2001 Vol. 22, No. 12

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Unified Way for Dealing With Three-Dimensional Problems of Solid Elasticity
XU Qiang, SUN Huan-chun
2001, 22(12): 1221-1229.
Abstract(2253) PDF(524)
Abstract:
Unified way for dealing with the problemsal of three dimensional solid, each type of plates and shells etc. was presented with the virtual boundary element least squares method(VBEM). It proceeded from the differential equations of three-dimensional theory of elasticity and employs the Kelvin solution and the least squares method. It is advantageous to the establishment of the models of a software for general application to calculate each type of three-dimensional problems of elasticity. Owing to directly employing the Kelvin solution and not citing any hypothesis, the numerical results of the method should be better than any others. The merits of the method are highlighted in comparison with the direct formulation of boundary element method(BEM). It is shown that coefficient matrix is symmetric and the treatment of singular integration is rendered unnecessary in the presented method. The examples prove the efficiency and calculating precision of the method.
Complex Inner Product Averaging Method for Calculating Normal Form of ODE
CHEN Yu-shu, SUN Hong-jun
2001, 22(12): 1230-1235.
Abstract(2489) PDF(877)
Abstract:
This paper puts forward a complex inner product averaging method for calculating normal form of ODE. Compared with conventional averaging method, the theoretic analytical process has such simple forms as to realize computer program easily. Results can be applied in both autonomous and non-autonomous systems. At last, an example is resolved to verify the method.
Study for the Bifurcation Topological Structure and the Global Complicated Character of a Kind of Non-Linear Finance System(Ⅱ)
MA Jun-hai, CHEN Yu-shu
2001, 22(12): 1236-1242.
Abstract(3231) PDF(829)
Abstract:
Based on the work discussed on the former study, this article first starts from the mathe matical model of a kind of complicated financial system, and analyses all possible things that the mod el shows in the operation of our country's macro-financial system:balance, stable periodic, fractal, Hopf-bifurcation, the relationship between parameters and Hopf-bifurcation, and chaotic motion etc. By the changes of parameters of all economic meanings, the conditions on which the complicated be haviors occur in such a financial system, and the influence of the adjustment of the macro-economic policies and adjustment of some parameter on the whole financial system behavior have been ana lyzed. This study will deepen people's understanding of the lever function of all kinds of financial policies.
New Principles of Power and Energy Rate of Incremental Rate Type for Generalized Continuum Field Theories
DAI Tian-min
2001, 22(12): 1243-1248.
Abstract(2327) PDF(1135)
Abstract:
The aim of this paper is to establish new principles of power and energy rate of incremental type in generalized continuum mechanics. By combining new principles of virtual velocity and virtual angular velocity as well as of virtual stress and virtual couple stress with cross terms of incremental rate type a new principle of power and energy rate of incremental rate type with cross terms for micropolar continuum field theories is presented and from it all corresponding equations of motion and boundary conditions as well as power and energy rate equations of incremental rate type for micropolar and nonlocal micropolar continua with the help of generalized Piola's theorems in all and without any additional requirement are derived. Complete results for micromorphic continua could be similarly derived. The derived results in the present paper are believed to be new. They could be used to establish corresponding finite element methods of incremental rate type for generalized continuum mechanics.
Interval Arithmetic and Static Interval Finite Element Method
GUO Shu-xiang, LÜ Zhen-zhou
2001, 22(12): 1249-1254.
Abstract(2385) PDF(683)
Abstract:
When the uncertainties of structures may be bounded in intervals, through some suitable discretization, interval finite element method can be constructed by combining the interval analysis with the traditional finite element method(FEM). The two parameters, median and deviation, were used to represent the uncertainties of interval variables. Based on the arithmetic rules of intervals, some properties and arithmetic rules of interval variables were demonstrated. Combining the procedure of interval analysis with FEM, a static linear interval finite element method was presented to solve the non-random uncertain structures. The solving of the characteristic parameters of n -freedom uncertain displacement field of the static governing equation was transformed into 2n-order linear equations. It is shown by a numerical example that the proposed method is practical and effective.
