Applied Mathematics and Mechanics (English Edition)

THE SECOND ORDER APPROXIMATION THEORY OF THREE DIMENSIONAL ELASTIC PLATES AND ITS BOUNDARY CONDITIONS WITHOUT USING KIRCHHOFFLOVE ASSUMPTIONS

Chien Wei-zang

1995, 16(5): 405-427.

Abstract ( 474 )

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The first order approximation theory o.f three dimensional elastic plates and its boundat T conditions presented hi the previous paper^[1] establishes six differential equations for the solutions o.f six undetermined functions u₀, u_a, A₍₀₎ and S_(2)a defined in the x, y platte. They can be divided into two groups, each constitutes three eqaations, to calculate u₀, S_(2)a, and u_a, A₍₀₎ respectiveh'. Their boundary conditions as well as these, equations are derived from the stationary conditions of variations of a functional for this problem based on the generalized variational principle. The solutions given by this theory are close to those given by the classical theory of thin plates as the ratio of thickness h to width a is small. For large ratiu, say h/a=0.3 a considerable difference arises between the two theories. It has not been made cleat" that in what range oJ the ratio such difference is reasonable to give more precise solutions, In order to solve this problem, we must study the second order approxhnation theory hi this paper. following the previous one, we shall establish the second order approximation theory by applying the stationary condition of variations of a functional for this problem based on the generalized variational principle to derive nine differential equations and the relate boundary conditions, which are used to calculate nine utidetermined functions u₀, u_a, A₍₀₎, S_(2)a, and S_(3)a. And the range of the validity of the first order approxhnation theol3, can be Jbund out by comparhtg the second order theory with the first order theory and the classical theory. It should be pohtted out here that the equations of the second order theot 3" can also be divided into two groups to be soh,ed separately, and the prncedure of solution is not too complicate to perform as nell. Here. we will use the same notations adopted in the previous paper, and not repeat their definitions.

COMPUTER ALGEBRA-PERTURBATION SOLUTION TO A NONLINEAR WAVE EQUATION

Wang Ming-qi;Dai Shi-qiang

1995, 16(5): 429-435.

Abstract ( 601 )

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In this paper, the higher-order asymptotic solution to the Cauchy problem of a nonlinear wave equation is found by using a computer algebra-perturbation method. The secular terms in the solution from straightforward expansions, are eliminated with the straining of characteristic coordinates and the use of the renormalization technique, and the four-term uniformly valid solution is obtained with the symbolic computation by using a computer algebra system. The comparison of the derived asymptotic solution dnd the numerical solution shows that they coincide with each other for smaller ε and agree quite well for larger ε(e. g., e=0.25)

TRANSIENT ANALYSIS OF ARTIFICIAL MECHANICAL VALVE--BLOOD INTERACTION

Chen Da-peng;Zhang Jian-hai;Zou Sheng-quan

1995, 16(5): 437-442.

Abstract ( 649 )

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Using finite elemcnt method,this paper has analyzed the blood-mechanical heart valve interaction system subjected to a step pressure when the vaiue is at closing position.As demonstrated in the present stud),,in such conditions mechanical values made of pyrolytic carbon,Ti alloy,Co-Cr alloy and ceramics tend to be very stiff which result in high impinging pressure.The impinging pressure acted on the value of the blood-valve sytem can be reduced by decreasing the elastic modulus of the mechanical value.

SOLUTION OF A 2-D WEAK SINGULAR INTEGRAL EQUATION WITH CONSTRAINT

Yun Tian-quan

1995, 16(5): 443-449.

Abstract ( 516 )

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In this paper, the solution of a 2-D weak singular integral equation of tire first kind

where(s,φ)is a local polar coordhrating with orighr at M(r,θ),(r,θ)is the global polar"coordinating n'ith origh7 at O(0,0):k and F are given continuous functions;φ₀ is a constant;F(r_*,θ)=c_*(const.)is the boundary contour of considering range Q. The method used can be extended to 3-D cases.

