowing-up and Quenching for Semilinear Heat Equation

Yan Zi-qian

1986, 7(8): 713-718.

Abstract(2002) PDF(559)

Abstract:
In this paper, the global existence of solutions to the IVP
u_t=Δu+g(t)f(u)(t>0),u|_t=0=u₀(x)
and the IBVP
u_t=Δu+g(t,x)f(u)(t>0,x∈Ω),u|_t=0=u|_∂Ω=0
is investigated, As has been done in[6],the introduction of factors g(t) or g(t,x) in nonlinear term is to prevent the occurrence of blowing-up or quenching of solutions, It is shown in this paper that most of the restrictions on f, g and u₀ in the theorems of [6] may be cancelled or relaxed,that the smallness of g is required only fortlarge,and that under certain conditions controlling initial state can avoid blowing-up.

A Feedback Tracking System for Robot

Zhang Hong-tao, Huang Lin

1986, 7(8): 719-727.

Abstract(1917) PDF(560)

Abstract:
The feedback information necessary for tracking is specified for a class of systems including robots, A feedback coatrol method is proposed by which a robot can track and grasp an arbitrarily moving object in space, It differs from the other methods in that it remains effective when orientation of the claw is impossible to 6e known is advance, Its validity is verified by digital simulation.

The Optimal Point of the Gradient of Finite Element Solution

Huang Xiao-fan

1986, 7(8): 729-738.

Abstract(1897) PDF(478)

Abstract:
We consider the first boundary value problem of the second order elliptic equation and serendipity rectangular elements. Papers [2,3,9] proved that the gradients of finite element solution possess superconvergence at Gaussianpoint. In this paper, we extend the results in papers [2,3,9] in the sense that the coefficients of the elliptic equations are discontinuous on a curve S which lies in the bounded domain Ω.

Thermal Bending of Thick Rectangular Plates of Bimodulus Composite Materials

Bai Zung-fang, Wang Di-xin

1986, 7(8): 739-745.

Abstract(1860) PDF(466)

Abstract:
Weighted residual solutions are presented for thermal bending of laminated composite plates, The material of each layer is assumed to be elastically and thermoelastically or-thotropic and bimodular, The formulations are based on the thermoelastic version of the theory of Whitney-Pagano laminated plate, which includes thickness shear deformations, The results are obtained for deflections and neutral-surface positions and are found to be in good agreement with the closed-form solution.

The Application of Perturbation Methods to Ecology

Wang Fu-jua

1986, 7(8): 747-750.

Abstract(1647) PDF(483)

Abstract:
In this paper,we study the application of perturbation methods to ecology.We obtain the asymptotic solution of an ecological differential equation.

Perfectly Plastic Stress Field at a Rapidly Propagating Plane-Stress Crack Tip

Lin Bai-song

1986, 7(8): 751-758.

Abstract(1829) PDF(621)

Abstract:
Under the condition that all the perfectly plastic stress components at a crack tip are the functions of B only, making use of the Tresca yield condition, steady-state motion equations and elastic perfectly-plastic constitutive equations, we derive the general analytic eapressions of perfectly plastic stress field at a rapidly propagating plane-stress crack tip, Applying these general analytic eapressions to the concrete crack, we obtain the analytic expressions of perfectly plastic stress fields at the rapidly propagating tips of Modes Ⅰ and Ⅱ plane-stress cracks.

Research of Visco-Elastic Type Ⅱ Rupture with Exciting and Attenuation Process

Fan Ja-shen

1986, 7(8): 759-767.

Abstract(1576) PDF(616)

Abstract:
With non-linear Rayleigh damping formula we describe the exciting process when the rupture velocity is low and the attenuation process w hen the rupture velocity reaches a certain high value, Assuming the medium of the earth crust is homogeneous and isotropic linear Voigt visco-elastic body,with small parameter perturbation method to deduce the non-linear governing partial differential equations into a system of asymptotic linear ones,we solve them by means of generalized Fourier series with moving coordinates as its variables,thus we transform them into non-homogeneous Mathieu equations. At last Mathieu equations are solved by WKBJ method.