SOLUTION OF GENERALIZED COORDINATE FOR WARPING FOR NATURALLY CURVED AND TWISTED BEAMS

A theoretical method for static analysis of naturally curved and twisted beams under complicated loads was presented, with special attention devoted to the solving process of governing equations which take into account the effects of torsion-related warping as well as transverse shear deformations. These governing equations, in special cases, can be readily solved and yield the solutions to the problem. The solutions can be used for the analysis of the beams, including the calculation of various internal forces, stresses, strains and displacements. The present theory will be used to investigate the stresses and displacements of a plane curved beam subjected to the action of horizontal and vertical distributed loads. The numerical results obtained by the present theory are found to be in very good agreement with the results of the FEM results. Besides, the present theory is not limited to the beams with a double symmetric cross-section, it can also be extended to those with arbitrary cross-sectional shape.

A Numerical Model of Nonlinear Wave Propagation in Curvilinear Coordinates

For the simulation of the nonlinear wave propagation in coastal areas with complex boundaries, a numerical model is developed in curvilinear coordinates. In the model, the Boussinesq-type equations including the dissipation terms are em- ployed as the governing equations. In the present model, the dependent variables of the transformed equations are the free surface elevation and the utility velocity variables, instead of the usual primitive velocity variables. The introduction of utility velocity variables which are the products of the contravariant components of the velocity vector and the Jacobi ma- trix can make the transformed equations relatively concise, the treatment of lateral boundary conditions easier and the de- velopment of the program simpler. The predictor-corrector method and five-point finite-difference scheme are employed to discretize the time derivatives and the spatial ones, respectively. The numerical model is tested for three cases. It is found that the numerical results are in good agreement with the analytical results and experimental data.

Streamwise Vorticity Equation

A streamwise vorticity equation is derived in generalized natural coordinates. This equation reveals that the total change and local change of the streamwise vorticity are mainly determined by the curvature of streamline, unsteady feature of streamline and magnitude of velocity. This equation enables the study of mesoscale or small-scale systems since the term associated with pressure gradient force in the original vorticity equation is replaced by terms associated with streamlines and wind speed. With this modification the wind field rather than the pressure field is used in the calculation considering that 1) the pressure field is to adapt wind field. 2) Smoother and more consecutive streamline pattern is easier to obtain either by data analysis or by the numerical simulation. From this sense, this present study suggests the application of this equation to studying the evolution of severe storm system as well as other simplified cases. Key words Wind field instead of pressure field - Generalized natural coordinate - Streamwise vorticity This work was supported by the project on the study of the formative mechanism and predictive theory of the significant climate and weather disaster in China under Grant G 1998040907 and by the key project on the Dynamic Study of Severe Mesoscale Covective Systems sponsored by the National Natural Science Foundation of China under Grant No. 49735180.

H_∞ fault estimation for a class of linear time-delay systems in finite frequency domain

This paper deals with the problem of H∞ fault estimation for linear time-delay systems in finite frequency domain.First a generalized coordinate change is applied to the original system such that in the new coordinates all the time-delay terms are injected by the system＇s input and output.Then an observer-based H∞ fault estimator with input and output injections is proposed for fault estimation with known frequency range.With the aid of Generalized Kalman-Yakubovich-Popov lemma,sufficient conditions on the existence of the H∞ fault estimator are derived and a solution to the observer gain matrices is obtained by solving a set of linear matrix inequalities.Finally,a numerical example is given to illustrate the effectiveness of the proposed method.

NUMERICAL SIMULATION OF 2D HORIZONTAL COOLING WATER DISCHARGE IN GENERALIZED CURVILINEAR COORDINATE

2D horizontal model is one of the major mathematical methods for the research on cooling water discharge from the power plant. In this paper, the shallow water equations are transformed under the generalized curvilinear coordinate system and the elliptic differential equations are used to generate curvilinear grids, so a model in generalized curviline ar coordinate is presented to simulate 2D horizontal cooling water, Governing equations of the model are discretized by finite volume method, and non-staggered grids and SIMPLE algorithm are introduced to simplify the program during the discretization. This model is used to simulate the movement of cooling water in a simplified meandering channel and a natural channel, calculating results indicate this model can correctly reflect the movement rules of cooling water, which verifies the model can be applied in engineering practice.

Universal D'Alembert Principle and Equation of Motion for Any Order Nonholonomic Systems in Derivative Space

The important development has been made in studying nonholonomic systems, but many theoretical and practical problems still need to be solved. In order to suit development of analytical mechanism itself and the need of wide-ranging application to other subjects and modem engineering technology, its research method, the mathematical models got with this method and final forms of differential equations of motion still need to be further studied. This article gives up the traditional method which was used to study the nonholonomic systems in 3N dimensional Euclid space "E3N".

Impurity effects of theΛhyperon in the hypernuclear systems^(25)ΛMg and(29)ΛSi

Based on the beyond-mean-field Skyrme-Hartree-Fock model,impurity effects of theΛhyperon in the hypernuclear systems^(25)ΛMg and^(29)ΛSi are investigated,respectively.Four cases,in which theΛhyperon occupies the single-particle orbitals L[000]1+/2,L[110]1-/2,L[101]3-/2 and L[101]1-/2,are focused.In each case,the potential energy surface and the energy curves projected on certain angular momenta are employed to show the influence of theΛhyperon on the nuclear core.Beside the shrinkage effect that is induced by theΛhyperon occupying the sΛorbital,it is found that theΛhyperon on the pΛorbital,L[110]1-/2,drives the nuclear core toward a prolate shape,while the ones on the other two pΛorbitals,L[101]3-/2 and L[101]1-/2,drive the nuclear core toward an oblate shape.The energy spectra and the corresponding intra-band E2 transition rates for the rotational bands are given as a prediction for future experiments.

A CONFORMING QUADRATIC POLYGONAL ELEMENT AND ITS APPLICATION TO STOKES EQUATIONS

In this paper,we construct an H1-conforming quadratic finite element on convex polygonal meshes using the generalized barycentric coordinates.The element has optimal approximation rates.Using this quadratic element,two stable discretizations for the Stokes equations are developed,which can be viewed as the extensions of the P2-P0 and the Q2-(discontinuous)P1 elements,respectively,to polygonal meshes.Numerical results are presented,which support our theoretical claims.

The Existence of Solutions to Sturm-Liouville Boundary Value Problems with Laplacian-like Operator

The existence of infinitely many solutions to Sturm-Liouville boundary value problem with a Laplacian-like operator is studied by applying generalized polar coordinates.