Least-squares finite-element method for shallow-water equations with source terms

Numerical solution of shallow-water equations （SWE） has been a challenging task because of its nonlinear hyperbolic nature, admitting discontinuous solution, and the need to satisfy the C-property. The presence of source terms in momentum equations, such as the bottom slope and friction of bed, compounds the difficulties further. In this paper, a least-squares finite-element method for the space discretization and θ-method for the time integration is developed for the 2D non-conservative SWE including the source terms. Advantages of the method include： the source terms can be approximated easily with interpolation functions, no upwind scheme is needed, as well as the resulting system equations is symmetric and positive-definite, therefore, can be solved efficiently with the conjugate gradient method. The method is applied to steady and unsteady flows, subcritical and transcritical flow over a bump, 1D and 2D circular dam-break, wave past a circular cylinder, as well as wave past a hump. Computed results show good C-property, conservation property and compare well with exact solutions and other numerical results for flows with weak and mild gradient changes, but lead to inaccurate predictions for flows with strong gradient changes and discontinuities.     

THE CRITERION ALGORITHM OF RELATION OF IMPLICATION BETWEEN PERIODIC ORBITS(Ⅰ)

In recent years,there is a wide interest in Sarkovskii’s theorem and the related study.According to Sarkovskii’s theorem if the continuous self-mapf of the closed interval has a3-periodic orbit.then f must has an n-periodic orbit for any positive integer n.But f can not hasall n-periodic orbits for some n.For example,letEvidently,f has only one kind of3-periodic orbit in the two kinds of3-periodic orbits.This explains that it isn’t far enough to uncover the relation between periodic orbits byinformation which Sarkovskii’s theorem has offered.In this paper.we raise the concept oftype of periodic orbits.and give a feasible algorithm which decides the relation ofimplication between two periodic orbits.     

THE CRITERION ALGORITHM OF RELATION OF IMPLICATION BETWEEN PERIODIC ORBITS(Ⅱ)

In recent years,there is a wide interest in Sarkovskii’s theorem and related study.According to Sarkovskii’s theorem,if the continuous self-map f of the closed interval has a3-periodic orbit,then f must has an n-periodic orbit for any positive integer n.But f can nothave all n-periodic orbits for some n.Example.LetEvidently f has only one kind of3-periodic orbit in the two kinds of3-periodic orbits,whichexplains that it isn’t far enough to uncover the relation between periodic orbits by theinformation which Sarkovskii’s theorem has offered.In this paper,we raise the concept oftype of periodic orbits,and give a feasible algorithm which decldes the relation ofimplication between the two kinds of periodic orbits.     

Near wake vortex dynamics of a hovering hawkmoth

Numerical investigation of vortex dynamics in near wake of a hovering hawkmoth and hovering aerodynamics is conducted to support the development of a biology-inspired dynamic flight simulator for flapping wingbased micro air vehicles. Realistic wing-body morphologies and kinematics are adopted in the numerical simulations. The computed results show 3D mechanisms of vortical flow structures in hawkmoth-like hovering. A horseshoe-shaped primary vortex is observed to wrap around each wing during the early down- and upstroke; the horseshoe-shaped vortex subsequently grows into a doughnut-shaped vortex ring with an intense jet-flow present in its core, forming a downwash. The doughnut-shaped vortex rings of the wing pair eventu- ally break up into two circular vortex rings as they propagate downstream in the wake. The aerodynamic yawing and rolling torques are canceled out due to the symmetric wing kinematics even though the aerodynamic pitching torque shows significant variation with time. On the other hand, the time- varying the aerodynamics pitching torque could make the body a longitudinal oscillation over one flapping cycle.     

Research on Haar Spectrum in fault diagnosis of rotating machinery

In this paper,Haar Transform(HT)is used in the fault diagnosis of rotatingmachinery,and the“Impulse Sharpness”is presented as a diagnostic index.At present,Fourier Spectrumanalysis is most widely used Compared with FFT,HT is more rapid incomputation and more effective in discrete approximation.It’s very suitable for theextraction of pulses in the signal.However,HT has some shortcomings.It’s greatlyaffected by the starting point and length of the sample.Here,the authors present a methodto improve the stability and comparability of Haar Spectrum.The fault imitating test ofrolling bearing is carried out,and the results obtained have verified the sensitivity of HaarSpectrum and Impulse Index to the fault.     

Melnikov function and Poincaré map

In this paper we give the relationship between Melnikov function and Poincare map, and a new proof for Melnikov’s method. The advantage of our paper is to give a more explicit solution and to make Melnikov function for the subharmonics bifurcation and Melnikoy function which the stable manifolds and unstable manifolds intersect transversely into a formula.     

