应用数学和力学

2000 Vol. 21, No. 1

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On the Convergence Problems of Ishikawa and Mann Iterative Processes With Error for Φ-Pseudo Contractive Type Mappings

Zhang Shisheng

2000, (1): 1-10.

Abstract(2311) PDF(773)

Abstract:
The purpose of this paper is to introduce the concept of Φ-pseudo contractive type mapping and to study the convergence problem of Ishikawa and Mann iterative processes with error for this kind of mappings.The results presented in this paper improve and extend many authors' recent results.

The Finite Element Method Based on Interpolating With Wavelet Basis Function

Luo Shaoming, Zhang Xiangwei

2000, (1): 11-16.

Abstract(2939) PDF(909)

Abstract:
The compactly supported wavelet basis functions are introduced into the construction of interpolating function of traditional finite element method when analyzing the problems with high gradient,and the traditional interpolating method is modified.The numerical stability of the new interpolating pattern is discussed and the convergence of the new method is also discussed by patch test analysis.The additional freedom of the new interpolating pattern is eliminated by static condensation method.Finally,the wavelet finite element formulations based on variational principles are put forward.

Topology Optimization Design of Continuum Structures Under Stress and Displacement Constraints

Yang Deqing, Sui Yunkang, Liu Zhengxing, Sun Huanchun

2000, (1): 17-24.

Abstract(3393) PDF(745)

Abstract:
Topology optimization design of continuum structures that can take account of stress and displacement constraints simultaneously is difficult to solve at present.The main obstacle lies in that,the explicit function expressions between topological variables and stress or displacement constraints can not be obtained using homogenization method or variable density method.Furthermore,large quantities of design variables in the problem make it hard to deal with by the formal mathematical programming approach.In this paper,a smooth model of topology optimization for continuum structures is established which has weight objective considering stress and displacement constraints based on the independent-continuous topological variable concept and mapping transformation method proposed by Sui Yunkang and Yang Deqing.Moreover,the approximate explicit expressions are given between topological variables and stress or displacement constraints.The problem is well solved by using dual programming approach,and the proposed element deletion criterion implements the inversion of topology variables from the discrete to the continuous.Numerical examples verify the validity of proposed method.

The Mixed Boundary-Value Problem for Nonlocal Asymmetric Elasticity

Dai Tianmin

2000, (1): 25-29.

Abstract(2636) PDF(667)

Abstract:
In this paper,the equations of motion and all boundary conditions as well as the energy equation for non-local asymmetric elasticity are derived together from the complete principles of virtual work and virtual power as well as the generalized Piola theorem.Adding the boundary conditions presented here to the results by Gao Jian and Dai Tianmin,the mixed boundary-value problem of the non-local asymmetric linear elasticity are formulated.

The Initial Value Problems of First Order Impulsive Differential Equations in Banach Spaces

Sun Qinfu, Luan Shixia

2000, (1): 30-38.

Abstract(3114) PDF(603)

Abstract:
In this paper,by using of monotone iterative technique,the existence and iterative approximation of the minimax quasi-solutions of the initial value problems for more general first order impulsive differential equations in Banach spaces are investigated.

Study on Anisotropic Buoyant Turbulence Model

Yang Kun, Hong Yiping, Zhou Xueyi, Li Yuliang

2000, (1): 39-44.

Abstract(2317) PDF(567)

Abstract:
By analyzing the components of Reynolds stresses of implicit algebraic stress model(IASM) in this paper,that Reynolds stresses in buoyant turbulent flows were produced by both strain and buoyancy is considered.Consequently,a nonlinear anisotropy buoyant turbulence model was developed by applying linearity of equilibrium hypothesis to Reynolds stress transports.The model avoids numerical singularity and its reliability is verified by the comparisons between predictions and experimental data.

The Numerical Solution of Green’s Functions for Transversely Isotropic Elastic Strata

Chen Rong, Xue Songtao, Chen Zhuchang, Chen Jun

2000, (1): 45-52.

Abstract(2779) PDF(911)

Abstract:
In this paper,a model of transversely isotropic elastic strata is used to simulate the soil layers situated on a half space.Instead of the half space,an artificial transmitting boundary is used to absorb the vibration energy.The displacement formulas at any soil layer interface under vertical or horizontal harmonic ring loads are obtained by using the thin layer element method.From these formulas,the explicit solutions of G_reen's functions-the displacement responses at any interface of these strata under vertical and horizon harmonic point loads-are derived.The examples show that the method presented in this paper is close to the theoretical method and the transversely isotropic property has evident influence on the Green's functions.

Noether’s Theory of Mechanical Systems With Unilateral Constraints

Zhang Yi, Mei Fengxiang

2000, (1): 53-60.

Abstract(3057) PDF(880)

Abstract:
Noether's theory of dynamical systems with unilateral constraints by introducing the generalized quasi-symmetry of the infinitesimal transformation for the transformation group G_r is presented and two examples to illustrate the application of the result are given.

