应用数学和力学

1995 Vol. 16, No. 5

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Chien Wei-zang

1995, 16(5): 381-395.

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Abstract:

Computer Algebra-Perturbation Solution to a Nonlinear Wave Equation

Wang Ming-qi, Dai Shi-qiang

1995, 16(5): 403-408.

Abstract(2521) PDF(577)

Abstract:
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 Artificlal Mechanical Valve-Blood Interaction

Chen Da-peng, Zbang Jian-hai, Zou Sheng-quan

1995, 16(5): 409-414.

Abstract(2276) PDF(548)

Abstract:
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): 415-420.

Abstract(2013) PDF(426)

Abstract:
In this paper, the solution of a 2-D weak singular integral equation of tire first kind subjected to constraint is found and listed p=p(r,θ)={2/[π²k(φ₀]}√F(r,θ)-c_*(0≤r≤r_*) where(s,φ)is a local polar coordhrating with orighr at M(r,θ),(r,θ)is the global polar coordinating with origin at O(0,0):k and F are given continuous functions;φ₀ and C are 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 Prohlem of Anisotro Fic Elastic Bodywith a Hyperbolic Boundary

Hu Yian-tai, Zhao Xing-hua

1995, 16(5): 421-430.

Abstract(2397) PDF(456)

Abstract:
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): 431-442.

Abstract(1883) PDF(529)

Abstract:
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 Analytis of Moierately Thick Plates

Shen Hui-shen, Zhu Xiang-geng

1995, 16(5): 443-450.

Abstract(2267) PDF(539)

Abstract:
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 Stahility Analysis of Numerical Nethods for Volterra integral Equations with Delay Argument

Tian Hong-jiong, Kuang Jiao-xun

1995, 16(5): 451-457.

Abstract(2091) PDF(693)

Abstract:
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): 459-470.

Abstract(1714) PDF(510)

Abstract:
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): 471-477.

Abstract(1957) PDF(436)

Abstract:
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.