THE GENERAL DERIVATION OF RITZ METHOD AND TREFFTZ METHOD IN ELASTOMECHANICS

This paper derives the Ritz method and Trefftz method in li-near elastomechanis with the help of general mathematicalexpressions.Thus it is proved that Ritz method gives theupper bound of the corresponding functional extremum,whileTrefftz method gives its lower bound.At the same time ithas been found that the eigenvalue problem(e.g.the naturalfrequency problem)concerning the functional variational me-thod in Trefftz method is in concord with the lower boundmethod of the loosened boundary condition which seeks forthe eigenvalue.of course,the results of this derivationare also applicable to the sort of functional variationalmethod of which Euler’s equation is linear positive defi-nite.     

THE APPLICATION AND EXTENSION OF SACHS METHOD

In this paper,we present the simplification of Sachs formulas for the measurement andcalculation of the residual stresses of the eylinder only with the plane stresses.Furthermore,we present the method for the meaurement and calculation of the residual stresses of thecylinder not only with the finite length but with the longitudinal stress.These can be appliedto the investigation on the residual stresses of the autofretted gun tube.     

VARIATIONAL METHOD AND COMPUTATION FOR H_∞ CONTROL

ＩｎｔｒｏｄｕｃｔｉｏｎＨ∞ｃｏｎｔｒｏｌｔｈｅｏｒｙｈａｓｂｅｅｎｗｅｌｌｄｅｖｅｌｏｐｅｄｓｉｎｃｅｔｈｅＤＧＫＦｐａｐｅｒ[1],ｗｈｅｒｅｔｈｅｆｕｎｄａｍｅｎｔａｌｅｑｕａｔｉｏｎｓｆｏｒＨ∞ ｍｅａｓｕｒｅｍｅｎｔｆｅｅｄｂａｃｋｃｏｎｔｒｏｌａｒｅｄｅｒｉｖｅｄｆｒｏｍｔｈｅｓｅｐａｒａｔｉｏｎｐｒｉｎｃｉｐｌｅ ,ａｓｉｎＬＱＧｃｏｎｔｒｏｌｔｈｅｏｒｙ[2～ 5 ].Ｈｏｗｅｖｅｒ,ｔｈｅｃｏｍｐｕｔａｔｉｏｎｆｏｒｆｉｎｉｔｅｈｏｒｉｚｏｎ [0 ,ｔｆ]ｐｒｏｂｌｅｍａｎｄｔｈｅｄｅｔｅｒｍｉ…     

SOLUTION OF NONLINEAR HEAT CONDUCTION EQUATION AND IMAGE METHOD

In this paper,the author proves that, for a nonlinear heat conduction equation, there is no discontinuous solution. Some methods of solution for a nonlinear conduction equation are depicted. For a plane interface, the reflection and transmission of a heat wave are given by the method of images. The 1st order of approximation of this method is proved. Lastly, the prevention of superheated electrons is laser implosion of deuterium tritium gas sphere with a shell made of high Z material is interpreted.     

MIXED HYBRID PENALTY FINITE ELEMENT METHOD AND ITS APPLICATION

The penalty and hybrid methods are being much used in dealing with the general incompatible element. With the penalty method convergence can always be assured, but comparatively speaking its accuracy is lower; and the condition number and sparsity are not so good. With the hybrid method, convergence can be assured only when the rank condition is satisfied. So the construction of the element isextremely limited. This paper presents the mixed hybrid penalty element method, which combines the two methods together.And it is proved theoretically that this new method is convergent, and it has the same accuracy, condition number and sparsity as the compatible element.That is to say, they are optimal to each other. Finally, a new triangle element for plate bending with nine freedom degrees is constructed with this method (three degrees of freedom are given on each corner——one displacement and two rotations), the calculating formula of the element stiffness matrix is almost the same as that of the old triangle     

A DISCRETE NONLINEAR STEPPING OPTIMIZATION METHOD AND ITS APPLICATION

Most of the practical design variables should always be discrete quantity within engineering optimization design problems. To obtain the true optimization solution, a discrete optimization method must be used. In this paper, a new method called step optimization search method is presented to solve the discrete quantity mathematic programming problems. The basic idea oft his method is to find out an initialfeasible point and then to search the optimum point step by step in the neighbouring region of this point so as to obtain an improved new discrete point. Respectively, the new point can be taken us initial one, and the whole process can be carried out once more until the optimum solution of the problem is obtained. Some results of numerical examples of practical problems show that this new method can solve problems quickly and simply and can be applied in a lot of engineering design problems.     

