Análise não linear de cascas utilizando uma abordagem isogeométrica

Abstract

Shells are present in different branches of engineering, being widely used in civil, aeronautical, mechanical, automotive, and naval structures. However, these structures are sensitive to collapse triggered by the loss of stability due to their characteristic high slenderness and, therefore, a careful investigation is extremely important to guarantee a safe design. Thus, nonlinear analyses are necessary, in which the consideration of large displacements and rotations is fundamental. The use of isogeometric analysis has been growing, due to its ability to exactly represent the geometry of the structure regardless of the degree of discretization and to facilitate model refinement. This work presents an isogeometric formulation based on NURBS for nonlinear geometric analysis of shells based on the Reissner-Mindlin theory and the degenerate solid approach. Geometrically nonlinear effects are incorporated using the Total Lagrangian approach, allowing the analysis of shells with large displacements and rotations. The implementations were carried out in the open-source software FAST (Finite element AnalySis Tool), written in C++ language using Object Oriented Programming. The initial normal vectors at the control points are obtained by solving a defined system of equations at the Greville points. Several director vectors update strategies and three different numerical integration schemes, used to alleviate the locking problem, are compared. The accuracy of the proposed formulation is evaluated through linear and nonlinear analyses of shell analysis benchmarks. The responses obtained were compared with those available in the literature and, in all tests, the formulation showed good results. In linear tests, the efficiency of the integration scheme used to alleviate, if not eliminate, locking was demonstrated through convergence studies. In nonlinear tests, large displacements and rotations were accurately described using a simple and efficient scheme for updating the director vector capable of removing the restriction of small nodal rotations between two successive load increments and guaranteeing quadratic convergence of equilibrium iterations. The uniform reduced integration slightly alleviated the locking and the non-uniform significantly reduced the locking in some examples, but the accuracy of the results was affected in some cases.