Pure bending of simply supported circular plate of transversely isotropic functionally graded material

INTRODUCTION In recent years, functionally graded materials (FGMs) have attracted more and more attention. Due to their continuously varying material properties in space on the macroscopic scale, FGMs, therefore, are usually superior to conventional fiber-matrix materi-als in mechanical behavior, especially for perform-ance under thermal loading. Now FGMs have been widely used in various fields including electronics, chemistry, optics, biomedicine, etc. Heretofore, volumes of literatu…     

Thermoelastic stresses in a uniformly heated functionally graded isotropic hollow cylinder

The axisymmetric themoelastic problem of a uniformly heated, functionally graded isotropic hollow cylinder is considered. An analytical form of solution is proposed. For the case when the Young's modulus and thermal expansion coefficient have a power-law dependence on the radial coordinate, explicit exact solution is obtained. For the degenerated case, i.e. when the cylinder is homogeneous and isotropic, no stresses will occur provided it is subjected to a uniform temperature. Numerical results are finally given and some important inclusions are obtained. Project (No.10002016) supported by the National Natural Science Foundation of China (NSFC).     

The Reissner-Sagoci problem for transversely isotropic piezoelectric half-space

INTRODUCTION In isotropic elasticity a class of mixed boundary value problems for elastic half-space can be classified as axisymmetric torsion. In this case the elastic field in cylinder components takes a particularly simple form consisting of only one nonzero displacement and two nonzero stress components. For this loading case, Reissner and Sagoci (1944) were possibly the first to examine a mixed boundary problem between the tangential displacement and stress on the half-space surface.…     

Analytical solutions of simply supported magnetoelectroelastic circular plate under uniform loads

INTRODUCTIONInelasticity ,theproblemofasimplysup portedcircularplatesubjectedtouniformloadsisaclassicone .Timoshenkoetal.(1970 )pre sentedasolutionforanisotropiccircularplate .Dingetal.(2 0 0 0 ;2 0 0 1)obtainedtheanalyti calthree dimensionalsolutionforat…     

Analytical layer-element solutions for a multi-layered transversely isotropic elastic medium subjected to axisymmetric loading

This paper presents an analytical layer-element method used to analyze the displacement of a multi-layered transversely isotropic elastic medium of arbitrary depth subjected to axisymmetric loading. Based on the basic constitutive equations and the HU Hai-chang’s solutions for transversely isotropic elastic media, the state vectors of a multi-layered transversely isotropic medium were deduced. From the state vectors, an analytical layer element for a single layer (i.e., a symmetric and exact stiffness matrix) was acquired in the Hankel transformed domain, which not only simplified the calculation but also improved the numerical efficiency and stability due to the absence of positive exponential functions. The global stiffness matrix was obtained by assembling the interrelated layer elements based on the principle of the finite layer method. By solving the algebraic equations of the global stiffness matrix which satisfy the boundary conditions, the solutions for multi-layered transversely isotropic media in the Hankel transformed domain were obtained. The actual solutions of this problem in the physical domain were acquired by inverting the Hankel transform. This paper presents numerical examples to verify the proposed solutions and investigate the influence of the properties of the multi-layered medium on the load-displacement response.     

EXACT SOLUTION OF AN EXTERNAL CIRCULAR CRACK IN A PIEZOELECTRIC SOLID SUBJECTED TO SHEAR LOADING

ＩＮＴＲＯＤＵＣＴＩＯＮＤｕｅｔｏｔｈｅｉｎｈｅｒｅｎｔｗｅａｋｎｅｓｓｏｒｂｒｉｔｔｌｅｎｅｓｓｏｆｐｉｅｚｏｅｌｅｃｔｒｉｃｃｅｒａｍｉｃｓ,ｔｈｅｆｒａｃｔｕｒｅｏｆｐｉｅｚｏ ｅｌｅｃｔｒｉｃｍａｔｅｒｉａｌｓｈａｓｇａｉｎｅｄｃｏｎｓｉｄｅｒａｂｌｅｉｎｔｅｒ ｅｓｔ.Ｍｏｓｔｐｕｂｌｉｓｈｅｄｗｏｒｋｓｄｅａｌｔｗｉｔｈｔｗｏ ｄｉｍｅｎ ｓｉｏｎａｌｓｔｕｄｙｏｆｃｒａｃｋｓｉｎｐｉｅｚｏｅｌｅｃｔｒｉｃｍａｔｅｒｉａｌｓ(Ｐａｋ ,1 990 ;Ｓｕｏｅｔａｌ.,1 992 ;ＺｈｏｎｇａｎｄＭｅｇｕｉ…     

