THE MECHANICAL METHOD OF CONSTRUCTING THE DISPLACEMENT FUNCTIONS IN ELASTICITY

In this Paper we have proven the general solution to the equations of linear operatorsAu=f as u=Cv+e . where v satisfies the equation Dv=g and D is adiagonal matrix. Basing on the consstructive proof of Hilbert Nullstellensat=. we haregiven the mechanical method of constucting C. D and e.and some of the mechanicalalgorithm displacement functions in elasticity are given by this method also .

THE DISPLACEMENT FUNCTION OF QUASI-CONFORMING ELEMENT AND ITS NODE ERROR

Based on the strain formulation of the quasi-conforming finite element, displacement functions are constructed which have definite physical meaning, and a conclusion can be obtained that the coefficients of the constant and the linear strain are uniquely determined, and the quasi-conforming finite element method is convergent to constant strain. There are different methods for constructing the rigid displacement items, and different methods correspond to different order node errors, and this is different from ordinary displacement method finite element.

THE DISPLACEMENT SOLUTION OF CONICAL SHELL AND ITS APPLICATION

In this paper, the displacement solution method of the conical shell is presented. From the differential equations in displacement form of conical shell and by introducing a displacement function, U,the differential equations are changed into an eight-order soluble partial differential equation about the displacement Junction U in which the coefficients are variable. A t the same time, the expressions of the displacement and internal force components of the shell are also given by the displacement function. As special cases of this paper, the displacement function introduced by V. Z. Vlasov in circular cylindrical shell, the basic equation of the cylindrical shell and that of the circular plate are directly derived.Under the arbitrary loads and boundary conditions, the general bending problem of the conical shell is reduced to finding the displacement functionU,and the general solution of the governing equation is obtained in generalized hypergeometric function, For the axisymmetric bending deformation of the conical shell, the general solution is expressed in the Bessel functionOn the basis of the governing equation obtained in this paper, the differential equation of conical shell on the elastic foundation (A Winkler Medium) is deduced, its general solutions are given in a power series, and the numerical calculations are carried out.

BUCKLING OF SPATIAL CURVED RODS WITH CIRCULAR CROSS-SECTIONS

Formulae for determining Green strain of an initially curved and twisted rod with circular cross-sections are derived by using the natural (curvilinear) coordinate system. Finite element analyses are performed for the flexural buckling of initially curved and twisted thin rods under simultaneous action of axial force and torque. Numerical examples demonstrate that the given formulae are correcte. Some numerical results are compared with existing analytical solutions and data obtained by commercial FE software. The convergence of the proposed curved element is better than that of elements in the commercial FE software. It is shown that good accuracy and convergency are achieved by solving three-dimensional problems.

FREE VIBRATION OF PIEZOELECTRIC CYLINDRICAL SHELLS

Three displacement functions are introduced to represent each mechanical displacement according to the 3-D theory in this paper. By expanding the displacement functions and the electric potential in orthogonal series, the free vibration equation of piezoelectric cylindrical shells satisfying SS3 boundary conditions can be obtained. The equation was solved by utilizing Bessel functions with complex arguments. Results are presented graphically as well as in table, and compared with those of other references. Some frequencies that were missing in Ref. [9] are discovered.

A time-dependent numerical model of the mild-slope equation

On the basis of the previous studies, the simplest hyperbolic mild-slope equation has been gained and the linear time - dependent numerical model for the water wave propagation has been established combined with different boundary conditions. Through computing the effective surface displacement and transforming into the real transient wave motion, related wave factors will be calculated. Compared with Lin＇s model, analysis shows that calculation stability of the present model is enhanced efficiently, because the truncation errors of this model are only contributed by the dissipation terms, but those of Lin＇s model are induced by the convection terms, dissipation terms and source terms. The tests show that the present model succeeds the merit in Lin＇ s model and the computational program is simpler, the computational time is shorter, and the computational stability is enhanced efficiently. The present model has the capability of simulating transient wave motion by correctly predicting at the speed of wave propagation, which is important for the real - time forecast of the arrival time of surface waves generated in the deep sea. The model is validated against analytical solution for wave diffraction and experimental data for combined wave refraction and diffraction over a submerged elliptic shoal on a slope. Good agreements are obtained. The model can be applied to the theory research an d engineering applications about the wave propagation in a biggish area.