A Fixed Point Theorem for Set-Valued Mappings
Amitabh Banerjee, Thakur Balwant Singh
2001, 22(12): 1255-1261.
Abstract(2140) PDF(683)
Abstract:
Fixed points for set-valued mappings from a metric space X(not necessarily complete) into B(X), the collection of nonempty bounded subsets of X are obtained. The result generalizes some known results.
Weighted Solution of Small-Deflection Buckling Equation of Thin Shell
WANG Zong-li, WANG Xi, HAO Wen-hua
2001, 22(12): 1262-1266.
Abstract(2548) PDF(685)
Abstract:
Based on small-deflection buckling equation, a weighted solution for critical load is presented. Usually, it is very difficult to solve the equation for general problems, especially those with complicated boundary conditions. Axisymmetric problem was studied as an example. Influencing factors were found from the equation and averaged as the buckling load by introducing weights. To determine those weights, some special known results were applied. This method solves general complicated problems by using the solutions of special simple problems, simplifies the solving procedure and expands the scope of solvable problem. Compared with numerical solution, it also has fine precision.
Study on Dynamics, Stability and Control of Multi-Body Flexible Structure System in Functional Space
XU Jian-guo, JIA Jun-guo
2001, 22(12): 1267-1277.
Abstract(2458) PDF(672)
Abstract:
The dynamics, stability and control problem of a kind of infinite dimensional system are studied in the functional space with the method of modern mathematics. First, the dynamical control model of the distributed paramater system with multi-body flexible and milti-topological structure was established which has damping, gyroscopic parts and constrained damping's econdly, the necessary and sufficient condition of controllability and observability, the stability theory and asymptotic property of the system were obtained. These results expand the theory of the field about the dynmaics and control of the system with multi-body flexible structure, and have important engineering significance.
Continuation Method Applied in Kinematics of Parallel Robot
DONG Bin, ZHANG Xiang-de
2001, 22(12): 1278-1284.
Abstract(1976) PDF(516)
Abstract:
Continuation method solving forward kinematics problem of parallel robot was discussed. And through a coefficient-parameter continuation method the efficiency and feasibility of continuation method were improved. Using this method all forward solutions of a new parallel robot model which was put forward lately by Robot Open Laboratory of Science Institute of China were obtained. Therefore it provided the basis of mechanism analysis and real-time control for new model.
Self-Similar Solutions of Fracture Dynamics Problems on Axially Symmetry
LÜ Nian-chun, CHENG Jin, CHENG Yun-hong, QU De-zhi
2001, 22(12): 1285-1290.
Abstract(2461) PDF(523)
Abstract:
By the theory of complex functions, a penny-shaped crack on axially symmetric propagating problems for composite materials was studied. The general representations of the analytical solutions with arbitrary index of self-similarity were presented for fracture elastodynamics problems on axially symmetry by the ways of self-similarity under the ladder-shaped loads. The problems dealt with can be transformed into Riemann-Hilbert problems and their closed analytical solutions are obtained rather simple by this method. After those analytical solutions are utilized by using the method of rotational superposition theorem in conjunction with that of Smirnov-Sobolev, the solutions of arbitrary complicated problems can be obtained.
Stability Analysis of Maxwell Viscoelastic Pipes Conveying Fluid With Both Ends Simply Supported
ZHAO Feng-qun, WANG Zhong-min, FENG Zhen-yu, LIU Hong-zhao
2001, 22(12): 1291-1298.
