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Full Description
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.
Contents
1 Interaction of arbitrary array of cracks in wide plates under classical bending.- 1.1 Introduction.- 1.2 Basic relations.- 1.3 Complex potentials for traction free cracks.- 1.4 Arbitrary array of cracks in wide plate.- 1.5 Numerical results.- 1.6 Discussions.- References.- 2 Improved approximate theories of the bending and extension of flat plates.- 2.1 Introduction.- 2.2 Approximate theories by variational methods.- 2.3 Applications to crack problems.- 2.4 Guidelines for practical applications.- References.- 3 Through cracks in multilayered plates.- 3.1 Introduction.- 3.2 Minimum complementary energy applied to a layered plate.- 3.3 An approximate three-dimensional theory of multi-layered plates.- 3.4 Through crack in a layered plate.- 3.5 Stress distribution across the plate thickness.- 3.6 Discussion of numerical results.- 3.7 Appendix: Definition of constants.- References.- 4 Asymptotic approximations to crack problems in shells.- 4.1 Introduction.- 4.2 General theory - classical.- 4.3 The stress field in a cracked spherical shell.- 4.4 The stress field in a cracked plate.- 4.5 The stress field in a cracked cylindrical shell.- 4.6 Approximate stress intensity factors for other shell geometries.- 4.7 Plates on elastic foundations.- 4.8 Particular solutions.- 4.9 Discussion.- References.- 5 Crack problems in cylindrical and spherical shells.- 5.1 Introduction.- 5.2 Formulation of the specially orthotropic cylindrical shell problem.- 5.3 The skew-symmetric problem.- 5.4 The symmetric problem.- 5.5 Results for a specially orthotropic cylindrical shell.- 5.6 The effect of Poisson's ratio.- 5.7 Interaction of two cracks.- 5.8 Further results for isotropic shells.- References.- 6 On cracks in shells with shear deformation.- 6.1 Introduction.- 6.2 Shell theory withshear deformation.- 6.3 Symmetric loading.- Appendix: Integrand and Kernel functions.- References.- 7 Dynamic analysis of cracked plates in bending and extension.- 7.1 Introduction.- 7.2 Classical plate bending theory.- 7.3 Mindlin's theory of plate bending.- 7.4 Kane-Mindlin's equation in plate extension.- 7.5 Plates subjected to sudden loading.- References.- 8 A specialized finite element approach for three-dimensional crack problems.- 8.1 Introduction.- 8.2 Three-dimensional elastic calculations.- 8.3 Finite element method — background.- 8.4 Specialized elements for the crack edge.- 8.5 Applications to crack problems.- 8.6 Details of the analysis.- 8.7 Results of the finite element analysis.- 8.8 Summary.- References.- Author's Index.
