Variational Principle for Studying the Long-Term Stability of Structural Materials Subjected to Neutron Irradiation Taking into Account Geometric Nonlinearity

In various branches of modern engineering, including nuclear power engineering and rocket and space technology, structural elements in various forms are widely used. During operation, they can be subjected to both force and non-mechanical loads (thermal, radiation). During operation, they are subjected to radiation loads. Thus, neutron fluxes, penetrating deep into the material, radically change its mechanical properties. Moreover, when irradiated for several years and at high temperatures, as is the case in nuclear reactors, creep deformations become significant, and irradiation and temperature affect the creep of materials differently. Therefore, in those areas of technology where neutron radiation and high temperatures are present, when designing structures, it is necessary to take into account the effect of radiation and temperature on the mechanical properties of the material. The task is further complicated when taking into account geometric nonlinearity.It is practically impossible to obtain an exact solution to such problems, therefore the development of approximate methods is of particular importance. In nonlinear problems, one of the effective approximate methods of solution is the variational method. To solve long-term stability problems by the variational method, it is necessary to develop these methods to be able to take into account geometric nonlinearity and changes in mechanical characteristics. This means that it is necessary to construct a functional that would take into account changes in the mechanical characteristics of the body, taking into account creep deformation and geometric nonlinearity.The article proposes a functional for studying the stability of structural materials (the stress-strain state (SSS) of a body) under neutron irradiation, taking into account geometric nonlinearity and creep deformations. It is proven that the Euler equations of the functional take the form of an equation describing the stress-strain state of a thin shell under irradiation, taking into account geometric nonlinearity and creep deformations.