Matrix Methods in Elasto Mechanics [antikvár]

PREFACE The field of linear elastomechanics has been in a highly developed state for many years, but it was not until the last decade, during which electronic computers were generally available, that the possibilities of matrix calculus were exploited for the static and dynamic treatment of complicated elastic systems. In the authors' opinion these matrix methods, which have proved to be so successful in the study of modern aircraft wings, rocket structures, turbine machinery, etc., have been developed to such a degree that a comprehensive treatise is unlikely to become quickly out of date. The basic philosophy adopted in the book is based on the idea of breaking up a complicated system into component parts with simple elastic and dynamic properties that can be readily expressed in matrix form. These component matrices are considered as building blocks that, when fitted together according to a set of predetermined rules, provide the static and dynamic properties of the entire system. The matrix formulation of these rules is superbly adapted for consumption by digital computers, and furthermore the concise matrix notation brings to light basic properties of linear elastic systems formerly obscured in a mass of algebraic baroque. A common type of system occurring in engineering practice consists of a number of elements linked together end to end in the form of a chain. Well-known examples are continuous beams, turbine-generator shafts, crankshafts, etc. The transfer-matrix method is ideally suited to such systems, because only successive matrix multiplications are necessary to fit the elements together. Intermediate conditions and the number of degrees of freedom present no difficulty since they have no effect on the order of the transfer matrices required; in fact, their size is dependent only on the order of the differential equations governing the behavior of the elements of the system. Although the transfer-matrix method is also suitable for the treatment of branched and coupled systems, its application is inadvisable for systems that lack a predominant chain topology. Then it becomes profitable to employ general methods capable of dealing with any system. Naturally the rules for fitting the building blocks together are more complicated than those of the transfer-matrix method, but nevertheless, with the help of the work principle, a surprisingly efficient and simple formulation is possible. Apart from the demand that the systems must be linearly elastic, no other restrictions are made, so that the methods presented should be of interest to those working in the fields of mechanical, civil, and aeronautical engineering and also to naval architects. It has been assumed in writing the book that the reader is already acquainted with elementary mechanics and strength of materials. In order to limit the mathematical prerequisites to the knowledge of elementary algebra and calculus, it was felt necessary to present in Chapter 1 an introduction to matrix algebra and matrix calculus. The material covered is strictly limited to that necessary for an understanding of the book, vii