TWO-DIMENSIONAL PROBLEM OF ANISOTROPIC ELASTIC BODY WITH A HYPERBOLIC BOUNDARY

Hu Yian-tai;Zhao Xing-hua

1995, 16(5): 451-460.

Abstract ( 559 )

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The general and shnplified formula for anisotropic medium with a hyperbolic boundary subjected to pure bending M₀ is provided in this paper. The stress and strain fields in medium are obtained. Based upon the above results, we analyse the hoop stress along the hyperbolic curve and the stress distributions on the plane x₂=0 for aluminium (cubic crystal). When the boundary curve degenerates into an external crack three kinds of stress intensity factors (k₁, k₂, k₃) are obtained, and it is easily found that the first stress intensio, factor k₁ is independent of the material constants.

THE SINGULAR PERTURBATION FOR THE BUCKLING OF A TRUNCATED SHALLOW SPHERICAL SHELL WITH THE LARGE GEOMETRICAL PARAMETER

Kang Sheng-liang

1995, 16(5): 461-474.

Abstract ( 560 )

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A problem of practical interest for nonlinear axisymmetrical stability of a truncated shallow spherical shell of the large geometrical parameter with an articulated external edge and a nondeformable rigid,body at the center under compound loads is investigated in this paper.By using modified method of multiple scales,the uniformly valid asymptotic solutions of this boundary value problem are obtained when the geometrical parameter k is large.

THERMAL POSTBUCKLING ANALYSIS OF MODERATELY THICK PLATES

Shen Hui-shen;Zhu Xiang-geng

1995, 16(5): 475-484.

Abstract ( 651 )

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A thernml postbuckling analysis is presenled for a moderately thick rectangular plale slthjeeled to(I) uniform and non-uniform tent-like temperature loading:and(2) combined axial compression and uniform temperature loading.The initial geometrical imperfection of plate is taken into accaunt.The formulations are based on the Reissner-Mindlin plale theory considering the effects of rotarl inertia and transverse shear deformation.The analysis uses a deflection-type perturbation technique to determine the thermal bucklittg loads attd postbuckling equilibrium paths.Numerical examples are presented that relate to the performances of perfect and imperfet.moderately thick rectangular plates and are compared with the results predicted by the thin plate theory.

NUMERICAL STABILITY ANALYSIS OF NUMERICAL METHODS FOR VOLTERRA INTEGRAL EQUATIONS WITH DELAY ARGUMENT

Tian Hong-jiong;Kuang Jiao-xun

1995, 16(5): 485-491.

Abstract ( 633 )

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The present paper deals with the stability properties of numerical methods for Volterra integral equations with delay argument. We assess the numerical stability of nunterical methods with respect to the followhlg test equations

where τ is a positive constant, and p and q are complex valued. We investigate the stability properties of reducible quadrature method~ and θ-methods in the case of the above test equations

A PHYSICAL THEORY OF ASYMMETRIC PLASTICITY

Gao Jian;Lin Xiao-ling

1995, 16(5): 493-506.

Abstract ( 542 )

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Experiments have shown the strong rotation in plastic deformation,which is caused by the diselination,specific arrangement of dislocation and inhomogeneity of the gliding motion of the defects in the microscopic scale.Based on the microscopic mechanism of the rotational plastic deformation,the conservation equation satisfied by the defects motion(dislocation and disclination)has been developed in this paper.Then the diffusion motion of the defects are reduced based on the asymmetric theory of continuum mechanics.By utilizing the maximization procedure for the micro plastic work and a scale-invariance argument,various models of Cosserat-type plasticity are obtained in this manner.

INTERIOR LAYER BEHAVIOR OF BOUNDARY VALUE PROBLEMS FOR SECOND ORDER-VECTOR EQUATION OF ELLIPTIC TYPE

Xu Yu-xing;Zhang Xiang

1995, 16(5): 507-513.

Abstract ( 577 )

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In this paper,making use of the theory of partial differential inequalities, we will investigate the boundary value problems for a class of singularly perturbed second order vector elliptic equations, and obtain the existence and asymptotic estimation of solutions, involving the interior layer behavior, of the problems described above.

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