应用数学和力学

1999 Vol. 20, No. 6

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On the Mann and Ishikawa Iterative Approximation of Solutions to Variational Inclusions with Accretive Type Mappings in Banach Spaces

Zhang Shisheng

1999, 20(6): 551-558.

Abstract(2323) PDF(841)

Abstract:
The purpose of this paper is to introduce and study the existence of solutions and convergence of Mann and Ishikawa iterative processes for a class of variational inclusions with accretive type mappings in Banach spaces. The results presented in this paper extend and improve the corresponding results by Chang,Ding, Hassouni, Kazmi, Siddiqi, Zeng,et al.

The Simple Shear Oscillation and the Restrictions to Elastic-Plastic Constitutive Relations

Chen Liangsen, Zhao Xinghua, Fu Minfu

1999, 20(6): 559-568.

Abstract(2452) PDF(601)

Abstract:
Based on the definitions of hardening, softening and ideal plastic behavior of elastic-plastic materials in the true stress tensor space, the phenomena of simple shear oscillation are shown to be relative to the oscillatory occurrence of hardening and softening behavior of elastic-plastic materials, namely the oscillation of hardening behavior, by analyzing a simple model of rigid-plastic materials with kinematical hardening under simple shear deformation. To make the models of elastic-plastic materials realistic, must be satisfied the following conditions: for any constitutive model, its response stresses to any continuous plastic deformation must be non-oscillatory, and there is no oscillation of hardening behavior during the plastic deformation.

The Bifurcation Problem of Columns Caused by Elastic-Plastic Stress Wave Propagation

Han Qiang, Hu Haiyan, Yang Guitong

1999, 20(6): 569-578.

Abstract(2601) PDF(688)

Abstract:
In this paper, the dynamic buckling of an elstic-plastic column is studied. Let its dynamic buckling under step load be reduced to a bifurcation problem caused by the propagation of axial elastic-plastic stress wave. The critical buckling condition is given and the reflection of the elastic-plastic stress wave is taken into consideration. In the end, numerical computation and conclusions are presented and obtained.

The Solution of Weak Formulation for Axisymmetric Problem of Orthotropic Cantilever Cylindrical Shell

Ding Kewei, Tang Limin

1999, 20(6): 579-584.

Abstract(2660) PDF(596)

Abstract:
Weak formulation of equilibrium equations including boundary conditions of laminated cylindrical shell are presented, and thermal stresses mixed state equation for axisymmetric problem of closed cantilever cylindrical shell is established. A unified approach and weak solutions are obtained for closed laminated cantilever cylindrical shell of arbitrary thickness under thermal and mechanical loadings. The equations and boundary conditions proposed in this paper are weakened, the method of this paper would be easy to popularize in dynamics analysis of elasticity.

On the Uniform Boundedness of Solutions of Some Non-Autonomous Differential Equations of the Fourth Order

Cemil Tun

1999, 20(6): 585-591.

Abstract(2277) PDF(611)

Abstract:
In this paper, sufficient conditions are established under which all solutions of some non～autonomous differential equations of the fourth order are bounded and uniformly bounded.

Lie Symmetries and Conserved Quantities of Holonomic Variable Mass Systems

Mei Fengxiang

1999, 20(6): 592-596.

Abstract(2761) PDF(802)

Abstract:
In this paper, the Lie symmetries and the conserved quantities of the holonomic variable mass systems are studied. By using the invariance of the ordinary differential equations under the infinitesimal transformations, the determining equations of the Lie symmetries of the systems are established, and the structure equation and the conserved quantities are given. And an example is given to illustrate the application of the result.

Lie Symmetries and Conserved Quantities of Nonconservative Nonholonomic Systems in Phase Space

Liu Rongwan, Fu Jingli

1999, 20(6): 597-601.

Abstract(2616) PDF(710)

Abstract:
The invariance and conserved quantities of the nonconservative nonholonomic systems are studied by introducing the infinitesimal transformations in phase space. The Lie's symmetrical determining equations are established. The Lie's symmetrical structure equation is obtained. An example to illustrate the application of the result is given.

The Target Wave Patterns of a Reaction-Diffusion Process in an Immobilized Enzyme

Gu Shengshi, Yue Jingliang, Jing Le

1999, 20(6): 602-606.

Abstract(2126) PDF(587)

Abstract:
In this paper, the target wave patterns of a reaction-diffusion process were discovered by numerical simulate of an immobilized enzyme mathematical model. The substrate concentration periodically diffuses from initial state to all around, and the product concentration also periodically increases with target wave patterns, and finally they reach the equilibrium state.

Periodic Solutions of a Class of Higher Order Neutral Type Equations

Cao Jinde

1999, 20(6): 607-612.

Abstract(2125) PDF(873)

Abstract:
In this paper, by using the theory of Fourier series, some necessary and sufficient conditions of existence and uniqueness of periodic solutions of a class of higher order neutral type equations are obtained. The main results by Shi Jianguo in "Discussion on the periodic solutions for linear equation of neutral type with constant coefficients" are improved, i.e., the condition |b₀|≠1 instead of the condition |b₀|<1/2 of Theorem 1 by Shi Jianguo is given. Other theorems by Shi are rebuilt and improved according to the new assumption.

