LARGE RANGE ANALYSIS FOR NONLINEAR DYNAMIC SYSTEMS——ELEMENT MAPPING METHOD

This paper presents a new method for global analysis of nonlinear system. By means of transforming the nonlinear dynamic problems into point mapping forms which are single-valued and continuous, the state space can be regularly divided into a certain number of finitely small triangle elements on which the non-linear mapping can be approximately substituted by the linear mapping given by definition. Hence, the large range distributed problem of the mapping fixed points will be simplified as a process for solving a set of linear equations. Still further, the exact position of the fixed points can be found by the iterative technique. It is convenient to judge the stability of fixed points and the shrinkage zone in the state space by using the deformation matrix of linear mapping. In this paper, the attractive kernel for the stationary fixed points is defined, which makes great advantage for describing the attractive domains of the fixed points. The new method is more convenient and effective than the cell     

ANALYSIS OF NONLINEAR LARGE DEFORMATION PROBLEMS BY BOUNDARY ELEMENT METHOD

In this paper, the author deduces an approximate solution of nonlinear influence function in rate form for two-dimensional elastic problems on current configuration by the method of comoving coordinate system. Here BEM formulation of large deformation based on Chen's theory is given. The computational processes of nonlinear boundary integral equation is discussed. The author also compiles a nonlinear computing program NBEM. Numerical examples show that the results presented here is available to the solution of engineering problems.     

NUMERICAL METHOD IN DYNAMIC RESPONSE OF NONLINEAR SYSTEMS

A kind of modal synthesis techniques.which is applicable to vibration analysis forlinear substructures with nonlinear coupling attachments,has been extended to nonlineardynamic analysis of large complex structural systems.In this paper,a process issuggested to dynamic analysis of large complex structural systems with nonlinearcharacteristics of each substructure.At the end of this paper,an example showsthe defendable accuracy of the results and high efficiency of this process.     

THE NONLINEAR NUMERICAL ANALYSIS METHOD FOR FRAMES

This paper gives the direct formulas of stiffness matrixes of two kinds of Kirchhoffnonlinear elements under total-Lagrange coordinate.For the first one,it includes not onlythe quadric terms of increments of strain and displacement but also.the influence ofrotations.For the second one,it is simplifies and its nonlinear is considered by taking intoaccount the influence of axial force on the equilibrium epuation in the linear beam.theory.The nonlinear equation obtained from both of the above-said elements is solved bymixed Newton-Raphson method,and by comparing the results obtained from two kinds ofnonlinear beam some important conclusions that we can know how to use them right aregiven in our paper.     

THE GLCBAL ANALYSIS OF HIGHER ORDER NONLINEAR DYNAMICAL SYSTEMS AND THE APPLICATION OF CELL-TO-CELL MAPPING METHOD

In this paper,the general characteristics and the topological consideration of theglobal behaviors of higher order nonlinear dynamical systems and the characteristics of theapplication of cell-to-cell mapping method in this analysis are expounded.Specifically,theglobal analysis of a system of two weakly coupled van der Poloscillators using cell-to-cellmapping method is presented.The analysis shows that for this system,there exist two stable limit cycles is 4-dimensional state space,and the whole 4-dimensional state space is divided into two almostequal parts which are,respectively,the two asymptotically stable domains of attraction ofthe two periodic motions of the two stable limit cycles.The validities of these conclusiosabout the global behaviors are also verified by direct lng term numerical integration.Thus.it can be seen that the cell-to-cell mapping method for global analysis of fourth ordernonlinear dynamical systems is quite effective.     

DYNAMIC ANALYSIS 0F NONLINEAR SYSTEMS BY MODAL SYNTHESIS TECHNIQUES

Different kinds of modal synthesis method have been used wide-ly in dynamic analysis of linear structure systems,but,ingeneral.they are not suitable for nonlinear systems.In this paper,a kind of modal synthesis techniques isextended to dynamic analysis of nonlinear systems.The proce-dure is based upon the method suggested in[20].[21].which isapplicable to vibration analysis for complex structure systemswith coupling attachments but with simplified forms of linearsprings and dampers.In fact.these attachments have nonlinearcharacteristics as those generally known to the cases of nonli-near elasticity and nonlinear damping,e.g.,piecewise-linearsprings.softening or hardening springs.coulomb damping,elas-toplastic hysteresis damping.etc..so long as the componentsof structure are still linear systems,we can get a set of in-dependent free-interface normal mode information but only keepthe lower-order for each component.This can be done by com-putations or experiments or both.The global equations of li-near vib     

