An adaptive modeling method with a local choice of optimal displacement fields for finite element analysis of structures

In the standard finite element procedure, the user chooses himself which mechanical theory will be used for a given application. To this end, he relies on some rules acquired through experience or some theoretical consideration. But choosing an appropriate theory may be a difficult task when geometry, boundary conditions, loadings, and materials are complex. This paper aims to define an adaptive methodology to identify, in the context of linear static analysis, optimal finite element models from a theory choice point of view. A criterion is defined to choose, in each part of the structure, the relevant mechanical theory: solid, shell or beam. A solid mesh is defined for the whole structure while specific solid-shell or solid-beam approaches are used in shell or beam areas respectively. This avoids the construction of mid-surface or mid-axis geometries from solid ones, which is a complicated task, in particular for industrial applications. Kinematic relations between nodes are imposed to apply the displacement fields of shell or beam theories. This leads to a set of linear equations which are used for eliminating slave degrees of freedom. The methodology proposed can also be interpreted as a model size reduction method, compared to a complete solid approach. The effectiveness of this approach is demonstrated through two numerical examples, including academic cantilever structures and an industrial multilayered composite structure.