Ebook: Elasticity of Transversely Isotropic Materials

This book aims to provide a comprehensive introduction to the theory and applications of the mechanics of transversely isotropic elastic materials. There are many reasons why it should be written. First, the theory of transversely isotropic elastic materials is an important branch of applied mathematics and engineering science; but because of the difficulties caused by anisotropy, the mathematical treatments and descriptions of individual problems have been scattered throughout the technical literature. This often hinders further development and applications. Hence, a text that can present the theory and solution methodology uniformly is necessary. Secondly, with the rapid development of modern technologies, the theory of transversely isotropic elasticity has become increasingly important. In addition to the fields with which the theory has traditionally been associated, such as civil engineering and materials engineering, many emerging technologies have demanded the development of transversely isotropic elasticity. Some immediate examples are thin film technology, piezoelectric technology, functionally gradient materials technology and those involving transversely isotropic and layered microstructures, such as multi-layer systems and tribology mechanics of magnetic recording devices. Thus a unified mathematical treatment and presentation of solution methods for a wide range of mechanics models are of primary importance to both technological and economic progress.

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This book presents a comprehensive and systematic analysis of problems of transversely isotropic materials that have wide applications in civil, mechanical, aerospace, materials processing and manufacturing engineering. Various efficient methods based on three-dimensional elasticity are developed under a unified framework, including the displacement method, the stress method, and the state-space method. In particular, a three-dimensional general solution is derived to solve practical problems such as the infinite space, half-space, bimaterial space, layered medium, bodies of revolution, thermal stresses and three-dimensional contact. Exact and analytical solutions are also derived for static and dynamic problems of plates and shells, which may be used as the benchmarks for numerical or approximate analysis. Coupling effects of inner/outer fluids and surrounding elastic media on the free vibration cylindrical and spherical shells are discussed in detail. New state-space formulations are established for the analysis of rectangular plates and spherical shells, from which two independent classes of vibrations can be easily clarified.