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	1. Gradient Piezoelectric Beam with Flexoelectric and Surface Effects
	YUE Yanmei,XU Kaiyu
	Mechanics 05 December 2015
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	Abstract:In this paper, a piezoelectric beam model with flexoelectricity and surface effects is proposed. An energy variational principle is postulated to develop the governing equations and boundary conditions. Moreover, the strain gradient coefficient and flexoelectric paprameter are introduced to account for higher order coupling effects of underlying microstructure. Then the bending problem of a cantilever beam is solved to illustrate the theory. It is found that the deflection of the cantilever may depend strongly on the so-introduced gradient-related effects and surface properties. Flexoelectricity can soften the beam stiffness, while strain gradient may enhance the beam striness. And also, the electric field distributions obtained by the models with and without the coupling of strian gradient have a great difference.
	TO cite this article:YUE Yanmei,XU Kaiyu. Gradient Piezoelectric Beam with Flexoelectric and Surface Effects[OL].[ 5 December 2015] http://en.paper.edu.cn/en_releasepaper/content/4666619


	2. The analytical analysis of the asymmetric elastic rod
	WANG Wei,CHEN Tao
	Mechanics 04 January 2014
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	Abstract:The analytical equation of the asymmetric elastic rod governed by the ordinary differential equation is obtained. We reconstruct the Kirchhoff equations with the complex coordinates and introduce a novel transformation parameter. They change the initial non-circular character of the cross section into a nearly cross section case, and approximately result the Duffing type ordinary differential equations. Perturbation methods basing on these equations permit our expectation to explore the intrinsic properties of DNA double helix within the framework of analytical research not merely the numerical simulations, such as structural inhomogeneity and periodically varying of bending rigidities.
	TO cite this article:WANG Wei,CHEN Tao. The analytical analysis of the asymmetric elastic rod[OL].[ 4 January 2014] http://en.paper.edu.cn/en_releasepaper/content/4580022

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	3. ON CONCEPT OF FRACTAL IN FRACTURE MECHANICS
	OU Zhuocheng,LI Guanying,DUAN Zhuoping,HUANG Fenglei
	Mechanics 02 August 2012
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	Abstract:Fractal, or generally a self-similar (or self-affine) structure of infinite order, has been extensively used as a nonlinear mathematical tool to describe various irregular and complex phenomena in fracture mechanics. However, there are still critical issues remaining ambiguous, leading to inherent difficulties mainly resulted from the contradiction between the integral dimension immeasurability of a fractal and the integral dimension characteristic of a physical object in nature. Here we demonstrate that conceptually a physical object in nature can never be described as a fractal, rather a ubiquitiform (a terminology coined here for a finite order self-similar or self-affine structure), and show mathematically that a ubiquitiform must be of integral dimension in Euclidean space, which is radically different from a fractal in the sense of the Hausdorff measure and makes the fractal approximation of a ubiquitiform unavailable. Our result implies that a natural object is of ubiquitiform rather than fractal, and thus, instead of the existing fractal theory, a new type of ubiquitiform theory must be established in future. We anticipate this result to be a starting point for the coming universal ubiquitiform theory in fracture mechanics. Moreover, it can be expected that the coming ubiquitiform theory will be more easy-to-use in practice than the fractal one, since it can be constructed completely on the base of "classical" mathematics, and hence some intrinsic difficulties in applied fractal science can be avoided.
	TO cite this article:OU Zhuocheng,LI Guanying,DUAN Zhuoping, et al. ON CONCEPT OF FRACTAL IN FRACTURE MECHANICS[OL].[ 2 August 2012] http://en.paper.edu.cn/en_releasepaper/content/4486167


	4. A bounded optimal control for maximizing the reliability of randomly excited nonlinear oscillators with fractional derivative damping
	CHEN Licong,ZHU Weiqiu
	Mechanics 18 July 2012
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	Abstract:In this paper, a bounded optimal control for maximizing the reliability of randomly excited nonlinear oscillators with fractional derivative damping is proposed. First, the partially averaged Itô equations for the energy processes are derived by using the stochastic averaging method. Then, the dynamical programming equations for the control problems of maximizing the reliability function and maximizing the mean first passage time are established from the partially averaged Itô equations by using the dynamical programming principle and solved to obtain the optimal control law. The conditional reliability function and mean first passage time of the optimal control system are obtained by solving the backward Kolmogorov equation and Pontryagin equation associated with the fully averaged Itô equations, respectively. The application of the proposed procedure and effectiveness of the control strategy are illustrated by using two examples. In addition, the effect of fractional derivative order on the reliability of optimally controlled system is examined.
	TO cite this article:CHEN Licong,ZHU Weiqiu. A bounded optimal control for maximizing the reliability of randomly excited nonlinear oscillators with fractional derivative damping[OL].[18 July 2012] http://en.paper.edu.cn/en_releasepaper/content/4485187