Abstract(2443) PDF(798)
Abstract:
On the basis of some studies of elastic pipe conveying fluid, the dynamic behavior and stability of Maxwell viscoelastic pipes conveying fluid with both ends simply supported, which are gyroscopic conservative system, were investigated by using the finite difference method and the corresponding recurrence formula. The effect of relaxation time of viscoelastic materials on the variation curve between dimensionless flow velocity and the real part and imaginary part of dimensionless complex frequencies in the first three order modes were analyzed concretely. It is found that critical flow velocities of divergence instability of Maxwell viscoelastic pipes conveying fluid with both ends simply supported decrease with the decrease of the relaxation time, while after the onset of divergence instability (buckling) critical flow velocities of coupled-mode flutter increase with the decrease of the relaxation time. Particularly, in the case of greater mass ratio, with the decrease of relaxation time, the onset of coupled-mode flutter delays, and even does not take place. When the relaxation time is greater than 103, stability behavior of viscoelastic pipes conveying fluid is almost similar to the elastic pipes conveying fluid.
Linear and Nonlinear Aerodynamic Theory of Interaction Between Flexible Long Structure and Wind
XU Xu, CAO Zhi-yuan
2001, 22(12): 1299-1308.
Abstract(2601) PDF(882)
Abstract:
In light of the characteristics of the interactions between flexible structure and wind in three directions, and based on the rational mechanical section-model of structure, a new aerodynamic force model is accepted, i. e. the coefficients of three component forces are the functions of the instantaneous attack angle and rotational speed Ci=Ci(β(t),θ),(#em/em#=D,L,M). so, a new method to formulate the linear and nonlinear aerodynamic items of wind and structure interacting has been put forward in accordance with "strip theory" and modified "quasi-static theory", and then the linear and nonlinear coupled theory of super-slender structure for civil engineering analyzing are converged in one model. For the linear aerodynamic-force parts, the semi-analytical expressions of the items so called "flutter derivatives" corresponding to the one in the classic equations have been given here, and so have the nonlinear parts. The study of the stability of nonlinear aerodynamic-coupled torsional vibration of the Old Tacoma Bridge shows that the form and results of the nonlinear control equation in rotational direction are in agreement with that of V. F. Bhm's.
Iterative Process for Certain Nonlinear Mappings With Lipschitz Condition
GU Feng
2001, 22(12): 1309-1316.
Abstract(2225) PDF(701)
Abstract:
Using the new analysis techniques, the problem of iterative approximation of solutions of the equation for Lipschitz φ-strongly accretive operators and of fixed points for Lipschitz φ-strongly pseudo-contractive mappings are discussed. The main results of this paper improve and extend the corresponding results obtained by Chang, Chidume, Deng, Ding, Tan-Xu and Osilike.
General Expressions of Constitutive Equations for Isotropic Elastic Damaged Materials
TANG Xue-song, JIANG Chi-ping, ZHENG Jian-long
2001, 22(12): 1317-1323.
Abstract(2690) PDF(807)
Abstract:
The general expressions of constitutive equations for isotropic elastic damaged materials were derived directly from the basic law of irreversible thermodynamics. The limitations of the classical damage constitutive equation based on the well-known strain equivalence hypothesis were overcome. The relationships between the two elastic isotropic damage models (i. e. single and double scalar damage models) were revealed. When a single scalar damage variable defined according to the microscopic geometry of a damaged material is used to describle the isotropic damage state, the constitutive equations contain two "damage effect functions", which describe the different influences of damage on the two independent elastic constants. The classical damage constitutive equation based on the strain equivalence hypothesis is only the first order approximation of the general expression. It may be unduly simplified and may fail to describe satisfactorily the damage phenomena of practical materials.
Existence and Multiplicity of Positive Solutions for a Fourth-Order p-Laplace Equations
BAI Zhan-bing
2001, 22(12): 1324-1328.
Abstract(2281) PDF(853)
Abstract:
The solvability of one-dimensional fourth-order p-Laplace equations of the type (g(u"))"+λa(t)f(u)=0 0p-2v,p>1 is investigated. With cone compression/extension theorem, some existence and multiplicity results of positive solution have been required according to different growth condition of nonlinear form f at zero and at infinity.
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