On the analysis of anisotropic rectangular plates dtic. New types of complete general solution for anisotropic as well as piezoelectric materials are then developed analytically. This paper describes the use of the edge function technique to study the stress intensity factors of a crack in a finite anisotropic plate. Tingb adepartment of mechanical engineering, university of michigan, ann arbor, mi 481092125, usa bdivision of mechanics and computation, stanford university, durand 262, stanford, ca 943054040, usa received 21 november 2006. Plane problems, plate bending problems as well as stretchingbending coupling problems are all treated in this book.
Lekhnitskii 1968, hardcover, reprint bending athwart a parallelstiffened plate. The plates have piecewise constant thickness and are subjected to the axisymmetric transverse pressure. Lekhnitskii, hardcover, reprint ebay sign in or create your free personal asme account. Buckling analysis of anisotropic sandwich plates faced with fiberreinforced plastics. The material properties need to be symmetrical about the crack line. General solution of the stress potential function in. Anisotropic plates with various openings under uniform loading or.
Apart from crystals a number of structures, such as corrugated plates and membranes, which are constructed from isotropic materials are elastically anisotropic. The material is treated as a quasi homogeneous anisotropic material and the problem is solved. Optimum design of effective parameters for orthotropic plates with. This work is an overview of available theories and finite elements that have been developed for multilayered, anisotropic, composite plate and shell structures. Anisotropic plates with various openings under uniform. Buckling of sandwich panels with laminated face plates. Bending of thin elastic plates containing two circular holes. This paper deals with stresses around rectangular and square openings with rounded corners in orthotropic plates. On the theory of laminated anisotropic shells and plates. Lekhnitskii author see all formats and editions hide other formats and editions. Pdf a strohtype formalism for anisotropic thin plates with bending.
The material on the problem of transverse vibrations of anisotropic plates which is collected in a special chapter. In the present book, i arrange one chapter named lekhnitskii formalism. Pdf in the present paper, a complete strohtype formalism for the. The multilayered plate is regarded as an anisotropic heterogeneous plate in which the material properties vary. A variant on an approximative solution indicated by. Elastostatic stress analysis of orthotropic rectangular centercracked plates by george s. Theories and finite elements for multilayered, anisotropic. Lekhnitskii, 1963, which can be arma 192062 expansion of horizontal wellbore stability model for elastically anisotropic shale formations with anisotropic failure criteria. Pdf dynamics of thin anisotropic plates researchgate.
Anisotropic plates are widely used in modern engineering structures. Using kolosovmuskhelishvilis 1 complex variable approach, some problems of simply connected regions are solved by savin 2,lekhnitskii 3, ukadgaonker and rao 4,5, ukadgaonker and kakhandki 6, nageswara rao et. For pure bending problems of anisotropic plates with outofplane variables. Trabalhador saocarlence 400, sao carlos, sp 566590, brazil. Please do not support the price gougers for this book. A general theory of strength for anisotropic materials. Stress concentration around circularellipticaltriangular. Theory of elasticity of an anisotropic elastic body by s. Sorry, we are unable to provide the full text but you may find it at the following locations. Lekhnitskii s purpose symmetry 2020, 12, 834 2 of 16 of this theory was to present an overall solution regarding infinite anisotropic plates consisting of. Although a comprehensive description of several techniques and approaches is given, most of this paper has been devoted to the so called axiomatic theories and related finite element implementations. A general boundary integral for anisotropic plate bending. Let us assume a simply supported rectangular orthotropic plate uniaxial loaded as presented in fig. Stress analysis of fibre reinforced plates with polar orthotropy.
Also reinforced structures con taining with a preferred orientation are elastically aniso tropic. Expansion of horizontal wellbore stability model for. Theory of anisotropic thick plates, paperback january 1, 1970 by s. The scf were also determined for isotropic and orthotropic cylindrical shells with circular cutout. The complex variable method for solving boundary value problems in two dimensional elasticity was firstly applied by muskhelishvili 1962 for isotropic plates. It is found that the original lekhnitskii general solution lekhnitskii, 1963 is far from being completeness, because some important terms were lost. Theory of elasticity of an anisotropic body 1981 edition. Through the use of identities developed in the literature, the lekhnitskoi stress along the opening boundary is obtained in real form. We choose the natural axes of the material to coincide.
