Problemas de Elasticidad Lineal: Resultados Teóricos y Numéricos Aplicaciones

Abstract

Solid mechanics studies the physical behavior of solids in general, establishing within it a distinction between rigid solids and deformable solids. Our study is included within the latter, but since it is a fairly extensive field we will impose some additional hypotheses, with which we manage to narrow the study and also facilitate the mathematical approach to the problem. We will assume that when our deformable solid is subjected to external forces, these will give rise to small displacements and small deformations, also having an elastic and linear behavior.In these specific circumstances we will find our object of study, the linear elasticity problems. In order to study these problems, we will resort to continuous media mechanics, with which a mathematical model is created whose geometric points are identified with the material particles of the body that we intend to study. The model that we will use in the theory of elasticity is continuous, elastic and is endowed with properties of homogeneity and isotropy. In the development of this work the implication that these properties have will be shown. As a previous step we will need to familiarize ourselves with the concepts of strain tensor, internal stress tensor, elastic constant tensor and finally we will see the relationship that exists between them.