Civil Engineering Association

‪Analytical Methods in Anisotropic Elasticity‬

Prior to the computer era, analytical methods in elasticity had already been developed and improvedup to impressive levels. Relevant mathematical techniques were extensively exploited,contributing significantly to the understanding of physical phenomena. In recent decades, numerical computerized techniques have been refined and modernized, and have reached highlevels of capabilities, standardization and automation. This trend, accompanied by convenient and high resolution graphical visualization capability, has made analytical methods less attractive, 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 capabilities to perform complex derivation processes that were once considered impractical. Generally speaking, it is well recognized that analytical solutions should be applied to relatively 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 complementary: 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. Nevertheless, from a practical point of view, analytic solutions are still considered as “art”, while numerical codes (such as codes that are based on the finite-element method) seem to offer a “straightforward” solution for any type and geometry of a new problem. One of the reasons for this view emerges from the variety of techniques that are used for analytical solutions. For example, one has the option to select either the deformation field or the stress field to construct the initial solution hypothesis, or, one has the option to formulate the governing equations using differential equilibrium, or by employing more integral energy methodologies for the same task. Hence, the main obstacle to using analytical approaches seems to be the fact that many researchers and engineers tend to believe that, as far as analytic solutions are considered, each problem is associated with a specific solution type and that a different solution methodology has to be tailored for every new problem.

Additional info:

Language English
ISBN-10: 0817642722
ISBN-13: 9780817642723


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