FINITE ELEMENT METHOD COMBINED WITH DYNAMIC PHOTOELASTIC ANALYSIS TO DETERMINE DYNAMIC STRESS-INTENSITY FACTORS

The present paper is addressed to the finite element method combined with dynamicphotoelastic analysis of propagating cracks,that is,on the basis of[1]by Chien Wei-zang,finite elements which incorporate the propagating crack-tip singularity intrinsic to two-dimensional elasticity are employed.The relation between crack opening length and timestep obtained from dynamic photoelastic analysis is used as a definite condition for solvingthe dynamic equations and simulating the crack propagations as well.As an example,theimpact response of dynamic-bending-test.specimen is investigated and the dynamic stress-intensity factor obtained from the mentioned finite element analysis and dynamicphotoelasticity is in reasonable agreement with each other.     

SEMI-ANALYTICAL AND SEMI-NUMERICAL METHOD FOR DYNAMIC ANALYSIS OF FOUNDATION

A semi-analytical and semi-numerical method is proposed for the dynamic analysis of foundations. The Lamb's solution and the approximate formulae were used to establish the relation of the contact force and deflection between the foundation and soil. Therefore, the foundation can be separated from soil and analyzed by FEM as for the static cases. The plate can be treated as that the known forces are acting on the upper surface, and the contact pressure from soil can be represented as the deflection. So that only the plate needs to be divided into elements in the analysis. By this method, a series of vibration problems, including various shapes and rigidities of foundations, different excitation frequencies, were analyzed. Furthermore, it can be used for the embedded foundation. The numerical examples show that this method has simplicity, highly accurate and versatile. It is an effective method for the dynamic analysis of foundations.     

A TIME DOMAIN BOUNDARY ELEMENT METHOD FOR WATER-SOLID IMPACT ANALYSIS

A reciprocal theorem of dynamics for potential flow problems is first derived by meansof the Laplace transform in which the compressibility of water is taken into account.Based on this the-orem,the corresponding time-space boundary integral equation is obtained.Then,a set of time do-main boundary element equations with recurrence form is immediately formulated through discretiza-tion in both time and boundary.After having carried out the numerical calculation two solutions arefound in which a rigid semicircular cylinder and a rigid wedge with infinite length suffer normal impacton the surface of a half-space fluid.The results show that the present method is more efficient than theprevious ones.     

THE CONSTRUCTION OF LARGE ELEMENT IN FINITE ELEMENT METHOD

In the usual finite element method.the order of the inter-polation in an element is kept unchanged.and the accuracyis raised by subdividing the grid denser and denser.Alter-natively.in the large element method.the grid is kept un-changed.and the terms of approximate series in the elementare increased to raise the accuracy.In this paper,a method for constructing large elementsis presented.when using this method,two sets of variables.one set defined inside the element.and the other defined onthe boundary of the element.are adopted.Then,these twosets of variables are combined by the hybrid-penalty functionmethod.This method can be applied to any elliptic equationsin a domain With arbitrary shape and arbitrary complex boun-dary condition.It is proved with strict mathematical methodin this paper.that in general cases,the accuracy of this me-thod is much higher than that of the usual element and thelarge element method presented in[7].Therefore.the deqreesof freedom needed in this method are much fewer than t     

INCREMENTAL ANALYSIS FOR NONLINEAR RUBBER-LIKE MATERIALS BY HYBRID STRESS FINITE ELEMENT

In this paper,on the basis of the incremental Reissner variational principle.a nonlinearfinite element analysis has been accomplished and a formulation of hybrid stress elementhas been presented for incompressible Mooney rubber-like materials.The corrected termsof the non-equilibrium force and the incompressibility deviation are considered in theformulation.The computed values of numerical example agree very closely with the exactsolution.     

BOUNDARY ELEMENT METHOD FOR BUCKLING EIGENVALUE PROBLEM AND ITS CONVERGENCE ANALYSIS

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DAMAGE ANALYSIS BY BOUNDARY ELEMENT METHOD

The response of cracked bodies subjected to loading was investigated bythe boundary element method in this paper.The two-law elastic-cohesive-softeningmodel was used for crack propagation analysis.The interface conditions foruncracked,craze,open crack,adhesive crack and slid crack parts were discussed andthe corresponding incremental iteration algorithm was given.A simplified damagepropagation model was presented.The technique has been applied to some specificexamples which give the evidence that the method is satisfactory and efficient.     