The Explicit Representation to the Principal Rotation Angle and the Principal Rotation Axis

Dui Guansuo, Zhuo Xiaobao

1999, 20(6): 613-618.

Abstract(1995) PDF(715)

Abstract:
By using Cayley-Hamilton theorem, two kinds of explicit representation for the rotation tensor are proposed. The one contains the lower powers of deformation gradient, by which the formula of the principal rotation angle and the explicit representation of principal axis are obtained;the other, a high efficient method to obtain the rotation tensor, does not contain the complicated coefficients and uses few variables. Some properties about the principal rotation angle and principal rotations axis are obtained.

The Energy Orthogonal Relation Between Conforming and Non-Conforming Displacements of Triangular Element

Nie Yufeng, Zhou Tianxiao, Nie Tiejun

1999, 20(6): 619-624.

Abstract(1917) PDF(631)

Abstract:
Based on the variational principle of combinative stability, combined hybrid methods posed by Zhou Tianxiao are absolutely convergent and stabilized. Zhou has advocated a systematic approach to enhanced stress/strain schemes and has designed a family of lower-order elements which are affine-equivalent to n-cube(n=2,3). The energy orthogonal relation between the conforming part and the non-conforming part of displacements interpolation functions in triangular element is given, in which the stress is interpolated by linear polynomials on each element, but the displacements are interpolated by the sum of conforming linear and non-conforming quadratic polynomials. Furthermore, this element is equivalent to the conforming triangular linear element, that is, the non-conforming parts have no contribution to enhanced strains.

Explicit Solitary-Wave Solutions to Generalized Pochhammer-Chree Equations

Zhang Weiguo, Ma Wenxiu

1999, 20(6): 625-632.

Abstract(2869) PDF(881)

Abstract:
For the solitary-wave solution u(ξ)=u(x-vt+ξ₀)to the generalized Pochhammer-Chree equation(PC equation) u_tt-u_ttxx+ru_xxt-(a₁u+a₂u²+a₃u³)_xx=0,r,a_i=consts(r≠0),(Ⅰ). the formula ∫_-∞^+∞[u'(ξ)]²dξ=1/12rv(C₊-C_-)³[3a₃(C₊+C_-)+2a₂], is established, by which it is shown that the generalized PC equations (Ⅰ) has not bell profile solitary-wave solutions but may have kink profile solitary-wave solutions. However a special generalized PC equation u_tt-u_ttxx-(a₁u+a₂u²+a₃u³)_xx=0 a_i=consts (Ⅱ) may have not only bell profile solitary-wave solutions, but also kink profile solitary wave solutions whose asymptotic values satisfy 3a₃(C₊+C_-)+2a₂=0. Furthermore all expected solitary-wave so-lutions are given. Finally some explicit bell profile solitary-wave solutions to another generalized PC equation u_tt-u_ttxx-(a₁u+a₃u³+a₅u⁵)_xx=0 a_i=consts are proposed.

Periodic Viable Trajectories of Differential Inclusions

Wang Zhihua

1999, 20(6): 633-639.

Abstract(2240) PDF(632)

Abstract:
In this paper,the periodic viable trajectories of differential inclusions are discussed.Firstly,a simplified property of differential inclusions is given. Then,an existence theorem of periodic viable trajectories of differential inclu sions in a finite dimensional space is proved.With the above results and Galerkin's approximation,an existence theorem of periodic viable trajectories of partial differential inclusions in a Hilbert space is proved.

Initial Value Problems for a Class of Nonlinear Integro-Partial Differential Equations

Guo Ai

1999, 20(6): 640-646.

Abstract(2794) PDF(673)

Abstract:
In this paper,the problem of global existence of solutions to the followin g initial value problem is studied: which comes from viscoelastic mechanics.By making u se of integral estimates method,it is proved that this problem has a global solution if,in addition to certain regularity assumptions on the given fun ctions,the following conditions are satisfied: p'(s)≥c₁>0,|q'(s)|≤const,λ(0)<0,λ'(0)<λ²(0).

Computation of Frequencies and Damping Ratios for Adaptive Structures

Zhang Lianwen, Xia Renwei, Zeng Guangwu

1999, 20(6): 647-653.

Abstract(2383) PDF(519)

Abstract:
In this paper,a new technique of state vector approach to solving damping ratios of adaptive structures is proposed,by which the state matrix can be analytically conducted the Cholesky decomposition,providing that the mass matrix is derived by lumped method.In this case,not only the computational accuracy is raised,but also the numerical operations are reduced.Finally,some numerical results are presented to show that the solution method is simple and efficient.

Asymptotic and Oscillation for a Class of First Order Neutral Differential Equation

Wang Peiguang

1999, 20(6): 654-660.

Abstract(2209) PDF(676)

Abstract:
In this paper,the first order neutral differential equation with continuous distributed delay is concerned,and the asymptotic behavior of nonoscillatory solution and the oscillatory criteria are given for Equation(1).