The Solution for Axisymmetrical Shells with Abrupt Curvature Change(Corrugated Shells)by the Finite Element Method

It has been noted in the present paper that the finite element method using linear elements for solving axisymmetrical shells cannot be applied to the analysis of axisymmetrical shells with abrupt curvature change,owing to the fact that the influence of the curvature upon the angular displace-ments has been neglected.The present paper provides a finite element method using linear elements in which the influence of curvature is considered and the angular displacements are treated as continuous parameters.This method has been applied to the calculation of corrugated shells of the type C,and compared with the experimental results obtained by Turner-Ford as well as with the analytical solution given by Prof.Chien Wei-zang.The compari-sons have been proved that this theory is correct.     

Expressions for pressure-velocity-gradient correlations

The term for pressure-velocity-gradient correlation was initiated by Rott’srewriting the correlation between the pressure fluctuation gradient and velocity fluctuation.However,it is very difficult to consider the effect of this term.Since Rotta’s work,Launderet al.has made some estimates of this term.In this paper according to the equations forvelocity fluctuation,the pressure fluctuation is solved so that the average value of theproduct of the pressure fluctuation and the velocity fluctuation gradient is obtained.Thus,the whole expressions for the pressure-velocity-gradient correlation are derived.The resultexplains that the limited expressions by Rotta and Launder are reasonable to a certaindegree.The whole expressions in this paper are discussed respectively in two situations:oneis without a separate consideration of large and small vortexes;the other is with a separateconsideration of three kinds of vortexes.Therefore,the paper gives the whole expressions forpressure-velocity-gradient correlation     

ASYMPTOTIC SOLUTION TO A NONLINEAR DIFFUSION PROCESS BY CHIEN-LATTA’S METHOD

In this paper,by using Chien Wei-zang—Latta’s compositeexpansion method[5],we have obtained the first-order asymptoticsolution to a system of equations for a nonlinear diffusion pro-cess,thus simplifying and improving the previous work[4]consi-derably.Moreover,a kind of complete analytical solution hasbeen given for a special case,and the periodic solution at thebifurcation point has been discussed,the related results beingin agreement with the experiments.     

A pre-strain strategy of current collectors for suppressing electrode debonding in lithium-ion batteries

The interfacial debonding between the active layer and the current collector has been recognized as a critical mechanism for battery fading, and thus has attracted great efforts focused on the related analyses. However, much still remains to be studied regarding practical methods for suppressing electrode debonding, especially from the perspective of mechanics. In this paper, a pre-strain strategy of current collectors to alleviate electrode debonding is proposed. An analytical model for a symme...     

EXPERIMENTAL AND NUMERICAL STUDIES ON PERFORMANCE OF MACRO FIBER COMPOSITES FOR BEAM TWISTING APPLICATIONS

This paper presents the use of macro-fiber composites (MFC) as actuators for twisting control of pre-twisted beams, which is one efficient method of vibration suppression techniques of helicopter rotors. An MFC is a piezoelectric fiber composite which has an interdigitated electrode, rectangular cross-section and unidirectional piezoceramic (PZT) fibers embedded in the polymer matrix. An MFC actuator has much higher actuation performance, flexibility and durability than a traditional piezoceramic (PZT) actuator. This study showed that an MFC could be used as an actuator to change the displacement and twist tip-angle of a pre-twisted beam. In the test, an MFC patch was pasted on the beam’s upper surface to twist the pre-twisted beam actively. Different twist tip-angle changes of the pre-twisted beam were measured under a series of actuation voltages, and a good agreement was observed when experimental results were compared with numerical results. In addition, the actuation performance of MFC was compared with those of PZT4 and PVDF and the influence of anisotropic property of the MFC on its actuation performance was also studied. The experimental and numerical results presented in this paper show the potential of MFC for use in the vibration control of helicopter rotors.     

Analytical solutions for thermal forcing vortices in boundary layer and its applications

Using the Boussinesq approximation, the vortex in the boundary layer is assumed to be axisymmetrical and thermal-wind balanced system forced by diabatic heating and friction, and is solved as an initial-value problem of linearized vortex equation set in cylindrical coordinates. The impacts of thermal forcing on the flow field structure of vortex are analyzed. It is found that thermal forcing has significant impacts on the flow field structure, and the material representative forms of these impacts are closely related to the radial distribution of heating. The discussion for the analytical solutions for the vortex in the boundary layer can explain some main structures of the vortex over the Tibetan Plateau.     