THE FINITE DYNAMIC ANNULAR ELEMENT FOR THE VIBRATION ANALYSIS OF VARIABLE THICKNESS DISCS

According to the gyro-periodicity of dynamic displacements, the two-dimensional problems of circular plates with variable thickness are simplified into one-dimensional ones in this paper. Taking the expanded form of frequency power series of the dynamic displacement functions as the dynamic shape functions of the finite annular element, the mass and stiffness matrices as well as their one-order revised matrices are given succinctly. The dynamic method is used to analyse the vibration characteristics of a bladed disc assembly and is compared with conventional finite element method and experiment, and is proved to be superior to other numerical methods.     

STUDY ON PREDICTION METHODS FOR DYNAMIC SYSTEMS OF NONLINEAR CHAOTIC TIME SERIES＊

The prediction methods for nonlinear dynamic systems which are decided by chaotic time series are mainly studied as well as structures of nonlinear self-related chaotic models and their dimensions. By combining neural networks and wavelet theories, the structures of wavelet transform neural networks were studied and also a wavelet neural networks learning method was given. Based on wavelet networks, a new method for parameter identification was suggested, which can be used selectively to extract different scales of frequency and time in time series in order to realize prediction of tendencies or details of original time series. Through pre-treatment and comparison of results before and after the treatment, several useful conclusions are reached:High accurate identification can be guaranteed by applying wavelet networks to identify parameters of self-related chaotic models and more valid prediction of the chaotic time series including noise can be achieved accordingly.     

NONLINEAR DYNAMIC ANALYSIS OF FLEXIBLE MULTIBODY SYSTEM

The nonlinear dynamic equations of a multibody system composed of ?exible beams are derived by using the Lagrange multiplier method. The nonlinear Euler beam theory with inclusion of axial deformation e?ect is employed and its deformation ?eld is …     

A FINITE ELEMENT METHOD FOR STRESS ANALYSIS OR ELASTOPLASTIC BODY WITH POLYGONAL LINE STRAIN——HARDENING

In this paper, the stress-strain curve of material is fitted bg polygonalline composed of three lines. According to the theory of proportional loading in elastoplasticity, we simplify the complete stress-strain relations, which are given by the increment theory of elastoplasticity. Thus, the finite element equation with the solution of displacement is derived. The assemblage elastoplastic stiffness matrix can be obtained by adding something to the elastic matrix, hence it will shorten the computing time. The determination of everg loading increment follows the yon Mises yield criteria. The iterative method is used in computation. It omits the redecomposition of the assemblage stiffness matrix and it will step further to shorten the computing time. Illustrations are givento the high-order element applicatioη departure from proportional loading, the computation of unloading fitting to the curve and the problem of load estimation.     

ANALYSIS OF NONLINEAR DYNAMIC RESPONSE FOR VISCOELASTIC COMPOSITE PLATE WITH TRANSVERSE MATRIX CRACKS

I. INTRODUCTION The composite material and the composite structure are liable to generate damage during manufactureand under load, which will lead to a decrease of the material and structure’s mechanical properties.It is accepted that there exist four…     

A FINITE ELEMENT METHOD FOR STRESS ANALYSIS OR ELASTOPLASTIC BODY WITH POLYGONAL LINE STRAIN——HARDENING

In this paper, the stress-strain curve of material is fitted by polygonal line composed of three lines. According to the theory of proportional loading in elastoplasticity, we simplify the complete stress-strain relations, which are given by the increment theory of elastoplasticity. Thus, the finite element equation with the solution of displacement is derived. The assemblage elastoplastic stiffness matrix can be obtained by adding something to the elastic matrix, hence it will shorten the computing time. The determination of every loading increment follows the von Mises yield criteria. The iterative method is used in computation. It omits the redecomposition of the assemblage stiffness matrix and it will step further to shorten the computing time. Illustrations are given to the high-order element application departure from proportional loading, the computation of unloading fitting to the curve and the problem of load estimation.     

SELF-ADAPTIVE STRATEGY FOR ONE-DIMENSIONAL FINITE ELEMENT METHOD BASED ON ELEMENT ENERGY PROJECTION METHOD

Based on the newly-developed element energy projection (EEP) method for computation of super-convergent results in one-dimensional finite element method (FEM), the task of self-adaptive FEM analysis was converted into the task of adaptive piecewise polynomial interpolation. As a result, a satisfactory FEM mesh can be obtained, and further FEM analysis on this mesh would immediately produce an FEM solution which usually satisfies the user specified error tolerance. Even though the error tolerance was not completely satisfied, one or two steps of further local refinements would be sufficient. This strategy was found to be very simple, rapid, cheap and efficient. Taking the elliptical ordinary differential equation of second order as the model problem, the fundamental idea, implementation strategy and detailed algorithm are described. Representative numerical examples are given to show the effectiveness and reliability of the proposed approach.