Analytical Methods in Anisotropic Elasticity e-bog

Prior to the computer era, analytical methods in elasticity had already been developed and - proved up to impressive levels. Relevant mathematical techniques were extensively exploited, contributing signi?cantly to the understanding of physical phenomena. In recent decades, - merical computerized techniques have been re?ned and modernized, and have reached high levels of capabilities, standardization and automation. This trend, accompanied by convenient and high resolution graphical visualization capability, has made analytical methods less attr- tive, and the amount of effort devoted to them has become substantially smaller. Yet, with some tenacity, the tremendous advances in computerized tools have yielded various mature programs for symbolic manipulation. Such tools have revived many abandoned analytical methodologies by easing the tedious effort that was previously required, and by providing additional capab- ities to perform complex derivation processes that were once considered impractical. Generally speaking, it is well recognized that analytical solutions should be applied to re- tively simple problems, while numerical techniques may handle more complex cases. However, it is also agreed that analytical solutions provide better insight and improved understanding of the involved physical phenomena, and enable a clear representation of the role taken by each of the problem parameters. Nowadays, analytical and numerical methods are considered as c- plementary: that is, while analytical methods provide the required understanding,numerical solutions provide accuracy and the capability to deal with cases where the geometry and other characteristics impose relatively complex solutions.