Shell Analysis Using a Solid-Shell Approach

Resumo

Shells are curved three-dimensional structures whose thickness is much smaller than their other two dimensions. They can be found in various sectors, such as aerospace, energy, naval and civil engineering. There are several structural theories in the literature to deal with this type of structure, such as Kirchhoff-Love, Reissner-Mindlin and Higher-order theories. However, these theories are based on assumptions that require rotational degrees of freedom in their kinematic description, making the problem complex, especially for geometrically nonlinear analysis, since large 3D rotations are not additive. Furthermore, in shell theories, it is usually assumed that there is no thickness stretching. In other words, the normal transversal strain is neglected, so it is not possible to use full 3D constitutive models for the analysis. With this in mind, the structural modeling in this work will be based on the solid-shell approach, which uses a 3D mesh with only one element through the thickness and does not require rotational degrees of freedom in the kinematic description, like in solid elements, but with a lower computational cost. Its formulation considers the general stress state, so a complete 3D constitutive relation is assumed. The use of this theory in structural problems results in partial differential equations whose analytical solutions are very complex or impossible to obtain, thus requiring the use of numerical methods to obtain approximate results. The presented formulation can be applied to develop isoparametric and isogeometric solid-shell elements. The performance of linear and quadratic elements is assessed using numerical examples.