It replaces the multiple user names and passwords necessary to access subscriptionbased content with a single user name and password that can be entered once per session. To the knowledge of the authors, the bem appears to have been used only twice. Solutions for stress analysis of anisotropic plates containing triangular holes have been provided. Journal of the mechanics and physics of solids 55 2007 19932006 threedimensional solutions for general anisotropy j. Lekhnitskii 2 developed a complex variable method for anisotropic plates and provided explicit solutions for a circular hole in an orthotropic plate. Gyekenyesi and alexander mendelson lewis research center summary a mappingcollocation method was developed for the elastostatic stress analysis of finite, anisotropic plates with centrally located tractionfree cracks. Stresses around rectangular holes in orthotropic plates. Determination of forces and moments per unit length in. Some general solutions for stresses around holes in anisotropic plates, ph.
Based on lekhnitskiis method, hsieh and hwu 3 developed a strohlike formalism and derived analytical solutions for. Optimum design of effective parameters for orthotropic. They used conformal mappings and complex variable method for stress analysis of isotropic and anisotropic. Anisotropic elastic plates find wide applications as structural elements in modern technology. Elastic buckling of multilayered anisotropic plates elastic buckling of multilayered anisotropic plates tarn, jiannquo 19960301 00.
The present derivation for the dynamic buckling of orthotropic rectangular plates under uniaxial loading is based on ekstroms fundamental study 11 presented already in 1973 using the models developed by lekhnitskii for anisotropic plates 44. An operationally simple strength criterion for anisotropic materials is developed from a scalar function of two strength tensors. Current shear deformation theories for laminated anisotropic plates have one drawback or another. Web of science you must be logged in with an active subscription to view this. In the case when an anisotropic plate contains a triangular, oval, or square opening, the only solution available lekhnitski the literature is an approximate solution for orthotropic plates with openings, which was obtained by lekhnitskii using the complex variable formulation.
All problems discussed are concerned only with small elastic strains of plates. Consequently, for analysis of composite plates, a satisfactory transverse shear deformation theory for laminated anisotropic plates is needed. Aliabadi c a faculty of mechanical engineering, state university of campinas, c. The problems of anisotropic plates containing holes, cracks andor inclusions have been studied extensively for twodimensional deformations. First, wu and altiero 6 proposed a numerical solution procedure for the bend ing problems of anisotropic plates based on an indirect method, and they com. Theory of elasticity of an anisotropic elastic body s. An improved transverse shear deformation theory for. Katsikadelis, in the boundary element method for plate analysis, 2014. A study of solutions for the anisotropic plate subjected.
Multilayered composite plates are an example of anisotropic plates whose design demands reliable modeling and. As structural elements, anisotropic elastic plates find wide applications in mod. In the case when an anisotropic plate contains a triangular, oval, or square opening, the only solution available in the literature is an approximate solution for orthotropic plates with openings, which was obtained by lekhnitskii using the complex variable formulation. Wu and mu6 investigated the scf for isotropic plates under uniaxial and bi axial loads. Differing from existing quadratic approximations of failure surfaces, the present theory satisfies the invariant requirements of coordinate transforma tion, treats interaction terms as independent components, takes into account the difference in strengths due to. This book is freely available as a high quality scan in djvu format, or visit your local university library.
L2 however, these solutions were limited to equilateral triangular holes in isotropic and orthotropic plates. Edge function analysis of stress intensity factors in. Anisotropic elastic plates with holescracksinclusions. Anisotropic plates lekhnitskii pdf download citation on researchgate anisotropic plates three main topics are considered.
Sih and liebowitz 102 studied a mode i crack of length 2a in an infinite anisotropic plate see figure 10. Anisotropic plates book free ebook download as pdf file. They used conformal mappings and complex variable method for stress analysis of isotropic and anisotropic plates containing a central cutout. Gives practical equations for the stresses and does not skip any important steps.
The sign convention for the different displace anisotropic plates. Elastic buckling of multilayered anisotropic plates. Anisotropic plate an overview sciencedirect topics. The plates are considered to be subjected to not only inplane loads but also transverse loads. The strength analysis of fastener consists of three components tension strength, shear strength and bending strength. Solutions for any kind of anisotropic plates with various. Pdf threedimensional solutions for antisymmetrically laminated. As no elastodynamic fundamental solution for anisotropic plate bending. Gordon and breach science publishers, new york, 2nd edition, 1968.
408 1075 1306 418 129 94 1271 1144 830 1324 429 1603 666 1322 1357 342 1584 1518 604 941 1142 1309 304 844 597 276 517 426 1561 1216 1135 622 958 878 350 1215 1219 763 738 792 622 441 880