Modeling of non-isothermal elastic-plastic behavior of reinforced shallow shells in the framework of a refined bending theory

The dynamic problem of non-isothermal and inelastic deformation of flexible shallow multidirectionally reinforced shells is formulated in the frameworks of the refined theory of bending. The temperature is approximated by a 7th order polynomial over the thickness of constructions. The geometric nonlinearity of the problem is modeled by the Karman approximation. The solution of the formulated coupled nonlinear two-dimensional problem is obtained using an explicit numerical scheme. The thermo-elastic-plastic response of fiberglass and metal-composite cylindrical elongated panels with an orthogonal reinforcement structure, loaded frontally with an air blast wave, has been studied. It is shown that, unlike reinforced plates similar in structure and characteristic dimensions, shallow shells under intense short-term loading must be calculated taking into account the occurrence of temperature fields in them. In this case, the refined theory of bending of curved panels should be used instead of the simplified version (the non-classical theory of Ambartsumyan). The temperature increment at separate points of shallow fiberglass shells can reach 14–34 \textcelsius, and in similar metal-composite panels can reach 50–150 \textcelsius. Cylindrical shallow shells are more intensively deformed when they are loaded by an air blast wave from the side of a convex front surface.