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 unloading 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 elasto-plastic 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 elasto-plastic deformation and cyclic loading.