Piezoelectric analogy of generalized torsion in anisotropic. Explanations, problems and solutions springer netherlands m. Anisotropic elastic materials for which the sextic equation. A twodimensional problem for an anisotropic body with a. The mechanical properties of these materials differ in different directions. Oct 16, 2004 piezoelectric analogy of generalized torsion in anisotropic elasticity piezoelectric analogy of generalized torsion in anisotropic elasticity chen, tungyang. In many cases, the solution to an anisotropic elasticity problem is much simplified. There are essentially two formalisms for twodimensional deformations of a general anisotropic elastic material. Buy theory of elasticity of an anisotropic elastic body. Plane problems of anisotropic elasticity were studied by lekhnitskii 1968, 1981 using a.
According to lekhnitskii 6 all bodies, on the whole, can be divided into homogeneous and nonhomogeneous bodies, and isotropic and anisotropic as well. Least squares boundary element method of calculating. Bone anisotropy analytical and finite element analysis. Gostekhizdat, moscow in russian has been the favorite among the engineering community, while the newer stroh formalism is wellknown in the material sciences, applied mathematics and physics community. Theory of elasticity of an anisotropic body sergei. The six chapters deal with 1 the general theory of the elasticity of an anisotropic body, 2 simple cases of elastic equilibrium, 3 and 4 the state of stress of an anisotropic body bounded by a cylindrical surface when the stress is constant along a generator, 5 the state of. Solovievthreedimensional problems of elastic theory. Theory of elasticity of an anisotropic body hardcover 1981. Holdenday, new york 1963 is far from being complete, because. We give the results of studies of the stress state for an infinite anisotropic body with a number of planar cracks along a single plane. An introduction to applied anisotropic elasticity, oxford university press 1961. Lekhnitskiitheory of elasticity of an anisotropic body. Recent developments in anisotropic elasticity sciencedirect. As a result, the material becomes anisotropicits properties differ between the direction it was rolled in and each of the two transverse directions.
Recent developments in anisotropic elasticity, international. In addition to the introduction of the theory of anisotropic elasticity, several. Pdf weight function theory for a rectilinear anisotropic body. When a body is considered to be homogeneous, its physical properties, such as density, remain invariant in all directions, in any of its points. For the anisotropic case, this strategy is no longer available, except for certain special cases such as that of transverse isotropy. Remarks on orthotropic elastic models applied to wood. Threedimensional elasticity solutions for isotropic and. Barber department of mechanical engineering and department of civil and environmental engineering, university of michigan, ann arbor, mi 481092125, u. Pdf general solution of the stress potential function in lekhnitskiis. Download pdf theory of elasticity of an anisotropic body. Examples are wood, composite materials and many biological materials. Theory of elasticity of an anisotropic body 1981 edition. Theory and applications oxford engineering science series.
Theory of elasticity of an anisotropic elastic body by s. These materials may not possess a plane of symmetry. Theory of elasticity of an anisotropic body lekhnitskii. General solution of the stress potential function in lekhnitskiis. Theory of elasticity of an anisotropic elastic body nasaads. Saintvenant torsion, anisotropic, elliptical cross section, torsional rigidity introduction the saintvenant torsion of homogeneous, anisotropic and linearly elastic bars have been the subject of several studies from both theoretical and numerical viewpoints. Theory of elasticity of an anisotropic elastic body lekhnitskii, s.
In less than 100 pages, this book covers the main vector variational methods developed to solve nonlinear elasticity problems. The purpose of this paper is to present other anisotropic elastic materials for which the sextic equation is a cubic equation in p 2. Based on the general solution of the stress potential function in the theory, a lot of research. Lekhnitskii 1963 starts from expressions for the stresses in terms of stress functions that. This paper establishes that the stroh orthogonality relations for an anisotropic body are a direct consequence of the fact that the system of equations of equilibrium is selfadjoint and positive definite. For anisotropic materials, some important contributions are found in lekhnitskii 1981 for general theory of elasticity, which is used as basis for this present analytical model. For an alternate treatment of the lekhnitskii formalism, i strongly recommend to the reader t. Classical methods of twodimensional elasticity can be extended to give an exact solution of the threedimensional problem for the beam i. A state space formalism for anisotropic elasticity. Tings book is dedicated to lekhnitskii s equations, including particularly helpful and complete derivations pp. It is found that the original lekhnitskii general solution g.