	5. Control of Vortex Structures on a Rectangular Slab via a Sinusoidal Surface
	Zou, Lin
	Mechanics 31 March 2010
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	Abstract:The present investigations focus attention on numerical simulations of three-dimensional flow around wavy rectangular slabs with sinusoidal variations in cross-section area along the spanwise direction at low Reynolds numbers of 100 and 500. The detailed near wake vortex structures of the wavy rectangular slab are captured and the influence of the wavy rectangular slab side ratio (L/Dm=1 to 8) is discussed compared with a straight rectangular slab with the same side ratio. Moreover, the pressure field, velocity field and force coefficients around the wavy surfaces are also calculated. The present numerical simulations show that the three-dimensional free shear layers behind the wavy rectangular slab are more stable than those of the straight rectangular slab. At L/Dm≥2, the free shear layers are even difficult to roll up into a mature vortex street behind the wavy slab at Re=100. The mean drag reduced with the r.m.s. lift of the wavy rectangular slabs being greatly suppressed compared with the straight rectangular slab for all side ratios at Re=500. A drag reduction of up to 32% at L/Dm=1 is obtained. It indicated that the wavy slab is capable of minimization of flow-induced vibration and drag reduction compared with the rectangular slab in cross flow conditions.
	TO cite this article:Zou, Lin. Control of Vortex Structures on a Rectangular Slab via a Sinusoidal Surface[OL].[31 March 2010] http://en.paper.edu.cn/en_releasepaper/content/41413


	6. A Novel Method for Wrinkling Analysis of Membrane Inflated Cone in Bending
	C.G.Wang,Z.Y.Du,H.F.Tan
	Mechanics 04 March 2010
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	Abstract:This paper presents a novel method– Extremum method–to perform wrinkling analysis of the membrane inflated conical cantilever beam subject to bending. Based on this method, the initial wrinkling location and the critical wrinkling load are determined by searching the maximum of the wrinkling factor. The nondimensional analyses show that the initial wrinkles will be initiated at a different location when the taper ratio is higher than the critical value. The critical wrinkling load nonlinearly increases as the taper ratio increases firstly, and then linearly increases after the critical taper ratio. The critical taper ratio reflects the highest load-carrying efficiency of the inflated cone in bending. The comparative analysis shows fairly good agreement between analytical and numerical results. This gives confidence to use extremum method for wrinkling analysis of inflated cone in bending.
	TO cite this article:C.G.Wang,Z.Y.Du,H.F.Tan. A Novel Method for Wrinkling Analysis of Membrane Inflated Cone in Bending[OL].[ 4 March 2010] http://en.paper.edu.cn/en_releasepaper/content/40398


	7. Galilean invariance in two-dimensional lattice BGK models
	Ran zheng
	Mechanics 03 February 2007
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	Abstract:The Galilean invariance inherent in Navier-Stokes equations is not really recovered in two dimensional lattice Boltzmann equation, especially for shock calculation. This paper presents a systematic analysis on this subject.
	TO cite this article:Ran zheng. Galilean invariance in two-dimensional lattice BGK models [OL].[ 3 February 2007] http://en.paper.edu.cn/en_releasepaper/content/11027


	8. NONLINEAR LOW FREQUENCY WATER WAVES IN A CIRCULAR CYLINDER
	HuaiWu Peng,Cunbiao Lee
	Mechanics 08 December 2005
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	Abstract:The experiment was carried out to study the low frequency surface waves due to the horizontal high frequency excitation. The puzzling feature of the phenomenon was that the big amplitude axisymmetric surface wave frequency was typically about 1/50 of the excitation frequency. The viscous effect of water was neglect as a first approximation in the earlier papers on this subject, but we found the viscosity was important to achieve the low frequency water wave with the cooperation of hundreds of “finger” waves.
	TO cite this article:HuaiWu Peng,Cunbiao Lee. NONLINEAR LOW FREQUENCY WATER WAVES IN A CIRCULAR CYLINDER[OL].[ 8 December 2005] http://en.paper.edu.cn/en_releasepaper/content/4176

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