Dynamics of Thin Elasto-Plastic Shells

In Chap. 6, a mathematical model governing the oscillations of a flexible shell with physical nonlinearity and coupling between the thermal and deformation fields has been presented. However, the loading and unoading processes overlap in the (σ _i (e _i ) diagram, and the remaining elasto-plastic deformation has not been taken into account. In a theoretical treatment of complicated shell oscillations, in order to analyse the stress-strain state properly, the elastoplastic deformation should be considered, as well as the fatigue behaviour of the material. Only in this case can the mathematical model be close to the real behaviour of a structure. The aim of this chapter is to describe the development of complex mathematical models of structures, including elastoplastic deformation and cyclic loading.