Solution of Crack Problems

Solution of Crack Problems

Author: D.A. Hills

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 314

ISBN-13: 9401586489

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This book is concerned with the numerical solution of crack problems. The techniques to be developed are particularly appropriate when cracks are relatively short, and are growing in the neighbourhood of some stress raising feature, causing a relatively steep stress gradient. It is therefore practicable to represent the geometry in an idealised way, so that a precise solution may be obtained. This contrasts with, say, the finite element method in which the geometry is modelled exactly, but the subsequent solution is approximate, and computationally more taxing. The family of techniques presented in this book, based loosely on the pioneering work of Eshelby in the late 1950's, and developed by Erdogan, Keer, Mura and many others cited in the text, present an attractive alternative. The basic idea is to use the superposition of the stress field present in the unfiawed body, together with an unknown distribution of 'strain nuclei' (in this book, the strain nucleus employed is the dislocation), chosen so that the crack faces become traction-free. The solution used for the stress field for the nucleus is chosen so that other boundary conditions are satisfied. The technique is therefore efficient, and may be used to model the evolution of a developing crack in two or three dimensions. Solution techniques are described in some detail, and the book should be readily accessible to most engineers, whilst preserving the rigour demanded by the researcher who wishes to develop the method itself.


Three-dimensional Stress Distribution Near a Sharp Crack in a Plate of Finite Thickness

Three-dimensional Stress Distribution Near a Sharp Crack in a Plate of Finite Thickness

Author: G. H. Sih

Publisher:

Published: 1966

Total Pages: 52

ISBN-13:

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An attempt has been made to investigate the three-dimensional stress distribution near the tip of a semi-infinite crack embedded in an infinite plate of arbitrary thickness. The problem is formulated by means of three biharmonic functions in the classical theory of elasticity as developed by Galerkin. The eigenfunction expansion technique of Williams for solving two-dimensional crack problems is incorporated into the three-dimensional crack analysis. It is found that the stresses rr, theta theta, zz, r theta are singular of the order of r( -1/2), r being the distance measured from the crack point, but the transverse shear components rz, theta z are bounded everywhere in the plate. Determined in an approximate manner is the intensity of the crack-edge stress field which depends on the thickness coordinate of the plate. The results provide an improved understanding of the three-dimensional aspects of fracture theories, particularly on the effect of plate thickness.


Plates and shells with cracks

Plates and shells with cracks

Author: George C. Sih

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 344

ISBN-13: 940101292X

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This third volume of a series on Mechanies of Fraeture deals with eraeks in plates and shelIs. It was noted in Volume 2 on three-dimensional eraek problems that additional free surfaees can lead to substantial mathematical complexities, often making the analysis unmanageable. The theory of plates and shelIs forms a part of the theory of elasticity in which eertain physieal assumptions are made on the basis that the distanee between two bounded surfaees, either fiat or eurved, is small in eomparison with the overall dimen sions of the body. In modern times, the broad and frequent applieations of plate- and shell-like struetural members have aeted as a stimulus to whieh engineers and researchers in the field of fracture meehanies have responded with a wide variety of solutions of teehnieal importanee. These eontributions are covered in this book so that the reader may gain an understanding of how analytieal treat me nt s ofplates and shells containing initial imperfeetions in the form of eraeks are earried out. The development of plate and shell theories has involved long standing controversy on the eonsisteney of omitting eertain small terms and at the same time retaining others of the same order of magnitude. This defieieney depends on the ratio of the plate or shell thiekness, h, to other eharaeteristie dimensions and eannot be eompletely resolved in view of the approximations inherent in the transverse dependence of the extensional and bending stresses.


Multiple Crack Problems in Elasticity

Multiple Crack Problems in Elasticity

Author: Y. Z. Chen

Publisher: Wit Pr/Computational Mechanics

Published: 2003-01

Total Pages: 336

ISBN-13: 9781853129032

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The authors investigate various integral equations for multiple crack problems in plane elasticity. Formulation of the problems is based on relevant elementary solutions in which the complex variable function method is used.


Crack Paths

Crack Paths

Author: L. P. Pook

Publisher: Witpress

Published: 2002

Total Pages: 176

ISBN-13:

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Many engineering structures and components contain cracks or crack-like flaws and it is widely recognized that crack growth must be considered both in the design and analysis of failures. The complete solution of a crack growth problem therefore includes determination of the crack path. At present the factors controlling the path taken by a propagating crack are not completely understood. In general crack paths are difficult to predict, while in practice their development in structures is often determined by large-scale structural tests. In introductory texts on fracture mechanics it is usually assumed that the crack path is known, either from theoretical considerations, or from the results of laboratory tests.


Advanced Finite Element Methods and Applications

Advanced Finite Element Methods and Applications

Author: Thomas Apel

Publisher: Springer Science & Business Media

Published: 2012-07-16

Total Pages: 380

ISBN-13: 3642303161

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This volume on some recent aspects of finite element methods and their applications is dedicated to Ulrich Langer and Arnd Meyer on the occasion of their 60th birthdays in 2012. Their work combines the numerical analysis of finite element algorithms, their efficient implementation on state of the art hardware architectures, and the collaboration with engineers and practitioners. In this spirit, this volume contains contributions of former students and collaborators indicating the broad range of their interests in the theory and application of finite element methods. Topics cover the analysis of domain decomposition and multilevel methods, including hp finite elements, hybrid discontinuous Galerkin methods, and the coupling of finite and boundary element methods; the efficient solution of eigenvalue problems related to partial differential equations with applications in electrical engineering and optics; and the solution of direct and inverse field problems in solid mechanics.


Fracture Mechanics

Fracture Mechanics

Author: Chin-Teh Sun

Publisher: Academic Press

Published: 2011-10-14

Total Pages: 337

ISBN-13: 0123850010

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From a leading expert in fracture mechanics, this text provides new approaches and new applications to advance the understanding of crack formation and propagation.


Meshfree Particle Methods

Meshfree Particle Methods

Author: Shaofan Li

Publisher: Springer Science & Business Media

Published: 2007-03-07

Total Pages: 509

ISBN-13: 3540222561

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Meshfree Particle Methods is a comprehensive and systematic exposition of particle methods, meshfree Galerkin and partitition of unity methods, molecular dynamics methods, and multiscale methods. Most theories, computational formulations, and simulation results presented are recent developments in meshfree methods. They were either just published recently or even have not been published yet, many of them resulting from the authors ́ own research. The presentation of the technical content is heuristic and explanatory with a balance between mathematical rigor and engineering practice. It can be used as a graduate textbook or a comprehensive source for researchers, providing the state of the art on Meshfree Particle Methods.


Extended Finite Element Method for Crack Propagation

Extended Finite Element Method for Crack Propagation

Author: Sylvie Pommier

Publisher: John Wiley & Sons

Published: 2013-03-04

Total Pages: 271

ISBN-13: 1118622693

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Novel techniques for modeling 3D cracks and their evolution in solids are presented. Cracks are modeled in terms of signed distance functions (level sets). Stress, strain and displacement field are determined using the extended finite elements method (X-FEM). Non-linear constitutive behavior for the crack tip region are developed within this framework to account for non-linear effect in crack propagation. Applications for static or dynamics case are provided.