Lekhnitskii, theory of elasticity of an anisotropic elastic body. In this paper, a weight function theory for the calculation of the mode iii stress intensity factor in a rectilinear anisotropic body is formulated. The theory of elasticity of an anisotropic body has been developed up to now for the cases of rectilinear referred to a cartesian coordinate system or cylindrical referred to a polar coordinate system anisotropy lekhnitskii, 1963. General solution of the stress potential function in. Neskorodev donetsk received 2april 1997 the twodimensional problem of the theory of elasticity for an. It is demonstrated that, assuming a complex representation of displacements and boundary tractions, the betti theorem of reciprocity implies the orthogonality, and positive. Dec 04, 2017 theory of elasticity of an anisotropic body by s.
Theory of elasticity of an anisotropic body book, 1981. Theory of elasticity of an anisotropic body sergei georgievich lekhnitskii. Pdf general solution of the stress potential function in. Abstract not available bibtex entry for this abstract preferred format for this abstract see preferences. The oldest theory of twodimensional anisotropic elasticity is due to lekhnitskii. Another example of an orthotropic material is sheet metal formed by squeezing thick sections of metal between heavy rollers. Theory of elasticity of filament wound anisotropic ellipsoids. We describe the results of numerical studies as functions of the geometric characteristics of the body. Theory of elasticity of an anisotropic body by sergei georgievich lekhnitskii and a great selection of related books, art and collectibles available now at. For the simplest types of load we prove that the stress intensity factors is independent of the type of anisotropy. Theory of elasticity of an anisotropic elastic body holden. Click download or read online button to theory of elasticity of an anisotropic body book pdf for free now. The problem of determining an appropriate partial integral can be reduced to a sequence of twodimensional body force problems barber, 2006b, which in turn could be solved by. Nonlinear field theories of mechanics truesdell and noll.
In lekhnitskiis theory for a plane strain problem in anisotropic materials, the. On the general solutions of transversely isotropic elasticity. Theory of elasticity of an anisotropic elastic body. Theory of elasticity of an anisotropic body download theory of elasticity of an anisotropic body ebook pdf or read online books in pdf, epub, and mobi format. Theory of elasticity of an anisotropic elastic body s. Weight function theory for a rectilinear anisotropic body. Based on the general solution of the stress potential function in the theory, a lot of research work has been done. Mir publishers, 1981, 431 pages, english translation, 2 edition the book covers the following topics. Theory of elasticity of an anisotropic elastic body author lekhnitskii, sergei georgievich formatbinding hardcover book condition used fine jacket condition very good edition first edition binding hardcover publisher holdenday place of publication san francisco, ca. The six chapters deal with 1 the general theory of the elasticity of an anisotropic body, 2 simple cases of elastic equilibrium, 3 and 4 the state of stress of an anisotropic body bounded by a cylindrical surface when.
In the present book, i arrange one chapter named lekhnitskii formalism. The relation between the equations of the twodimensional. Threedimensional solutions for general anisotropy university of. Theory of elasticity of an anisotropic body sergei georgievich lekhnitskii download bok. Part i presents the formalism for the rectilinearly anisotropic body in. Anisotropic elasticity has been an active research subject for the last thirty years due to its applications to composite materials. The lekhnitskii theory is not only outdated, it is inefficient. Pdf it is found that the original lekhnitskii general solution g. However, formatting rules can vary widely between applications and fields of interest or study. The latter one is the underlying theory for studying the mechanics of fila. Presenting a general framework with a tight focus, the author provides a comprehensive exposition of a technically difficult, yet rapidly developing area of modern applied mathematics. Threedimensional elasticity solutions for isotropic and generally anisotropic bodies j. The boundary element method, combined with the least squares method is proposed to determine the anisotropic elastic plane laurent series of coefficients a boundary element method of least squares. The iucr is a scientific union serving the interests of crystallographers and other scientists employing crystallographic methods.
Selecting this option will search all publications across the scitation platform selecting this option will search all publications for the publishersociety in context. We have new and used copies available, in 0 edition starting at. The stress components in a continuous body which is in equilibrium must satisfy. S0021892898000422 0o21892898ssee front matter the relation between the equations of the twodimensional theory of elasticity for anisotropic and isotropic bodies1 a. There are many examples of the theory of elasticity applied to isotropic materials, as for instance, in sokolnikoff 1956.
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