Treatise on classical elasticity : theory and related problems

Abstract

Deformable solids have a particularly complex character; mathematicalmodeling is not always simple and often leads to inextricable difficultiesof computation. One of the simplest mathematical models and, at thesame time, the most used model, is that of the elastic body - especiallythe linear one. But, notwithstanding its simplicity, even this modelof a real body may lead to great difficulties of computation.The practical importance of a work about the theory of elasticity,which is also an introduction to the mechanics of deformable solids,consists of the use of scientific methods of computation in a domainin which simplified methods are still used.This treatise takes into account the consideration made above, withspecial attention to the theoretical study of the state of strainand stress of a deformable solid. The book draws on the known specializedliterature, as well as the original results of the author and his50+ years experience as Professor of Mechanics and Elasticity atthe University of Bucharest. The construction of mathematical modelsis made by treating geometry and kinematics of deformation, mechanicsof stresses and constitutive laws. Elastic, plastic and viscous propertiesare thus put in evidence and the corresponding theories are developed.Space problems are treated and various particular cases are takeninto consideration. New solutions for boundary value problems offinite and infinite domains are given and a general theory of concentratedloads is built. Anisotropic and non-homogeneous bodies are studiedas well. Cosserat type bodies are also modeled. The connection withthermal and viscous phenomena will be considered too.Audience: researchers in applied mathematics, mechanical and civilengineering.