平面体波在各向异性媒质中的传播

Combining the linear transformation and the solution technique for the cubic equation,a general closed-form analyti solution for bulk waves in orthotropic anisotropic materials is obtained.This method is straightforward and general.Degenerated cases include transversely isotropic,cubic,and isotropic materials.Numerical computations are carried out on a fiber-reinforced composite plate modeled as a transversely isotropic media.The fibers are parallel to the top and bottom surfaces of the plate ,and they are rotated counterclockwise around the plate normal through different angles.The two-dimensional slowness curves corresponding to different rotations are presented graphically.The wave propagation characteristics displayed in slowness surfaces for different fiber orientation are analyzed.     

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)     

Exact solution of an external circular crack in a piezoelectric solid subjected to shear loading

A three-dimensional, exact analysis is presented in this paper for the problem of an external circular crack in a transversely isotropic piezoelectric medium subjected to arbitrary antisymmetric shear loading. A recently proposed general solution of three-dimensional piezoelectricity is employed. It is shown that four quasi harmonic functions involved in the general solution can be respresented by just one complex potential. Previous results in potential theory are then used to obtain the exact solution of the problem. For point shear loading, Green’s functions for the elastoelectric field are derived in terms of elementary functions. Project supported by Scientific Research Foundation for Returned Overseas Chinese Scholars, State Education Ministry and partly by National Natural Science Foundation of China (NSFC) (10002016).     

Analytical solution for functionally graded anisotropic cantilever beam under thermal and uniformly distributed load

The bending problem of a functionally graded anisotropic cantilever beam subjected to thermal and uniformly dis-tributed load is investigated,with material parameters being arbitrary functions of the thickness coordinate. The heat conduction problem is treated as a 1D problem through the thickness. Based on the elementary formulations for plane stress problem,the stress function is assumed to be in the form of polynomial of the longitudinal coordinate variable,from which the stresses can be derived. The stress function is then determined completely with the compatibility equation and boundary conditions. A practical example is presented to show the application of the method.     

Three-dimensional analysis of a thick FGM rectangular plate in thermal environment

ＩＮＴＲＯＤＵＣＴＩＯＮＡｓｋｎｏｗｎ ,ｔｈｅｒｍａｌｂｅｈａｖｉｏｒｓｏｆｓｔｒｕｃｔｕｒｅｓｍｕｓｔｂｅｃｏｎｓｉｄｅｒｅｄｉｎｍａｎｙｓｉｔｕａｔｉｏｎｓ.Ｓｔｕｄｙｏｆｔｈｅｒｍａｌｅｆｆｅｃｔｏｎｄｅｆｏｒｍａｔｉｏｎｓａｎｄｓｔｒｅｓｓｅｓｏｆ     

Three-dimensional analysis of a thick FGM rectangular plate in thermal environment

The thermal behavior of a thick transversely isotropic FGM rectangular plate was investigated within the scope of three-dimensional elasticity. Noticing many FGMs may have temperature-dependent properties, the material constants were further considered as functions of temperature. A solution method based on state-space formulations with a laminate approximate model was proposed. For a thin plate, the method was clarified by comparison with the thin plate theory. The influences of material inhomogeneity and temperature-dependent characteristics were finally discussed, through numerical examples. Project (No. 10002016) supported by National Natural Science Foundation of China     

General solutions for special orthotropic piezoelectric media

INTRODUCTION General solution is a convenient, effective method for solving space problems such as problems of infinite, semi-infinite and two-phase infinite media. For linear theory of piezoelasticity, Ding et al.(1996; 1997a) gave the general solution for coupled equa-tions for transversely piezoelectric media using po-tential theory. Ding et al.(1997b; 1997c) gave the general solution of plane problem. Based on the gen-eral solution, Ding et al.(1997a) presented the closed form fundam…     

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.     

