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.

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.

''It is true that "Nothing is more practical than a theory" Provided - however - That the assumptions on which the theory is founded Are well understood. - But, indeed, engineering experience shows that "Nothing can be more disastrous than a theory When applied to a real problem Outside of the practicailimits of the assumptions made", Because of an homonymous identity With the problem under consideration. " (J. T. P. ) The primary objective of this work is to present the theories of analytical and optical isodynes and the related measurement procedures in a manner com patible with the modem scientific methodology and with the requirements of modem technology pertaining to the usefulness of the stress analysis proce dures. The selected examples illustrate some major theses of this work and demonstrate the particular efficiency of the isodyne methods in solving the technologically important problems in fracture mechanics and mechanics of composite structures including new materials. To satisfy this objective it was necessary to depart from the common practice of presenting theories and techniques of experimental methods as a compatible system of equations and procedures without mentioning the tacitly accepted assumptions and their influence on the theoretical admissibility of analytical expressions and the reliability of the experimental or analytical results. It was necessary to design a more general frame of reference which could allow to assess the scientific correctness of isodyne methods and the reliability of experimental results.

This book is based on 40 years of research and teaching in the fields of fracture mechanics and plasticity. It will bring students and engineers from various disciplines up to date on key concepts that have become increasingly important in the design of safety-relevant engineering structures in general and in modern lightweight structures in the transportation industry in particular. Primarily intended for graduate students in the engineering sciences and practicing structural engineers, it employs a multidisciplinary approach that comprises theoretical concepts, numerical methods, and experimental techniques. In addition, it includes a wealth of analytical and numerical examples, used to illustrate the applications of the concepts discussed.