Mathematical models for elastic structures / Piero Villaggio.

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Basic concepts. Density, motion, and temperature. Balance equations. Constitutive equations. The search for solutions. The notion of a loading device. An example of alternative modeling -- Rod theories: three-dimensional approach. Geometrical properties of rods. Approximation of three-dimensional equations. Rod problems in linear elasticity. Uniformly loaded beams (Michell's Theory). Timoshenko's Correction. Vlasov's theory for thin-walled beams. The influence of concentrated loads. The Influence of curvature. The influence of initial twist. The Energy of an elastic rod. The Influence of large strains.

Elastic structures, conceived as slender bodies able to transmit loads, have been studied by scientists and engineers for centuries. By the seventeenth century several useful theories of elastic structures had emerged, with applications to civil and mechanical engineering problems. In recent years improved mathematical tools have extended applications into new areas such as geomechanics and biomechanics. This book, first published in 1998, offers a critically filtered collection of the most significant theories dealing with elastic slender bodies. It includes mathematical models involving elastic structures, which are used to solve practical problems with particular emphasis on nonlinear problems. This collection of interesting and important problems in elastic structures will appeal to a broad range of scientists, engineers and graduate students working in the area of structural mechanics.