A NURBS-based isogeometric formulation for geometrically nonlinear analysis of shells

Resumo

Due to their high slenderness, shell structures are vulnerable to collapse caused by loss of stability, hence nonlinear analysis is crucial to ensure a safe design. The advantage of isogeometric analysis (IGA) to exactly describe the geometry of the problem independently of the degree of discretization and allow easy refinements has led to its increasing application in shell analysis. However, IGA does not remove the shear and membrane locking presented by fully integrated shell elements based on Reissner-Mindlin's theory. Thus, several alternatives have been proposed in the literature to solve the locking problem, such as mixed formulation and reduced integration. This work aims to study the effectiveness of different reduced integration schemes to eliminate or alleviate locking in the context of stability and geometrically nonlinear analysis of Reissner-Mindlin shells based on the degenerated solid approach. The proposed formulation is applied to the stability analysis of plates and shells, where critical loads and nonlinear equilibrium paths are evaluated and compared to solutions available in the literature or obtained by the Finite Element Method. Excellent results were obtained, demonstrating that a very accurate and efficient approach for nonlinear analysis of plates and shells can be achieved by using high regularity basis functions obtained by k-refinement and an appropriate reduced integration scheme. This approach not only avoids locking but also reduces the computational cost of nonlinear analysis of shells.