Old and new problems in continuum structural materials

Abstract

The PhD thesis in Mathematics titled "Old and New Problems in continuum structural masterials " is divided into two parts. In Part I ( Chapter I and II relative to the " Old Problems" ) is studied in particular the classic behavior of materials from the mechanical point of view. In Chapter I were determined tensors of stress and strain in a solid having the shape of a hollow cylindrical , that is not simply connected , when it does act on it a displacement field able to induce all six elementary distortions of Volterra in the case where the material constituting the solid is homogeneous , linearly elastic and transversely isotropic . Unlike Volterra considers an isotropic body, characterized by two elastic constants : (E and G) , presents in the constitutive relations of the material become five (A, C, F, L and N). The result obtained is that the functions of displacement [u1 (x,y,z), u2 (x,y,z), u3 (x,y,z) ] . meet the indefinite equations of elastic written using the five elastic constants , but as Volterra , they do not cancel the load over the entire border of the hollow cylinder . In other words, do not give rise to a real distortion in that the action of the shift functions do not carry the cylinder from a natural configuration to a spontaneous through an isothermal transformation in which the load boundary is null but only self- balanced... [edited by Author]