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.     

GENERALIZED VARIATIONAL PRINCIPLES WITH SEVERAL ARBITRARY PARAMETERS AND THE VARIABLE SUBSTITUTION AND MULTIPLIER METHOD

The functional transformations of variational principles in elasticity are classified asthree patterns:Ⅰ relaxation pattern,Ⅱ augmented pattern and Ⅲ equivalent pattern.On the basis of pattern Ⅲ,the generalized variational principles with several arbitraryparameters are formulated and their functionals are defined They are:the generalizedprinciple of single variable u with several parameters,the generalized principle of twovariables u,σ with several parameters,the generalized principle of two variables u,εwith several parameters,and the generalized principle of three veriables u,ε.σ withseveral parameters.From these principles,a series of new forms of equivalent functionalscan be obtained.When the values of these parameters are properly chosen.a series of finiteelement models can be formulated.In this paper,the question of losing effectiveness for Lagrange multiplier method isalso discussed.In order to“recover”effectiveness for multiplier method,a modifiedmethod,namely,the variable substitutio     

EXTENSION AND APPLICATION OF NEWTON''''S METHOD IN NONLINEAR OSCILLATION THEORY

In this paper we suggest and prove that Newton's method may calculate the asymptotic analytic periodic solution of strong and weak nonlinear nonautonomous systems, so that a new analytic method is offered for studying strong and weak nonlinear oscillation systems. On the strength of the need of our method, we discuss the existence and calculation of the periodic solution of the second order nonhomogeneous linear periodic system. Besides, we investigate the application of Newton's method to quasi-linear systems. The periodic solution of Duffing equation is calculated by means of our method.     

AN IMPROVED M-C METHOD AND ITS APPLICATION TO STRUCTURAL RELIABILITY

An improved Monte-Carlo method for the failure calculation of structureis proposed.The present method can determine whether some sample points are in thesafe region without doing structural analysis,so the calculation work is greatly reducedcompared with the ordinary M-C method.Finally,the new M-C method is applied toreliability analysis of frame and the torsional buckling reliability analysis of cylindricalshells.     

THE CONVERGENT CONDITION AND UNITED FORMULA OF STEP REDUCTION METHOD

The step reduction method was first suggested by Prof. Yeh Kai-yuan. This method has more advantages than other numerical methods. By this method, the analytic expression of solution can he obtained for solving nonuniform elastic mechanics. At the same time. its ealculuting time is very short and convergent speed very fast. In this paper, the convergent condition and nited formula of step reduction method are given by mathemutical method. It is proved that the solution of displacement and stress resultants obtained by this method can eonverge to exact solution uniformly, when the convergent condition is sutisfied. By united formula, the analytic solution solution can be expressed as matrix form, and therefore the former complicated expression can be avoMed. Two numerical examples are given at the end of this paper which indicate that. by the theory in this paper, a right model can be obtained for step reduction method.     

NEW METHOD FOR LOW ORDER SPECTRAL MODEL AND ITS APPLICATION

In order to overcome the deficiency in classical method of low order spectral model, a new method for low order spectral model was advanced. Through calculating the multiple correlation coefficients between combinations of different functions and the recorded data under the least square criterion, the truncated functions which can mostly reflect the studied physical phenomenon were objectively distilled from these data. The new method overcomes the deficiency of artificially selecting the truncated functions in the classical low order spectral model. The new method being applied to study the inter-annual variation of summer atmospheric circulation over Northern Hemisphere, the truncated functions were obtained with the atmospheric circulation data of June 1994 and June 1998. The mechanisms for the two-summer atmospheric circulation variations over Northern Hemisphere were obtained with two-layer quasi-geostrophic baroclinic equation.     

DEFECT AND IMPROVEMENT OF TWO-TIME EXPANSION METHOD IN NONLINEAR OSCILLATIONS

In this paper,the defect of the Two-Time Expansion method is indicated and animprovement of this method is suggested.Certain examples,in which the present method isused,are given.Moreover,the paper shows the equivalence of the improved Two-TimeExpansion Method and the method of KBM‘(Krylov-Bogoliubov-Mitropolsk i).     