The elastic dynamics analysis of band saw tightening system

In this paper, the node movement analysis of the levers of band saw tightening system is developed. A group of theoretical displacement and distortion equations of levers are presented using the Lagrange’s equation. This could be the basis for the future research in the field of band saw’s tightening system dynamics analysis.

Bolt support mechanism based on elastic theory

Mechanical model of anchorage surrounding rock considering tray effect was established based on elastic theory,in order to study the mechanism of bolt supporting.Elastic solutions of normal force at point in the interior of a semi-infnite solid were obtained by means of classical displacement function method in elasticity.The factors which influence stress of bolted surrounding rock,such as the length of bolt and tray effect,were analyzed.The absolute value of stress along bolt axes decreased rapidly with an increase in radical distance and the maximum appeared near ends of bolt.With increasing radical distance,the value of radical stress changed from positive to negative roughly and then increased to zero,with maximum at the middle of bolt.The evolution of hoop stress as radical distance increasing was similar with stress along bolt axes.With an increase in depth,the radical effect ranges of all normal stress components were reduced.These suggest that the effect from tray on stress along bolt axes of bolted surrounding rock could be neglected,except near surface of surrounding rock.

NATURAL FREQUENCY FOR RECTANGULAR ORTHOTROPIC CORRUGATED-CORE SANDWICH PLATES WITH ALL EDGES SIMPLY-SUPPORTED

A simple approach to reduce the governing equations for orthotropic corrugated core sandwich plates to a single equation containing only one displacement function is presented, and the exact solution of the natural frequencies for rectangular corrugated-core sandwich plates with all edges simply-supported is obtained. Furthermore, two special cases of practical interests are discussed in details.

EXACT STATIC ANALYSIS OF A ROTATING PIEZOELECTRIC SPHERICAL SHELL

An exact analysis of a rotating piezoelectric spherical shell with arbitrary thickness is given. Three displacement functions are introduced to simplify the basic equations of a spherically isotropic, piezoelectric medium. By expanding the displacement functions as well as the electric potential in terms of spherical harmonics, the basic equations of equilibrium are converted to an uncoupled Euler type, second order ordinary differential equation and a coupled system of three second order ordinary differential equations. A general solution to the homogeneous equations of equilibrium is then derived. The static analysis of a rotating spherical shell is performed and the numerical example is presented. (Edited author abstract) 13 Refs.

Fractional viscoelastic solution of stratum displacement of a shallow tunnel under the surface slope condition

The unified displacement function(UDF)is presented to describe the deformation behaviours of the tunnel profile along with time under the surface slope condition.Based on the discrete Fourier method,the third-order UDF in the physical plane is expanded to the Laurent series in the complex variable plane.The complex variable method is employed to derive the elastic analytical solution of stra-tum displacement,when the third-order UDF is taken as the displacement boundary condition of tunnel cross-section(DBCTC).The proposed elastic solution agrees well with the results of the finite element method for the consistent model,which verifies the correctness of the proposed analytical solution.Combining the corresponding principle and fractional Generalized Kelvin viscoelastic constitutive model,the fractional viscoelastic solution under the surface slope condition is determined.The time effect of stratum displacement is presented in two aspects:time-dependent DBCTC and time-dependent material parameters.The parameter analysis is performed to investigate influences of deformation modes of the third-order UDF,slope angle,tunnel radius and fractional order on the time effect of stratum vertical and horizontal displacement.

A LAGRANGIAN LATTICE BOLTZMANN METHOD FOR EULER EQUATIONS

A Lagrangian lattice Boltzmann method for solving Euler equations is proposed. The key step in formulating this method is the introduction of the displacement distribution function. The equilibrium distribution function consists of macroscopic Lagrangian variables at time steps n and n + 1. It is different from the standard lattice Boltzmann method. In this method the element, instead of each particle, is required to satisfy the basic law. The element is considered as one large particle, which results in simpler version than the corresponding Eulerian one, because the advection term disappears here. Our numerical examples successfully reproduce the classical results.