The analytical solutions for orthotropic cantilever beams (II):Solutions for density functionally graded beams

INTRODUCTION Functionally graded materials (FGM) possesselastic constants and density that vary gradually withlocation within the material. In one kind of FGM,only the elastic constants vary continuously along oneor more directions, and in the other kind, only thedensity varies gradually with location. We call thelater one density functionally graded materials. Functionally graded materials have attractedmuch interest. Tutuncu and Ozturk (2001) obtainedclosed-form solutions…     

Guest Review:Potential theory method for 3D crack and contact problems of multi-field coupled media:A survey

This paper presents an overview of the recent progress of potential theory method in the analysis of mixed boundary value problems mainly stemming from three-dimensional crack or contact problems of multi-field coupled media.This method was used to derive a series of exact three dimensional solutions which should be of great theoretical significance because most of them usually cannot be derived by other methods such as the transform method and the trial-and-error method. Further, many solutions are obtained in terms of elementary functions that enable us to treat more complicated problems easily. It is pointed out here that the method is usually only applicable to media characterizing transverse isotropy,from which, however, the results for the isotropic case can be readily obtained.     

Free vibration of piezoelectric annular plate

General solutions for coupled three dimensional equations of piezoelectric media were used in this work to obtain some analytical solutions for free vibration of piezoelectric annular plates. These solutions not only satisfy the governing equations at every point in the concerned region but also satisfy the prescribed boundary conditions at every point on the boundaries. Therefore, they are three-dimensional exact. Numerical results are finally tabulated. Project (No. 10002016) supported by the National Natural Science Foundation of China     

A PENNY-SHAPED CRACK IN AN INFINITE PIEZOELECTRIC BODY UNDER ANTISYMMETRIC POINT LOADS

ＩＮＴＲＯＤＵＣＴＩＯＮＰｉｅｚｏｅｌｅｃｔｒｉｃｃｅｒａｍｉｃｍａｔｅｒｉａｌｓｈａｖｅｍａｎｙａｐｐｌｉｃａｔｉｏｎｓｉｎｍｏｄｅｒｎｔｅｃｈｎｏｌｏｇｉｅｓｂｅｃａｕｓｅｏｆｔｈｅｉｒｅｘｃｅｌｌｅｎｔｐｉｅｚｏｅｌｅｃｔｒｉｃｐｒｏｐｅｒｔｉｅｓ.Ｂｕｔｃｒａｃｋｓａｒｉｓｉｎｇｆｒｏｍｔｈｅｉｒｉｎｔｒｉｎｓｉｃｂｒｉｔｔｌｅｎｅｓｓｏｆ ｔｅｎｃａｕｓｅｐｉｅｚｏｅｌｅｃｔｒｉｃｃｏｍｐｏｎｅｎｔｓｆａｉｌｕｒｅ .Ｓｔｕｄｙｏｆｗｈａｔｃａｕｓｅｓｔｈｉｓｒｅｑｕｉｒｅｓｔｈｅｏｒｅｔ…     

Analytical solutions of simply supported magnetoelectroelastic circular plate under uniform loads

In this paper, the axisymmetric general solutions of transversely isotropic magnetoelectroelastic media are expressed with four harmonic displacement functions at first. Then, based on the solutions, the analytical three-dimensional solutions are provided for a simply supported magnetoelectroelastic circular plate subjected to uniform loads. Finally, the example of circular plate is presented. Project supported by the National Natural Science Foundation of China (No. 10172075) and Ningbo Natural Science Foundation for Young Scientist (No. 02J20102-13)     

The analytical solutions for orthotropic cantilever beams （Ⅱ）：Solutions for density functionally graded beams

In this paper, the specific solutions of orthotropic plane problems with body forces are derived. Then, based on the general solution in the case of distinct eigenvalues and the specific solution for density functionally graded orthotropic media, a series of beam problem, including the problems of cantilever beam with body forces depending only on z or on x coordinate and expressed by z or x polynomial is solved by the principle of superposition and the trial-and-error method.     

Numerical approach for a system of second kind Volterra integral equations in magneto-electro-elastic dynamic problems

INTRODUCTION In scientific and engineering problems, Volterra integral equations are always encountered and have attracted much attention (Christopher and Baker, 1977; Delves and Mohamed, 1985; Brunner and van der Houwen, 1986; Kress, 1989; Oja and Saveljeva, 2002; Maleknejad and Shahrezaee, 2004; Maleknejad and Aghazadeh, 2005; Zerarka and Soukeur, 2005). Generally, exact solutions are very difficult to find and solutions have been obtained for only some few special cases (Yan and …     

唐代今体诗格律一得

唐代今体诗的格律最完美。本文抓住唐代今体诗的格律作些探讨。今体诗从每行字数多、少的角度分有:五言(字),七言(字);今体诗从每首句数多、少的角度分有:绝句(每首四句),律诗(每首八句),排律(每首十句以上);今体诗从声调角度分有:平起首句入韵,平起首句不入韵,仄起首句入韵,仄起首句不入韵。把字数多、少与句数多、少结合起来分,这就是通常说的:五绝、七绝,五律、七律,五言排律、七言排律。