Applied Mathematics and Mechanics (English Edition)

ON THE MANN AND ISHIKAWA ITERATIVE APPROXIMATION OF SOLUTIONS TO VARIATIONAL INCLUSIONS WITH ACCRETIVE TYPE MAPPINGS IN BANACH SPACES

张石生

1999, 20(6): 585-592.

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The purpose of this paper is to introduce and study the existence of solution s 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 Chan g,Ding,Hassouni,Kazmi,Siddiqi,Zeng et al.

THE SIMPLE SHEAR OSCILLATION AND THE RESTRICTIONS TO ELASTIC-PLASTIC CONSTITUTIVE RELATIONS

陈良森;赵兴华;扶名福

1999, 20(6): 593-603.

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Based on the definitions of hardening,softening and ideal plastic behavior of elastic-plastic materials in th e true stress tensor space,the phenomena of simple shear oscillation are shown to be relative to the oscillatory occurrence of hardenin g and softening behavior of elastic-plastic materials,namely the oscillation of hardening behavior,by analyzin g a simple model of rigid-plastic materials with kinematical hardening under simple sh ear deformation.To make the models of elastic-plastic materials realistic,must be satisfied the followin g 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 durin g the plastic deformation.

THE BIFURCATION PROBLEM OF COLUMNS CAUSED BY ELASTIC-PLASTIC STRESS WAVE PROPAGATION

韩强;胡海岩;杨桂通

1999, 20(6): 604-614.

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In this paper,the dynamic buckling of an elastic-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 bucklin g condition is given and the reflection of th e 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

丁克伟;唐立民

1999, 20(6): 615-621.

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Weak formulation of equilibrium equations including boundary conditions of laminated cylindrical shell is 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): 622-628.

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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

梅凤翔

1999, 20(6): 629-634.

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In this paper,the Lie symmetries and the conserved quantities of the holonomic variable mass systems are studied.By usin g 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 stru cture 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

刘荣万;傅景礼

1999, 20(6): 635-640.

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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 establish ed.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

顾圣士;乐经良;金乐

1999, 20(6): 641-646.

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

PERIODIC SOLUTIONS OF A CLASS OF HIGHER ORDER NEUTRAL TYPE EQUATIONS

曹进德

1999, 20(6): 647-652.

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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 Jian guo in “Discussion on the periodic solutions for linear equation of neutral type with constant coefficients” are improved,i.e.,the condition|b₀|≠1 inst ead of the condition |b₀|<1/2 of Theorem 1 by Shi Jian guo 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

兑关锁;左晓宝

1999, 20(6): 653-659.

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By using Cayley-Hamilton theorem,two kinds of explicit representation for th e rotation tensor are proposed.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 th e rotation tensor,does not contain the complicated coefficients and u ses few variables.Some properties about the principal rotation angle and the principal rotation axis are obtained.

THE ENERGY ORTHOGONAL RELATION BETWEEN CONFORMING AND NON-CONFORMING DISPLACEMENTS OF TRIANGULAR ELEMENT

聂玉峰;周天孝;聂铁军

1999, 20(6): 660-665.

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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 nonconforming 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

张卫国;马文秀

1999, 20(6): 666-674.

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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).

PERIODIC VIABLE TRAJECTORIES OF DIFFERENTIAL INCLUSIONS

王志华

1999, 20(6): 675-682.

摘要 ( 633 )

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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

郭艾

1999, 20(6): 683-689.

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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:

COMPUTATION OF FREQUENCIES AND DAMPING RATIOS FOR ADAPTIVE STRUCTURES

张连文;夏人伟;曾广武

1999, 20(6): 690-697.

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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 OF THE SOLUTIONS FOR A CLASS OF THE FIRST ORDER NEUTRAL DIFFERENTIAL EQUATIONS

王培光

1999, 20(6): 698-704.

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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).

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