NEW METHOD OF SOLVING LAME-HELMHOLTZ EQUATION AND ELLIPSOIDAL WAVE FUNCTIONS

Despite the great significance of equations with doubly-periodic coefficients in the methods of mathematical physics, the problem of solving Lamé-Helmholtz equation still remains to be tackled. Arscott and M(?)glich method of double-series expansion as well as Malurkar nonlinear integral equation are incapable of reaching the final explicit solution. Our main result consists in obtaining analytic expressions for ellipsoidal wave functions of four species including the well known Lame functions E_(ci)(sna),E_(si)(sna) as special cases.This is effected by deriving two integro-differential equations with variable coefficients and solving them by integral transform. Generalizing Riemann's idea of P function, we introduce D function to express their transformation properties o     

GENERALIZED WHITTAKER EQUATIONS AND FIELD METHOD IN GENERALIZED CLASSICAL MECHANICS

This paper presents the energy integral in generalized classical mechanics.Theintegral enables us to reduce a given canonical system with2n order to another system withonly(2n-2)order and to obtain generalized Whittaker equations.And then,this paperextends a field method integrating the equations of motion for classical mechanics togeneralized classical mechanics.Finally,this paper gives an example to illustrate theapplication of these equations and the field method.     

C- METHOD AND ITS APPLICATION TO ENGINEERING NONLINEAR DYNAMICAL PROBLEMS

ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｓｉｄｅｒｔｈｅｄｙｎａｍｉｃｓｙｓｔｅｍｓｄｅｓｃｒｉｂｅｄｂｙｔｈｅｆｏｌｌｏｗｉｎｇｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎ : ｘ=ｆ(ｘ) ,( 1 )ｗｈｅｒｅｘａｎｄｆａｒｅｎ＿ｄｉｍｅｎｓｉｏｎａｌｒｅａｌｖｅｃｔｏｒｓ,ａｎｄｔｈｅｄｏｔｉｎｄｉｃａｔｅｓｄｉｆｆｅｒｅｎｔｉａｔｉｏｎｗｉｔｈｒｅｓｐｅｃｔｔｏｔｉｍｅ ,ｔ.Ｓｕｐｐｏｓｅｔｈａｔｘ=ｕ(ｔ)ｉｓａｐｅｒｉｏｄｉｃｓｏｌｕｔｉｏｎｏｆＥｑ .( 1 )ｗｉｔｈｐｅｒｉｏｄｉｃ,ｓａｙ ,Ｔ .ＫｒｙｌｏｖａｎｄＢ…     

SPACE-TIME FINITE ELEMENT METHOD FOR SCHRODINGER EQUATION AND ITS CONSERVATION

Energy conservation of nonlinear Schrodinger ordinary differential equation was proved through using continuous finite element methods of ordinary differential equation; Energy integration conservation was proved through using space-time continuous fully discrete finite element methods and the electron nearly conservation with higher order error was obtained through using time discontinuous only space continuous finite element methods of nonlinear Schrodinger partial equation. The numerical results are in accordance with the theory.     

DYNAMIC CHARACTERISTIC ANALYSIS OF FUZZY- STOCHASTIC TRUSS STRUCTURES BASED ON FUZZY FACTOR METHOD AND RANDOM FACTOR METHOD

A new fuzzy stochastic finite element method based on the fuzzy factor method and random factor method is given and the analysis of structural dynamic characteristic for fuzzy stochastic truss structures is presented. Considering the fuzzy randomness of the structural physical parameters and geometric dimensions simultaneously, the structural stiffness and mass matrices are constructed based on the fuzzy factor method and random factor method; from the Rayleigh's quotient of structural vibration, the structural fuzzy random dynamic characteristic is obtained by means of the interval arithmetic; the fuzzy numeric characteristics of dynamic characteristic are then derived by using the random variable's moment function method and algebra synthesis method. Two examples are used to illustrate the validity and rationality of the method given. The advantage of this method is that the effect of the fuzzy randomness of one of the structural parameters on the fuzzy randomness of the dynamic characteristic can be reflected expediently and objectively.     

THE CONJUGATE GRADIENT METHOD AND BLOCK ITERATIVE METHOD FOR PENALTY FINITE ELEMENT OF THREE DIMENSIONAL NAVIER-STOKES EQUATION

A conjugate gradient and block iterative algorithm for ele-ment solution of penalty variational form of Navier-Stokes eq-uations are presented.Because the algorithm of solving single variable minimizing problem is simplified,the computing time is greatly saved.In this paper numerical examples are also provided.