Formulae of force at a point in the interior of a half space with shear modulus linearly varied with depth

According to a lemma and an assumption, this paper prexenis formulae of force at a point in the interior of a half space with Poisson’s ratio v = constant and shear modulus G linearly varied with depth. These formulae can be used as an approximate basic solution when the integral equation method is employed for the analysis of piles and other geotechnical engineering problems.     

A perturbation-variational solution of the large deflection of rectangular plates under uniform load

In this paper, von Karman’s set of nonlinear equation for large deflection of rectangular plates is at first converted into several sets of linear equations by taking central dimensionless deflection as perturbation parameter, and then, the sets of linear equations for plates with various ratio λ of length to width are solved with application of variational method. The analytical expressions for displacements and stresses as well as formulas for numerical calculation are worked out. The figures of maximum deflection-load end maximum stress with ratio H of length to width as a parameter are given in this paper. Through comparison, it is found that the results of this paper are quite in accord with experiments.     

The criterion algorithm of relation of implication between periodic orbits (I)

In recent years, there is a wide interest in Sarkovskii’s theorem ami the related study. According to Sarkovskii’s theoren if the continuous self-mapf of the closed interval has a 3-pcriodic orbit, then fmust has an n-pcriodic orbit for any positive integer n. But f can not has all n-periodic orbits for some n.For example, let Evidently, f has only one kind of 3-periodic orbit in the two kinds of 3-periodic orbits. This explains that it isn’t far enough to uncover the relation between periodic orbits by information which Sarkovskii’s theorem has offered. In this paper, we raise the concept of type of periodic orbits, and give a feasible algorithm which decides the relation of implication between two periodic orbits.     

Recent investigations on strain and stress rates in nonlinear continuum mechanics

Presenting some recent considerations and results, the present paper deals with two basic concepts of the continuum mechanics: strain-and stress-rates. Upon a brief systematic survey of concepts of strain and stress, a so far unknown explicit expression for the rate of the right stretch tensor is offered in absolute notation. This paper then suggests to distinguish two ways of defining objective stress-rates. Following the second procedure, after analyzing several particular cases, the author proposes a generalized Jaumann flux, which contains the majority of the existing definitions for stress-rate and the Hill’s result as well.     

Numerical study on wake characteristics of high-speed trains

Intensive turbulence exists in the wakes of high speed trains, and the aerodynamic performance of the trailing car could deteriorate rapidly due to complicated features of the vortices in the wake zone. As a result, the safety and amenity of high speed trains would face a great challenge. This paper considers mainly the mechanism of vortex formation and evolution in the train flow field. A real CRH2 model is studied, with a leading car, a middle car and a trailing car included. Different running speeds and cross wind conditions are considered, and the approaches of un- steady Reynold-averaged Navier-Stokes （URANS） and de- tached eddy simulation （DES） are utilized, respectively. Re- suits reveal that DES has better capability of capturing small eddies compared to URANS. However, for large eddies, the effects of two approaches are almost the same. In conditions without cross winds, two large vortex streets stretch from the train nose and interact strongly with each other in the wake zone. With the reinforcement of the ground, a complicated wake vortex system generates and becomes strengthened as the running speed increases. However, the locations of flow separations on the train surface and the separation mechanism keep unchanged. In conditions with cross winds, three large vortices develop along the leeward side of the train, among which the weakest one has no obvious influence on the wake flow while the other two stretch to the tail of the train and combine with the helical vortices in the train wake. Thus, optimization of the aerodynamic performance of the trailing car should be aiming at reducing the intensity of the wake vortex system.     

ON THE MODIFIED CASTIGLIANO’S THEOREM

This paper gives the modified Castigliano’s theorem, which is more convenient and more extensive for applications than the classical Castigliano’s theorem.The modifications to the classical Castigliano ’s theorem are in following two respects, the first respect is that the expression of the partial derivative with respect to the concentrated load p of the complementary energy density in the clasical Castigliano ’s theorem is replaced by the expressions with teh products of the external loads and influence functions, the modification brings us greatest simplicity and greatest convenience for calculations under various loads; the second respect is that the expressions with the products of the inhomogeneous boundary displacements and the influence functions are introduced into the classical Castigliano’s theorem, the modification provides the theoretical fundamental for solving the problems of various boundary conditions.We show also the method of how to apply the modified Castigliano’s theorem to solve the problems of the surface structural mechanics.Finally, as a calculated example of the applications of the modified Castigliano’s theorem we solved the equation of the deflection surface of the rectangular plate with two adjacent edges built-in and other two adjacent edges free.