The Existence and Uniqueness of Weak Solution of the Flow Between Two Concentric Rotating Spheres

Feng Weibing, Li Kaitai

2000, (1): 61-66.

Abstract(2306) PDF(584)

Abstract:
The unsteady axisymmetric incompressible flow between two concentric spheres was discussed in this paper.It is useful to most astrophysical,geophysical and engineering applications.In order to get the existence and uniqueness of weak solution of this flow with the stream-velocity form,firstly,the relations among the nonlinear terms in this equation is found; then,the existence is proved by an auxiliary semi-discrete scheme and a compactness argument.

The Addendum for the Generalized d’Alembert Equations of Motion

Zhang Dingguo

2000, (1): 67-72.

Abstract(2355) PDF(607)

Abstract:
In this paper,the traditional generalized d'Alembert equations of motion(G_D) in the field of robot dynamics are extended to the circumstances as follows:1 Considering the robots not only with rotary joints but also with translational joints.2 Extending the application range of the G_D dynamic equations from the simple chained robots to the tree-structured robots.

A Simple Postprocess Procedure for Galerkin Method

Hou Yanren, Li Kaitai

2000, (1): 73-79.

Abstract(2968) PDF(666)

Abstract:
A kind simple postprocess procedure for classical Galerkin method for steady Navier-Stokes equations with stream function form was presented in this paper.The main ideal was to construct an approximate interactive rule between lower frequency components and higher frequency components by using the conception of Approximate Inertial Manifold(AIM) and a kind of new decomposition of the true solution.It is demonstrated in this paper that this kind of postprocess Galerkin method could derive a higher accuracy solution with lower computing efforts.

A New Method for Stress Analysis of a Cyclically Symmetric Structure

Tang Guoan, Ding Jun, Xu Xiaofeng

2000, (1): 80-86.

Abstract(2696) PDF(570)

Abstract:
In this paper,a computational method for finite element stress analysis of a cyclically symmetric structure subjected to arbitrary loads is provided.At first,using discrete Fourier transformation technique,the complete structure is analyzed by considering only one sector with appropriate complex constraints on its boundary with the adjacent sectors.Next,an imaginary structure which is composed of two identically overlapping sectors is constructed,and that the complex constraints mentioned above can be equivalently replaced by a set of real constraints on this imaginary structure is proved.Therefore,the stress analysis of a cyclically symmetric structure can be solved conveniently by most of finite element programs.

Axisymmetric Bending for Thick Laminated Circular Plate Under a Concentrated Load

Sheng Hongyu, Fan Jiarang

2000, (1): 87-93.

Abstract(2520) PDF(895)

Abstract:
Based upon the fundamental equations of three dimensional elasticity,the state equation for axisymmetric bending of laminated transversely isotropic circular plate is established and the concentrated force on plate surface is expanded into Fourier-Bessel's series,therefore,an analytical solution for the problem is presented.Every fundamental equation of three dimensional elasticity can be exactly satisfied by the solution and all the independent elastic constants can be taken into account fully,furthermore,the continuity conditions between plies can also be satisfied.

An Automatic Constraint Violation Stabilization Method for Differential/Algebraic Equations of Motion Multibody System Dynamics

Zhao Weijia, Pan Zhenkuan, Wang Yibing

2000, (1): 94-98.

Abstract(3169) PDF(663)

Abstract:
A new automatic constraint violation stabilization method for numerical integration of Euler-Lagrange equations of motion in dynamics of multibody systems is presented.The parameters α,β used in the traditional constraint violation stabilization method are determined according to the integration time step size and Taylor expansion method automatically.The direct integration method,the traditional constraint violation stabilization method and the new method presented in this paper are compared finally.

Planning Motion Trace of Robot by Spinor Method

Lin Ruilin

2000, (1): 99-105.

Abstract(3062) PDF(1015)

Abstract:
The spinors applied to describe position and attitude of robot are studied.In dual spaces,the terminal trace of robot is planned through the mapping point,of attitude spinors.As a handy method directly perceived through the sense,the spinor method directly converges tracking error in the planning.It promotes the dynamic accuracy of trace operation.It is also suitable to the exerciser with redundant freedom.

Bending of Uniformly Loaded Rectangular Plates With Two Adjacent Edges Clamped,One Edge Simply Supported and the Other Edge Free

Zhao Fangxin, Zhang Yingjie, Zhao Zuxin, Zhang Song, Yu Bingyi

2000, (1): 106-110.

Abstract(2614) PDF(830)

Abstract:
In this paper,an exact solution for an uniformly loaded rectangular plate with two adjacent edges clamped,one edge simply supported and the other edge free,was given by using the concept of generalized simply supported edges and superposition method.The numerical results were given for the deflections along the free edge and bending moments along the clamped edges of a square plate.