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…     

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

ＩＮＴＲＯＤＵＣＴＩＯＮＰｉｅｚｏｅｌｅｃｔｒｉｃｃｅｒａｍｉｃｍａｔｅｒｉａｌｓｈａｖｅｍａｎｙａｐｐｌｉｃａｔｉｏｎｓｉｎｍｏｄｅｒｎｔｅｃｈｎｏｌｏｇｉｅｓｂｅｃａｕｓｅｏｆｔｈｅｉｒｅｘｃｅｌｌｅｎｔｐｉｅｚｏｅｌｅｃｔｒｉｃｐｒｏｐｅｒｔｉｅｓ.Ｂｕｔｃｒａｃｋｓａｒｉｓｉｎｇｆｒｏｍｔｈｅｉｒｉｎｔｒｉｎｓｉｃｂｒｉｔｔｌｅｎｅｓｓｏｆ ｔｅｎｃａｕｓｅｐｉｅｚｏｅｌｅｃｔｒｉｃｃｏｍｐｏｎｅｎｔｓｆａｉｌｕｒｅ .Ｓｔｕｄｙｏｆｗｈａｔｃａｕｓｅｓｔｈｉｓｒｅｑｕｉｒｅｓｔｈｅｏｒｅｔ…     

A penny-shaped crack in an infinite piezoelectric body under antisymmetric point loads

In this study, Fabrikant (1989, 1991)'s new results in potential theory were used to obtain the exact and complete solution for the problem of a penny-shaped crack in an infinite transversely isotropic piezoelectric body subjected to antisymmetric point loads (point charges and normal point forces); then the complete solution for the problem of one-sided loading of a penny-shaped crack was obtained by the superposition of the symmetric loading solution in Chen and Shioya (1999) and the antisymmetric one presented here; and then the reciprocity theorem of piezoelectric media was used to deal with the problem of interaction between arbitrarily located point forces and a point charge with a penny-shaped crack and obtained the exact expressions of the crack faces' normal displacement in terms of elementary functions and some non-singular integrals; and finally obtained the normal displacement of the positive and negative faces of the crack under many loading cases as shown in figures for an infinite PZT-4 piezoelectric ceramic body weakened by a penny-shaped crack. Project (19872060) supported by the Natural Science Foundation of China.     

Three-dimensional vibration of thick plate

１ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｃｌａｓｓｉｃａｌｔｈｉｎｐｌａｔｅｔｈｅｏｒｙｏｆｖｉｂｒａｔｉｏｎｉｓｂａｓｅｄｏｎｔｈｅＫｉｒｃｈｈｏｆｈｙｏｔｈｅｓｉｓ,ａｎｄｔｈｅｅｆｅｃｔｏｆｔｒａｎｓｖｅｒｓａｌｓｈｅａｒｄｅｆｏｒｍａｔｉｏｎａｎｄｒ...     

A generalized plane strain theory for transversely isotropic piezoelectric plates

INTRODUCTION For moderate thickness plate containing notches or holes, neither plane stress nor plane strain theory can describe its true deformation states (Jin and Hwang, 1989). This well known drawback has mo- tivated many analytical and numerical studies carried out to determine the effect of plate thickness on the in-plane stress distribution. Pioneering work on the along depth stress components, i.e. the K-M gener- alized plane strain theory was proposed by Kane and Mindlin (1956)…     

Solution of stress intensity factors of multiple cracks in plane elasticity with eigen COD formulation of boundary integral equation

The concept of eigen crack opening displacement (COD) can be defined as the COD of a crack in infinite plate under the tractions acting on the crack surface. By introducing this concept, the eigen COD formulation of boundary integral equation is proposed in this paper, together with the solution procedures for multiple crack problems in plane elasticity. With the proposed approach, the multiple crack problems can be solved with the conventional displacement discontinuity boundary integral equations in an it...