Study of the influence of physical nonlinearities of spherical caps made by Elastomeric Materials

Resumo

The analysis of the behavior of structural elements in terms of variations in physical and geometric influences has been the subject of study since the early days of mechanical and structural engineering research. When it comes to shells, especially those composed of hyperelastic materials, many researchers have carried out work evaluating both the influences of the type of curvature of these elements and the type of deformation expected due to hyperelasticity. This work will investigate the behavior of a spherical cap with a boundary condition established by the locking of the circumference that makes up its base and subjected to uniformly distributed loading on its surface. Two different types of material were considered, one elastic following Hooke's Law and the other hyperelastic represented by elastomeric constitutives models. The Novozhilov and Donnell-Mushtari-Vlasov (DMV) shell theories together with the Rayleigh-Ritz method are used to obtain the governing equations of the problem. The displacements will be approximated using trigonometric functions in the circumferential direction and the Legendre polynomial of the first type in the meridional direction. Linear results are obtained, such as natural frequencies, and non-linear results, such as frequency-displacement and load-displacement relationships.