A seven-parameter high-order finite element model for multi-stable analysis of variable stiffness laminated shells

Abstract

Variable angle fiber composites provide large design space for multi-stable structures. However, they require reliable numerical models to accurately predict their mechanical behavior characterized by a complex material response and large deformation. To this end, we propose an accurate yet efficient model for stability analysis of variable angle fiber laminated shells. In this model, first a seven-parameter shell formulation with Equivalent Single Layer theory, which is suitable for three-dimensional constitutive laws, is utilized to accurately characterize the large deformation. The fiber orientation angle is described by a linear variation from the center to the end of the shell. Then, to improve the accuracy and to reduce the computational cost, the spectral/hp element with high-order polynomial basis functions is adopted for discretization. Finally, complex nonlinear equilibrium paths are effectively tracked by the Riks method. By comparison with ABAQUS solutions, the proposed model shows to be efficient and accurate for variable angle fiber laminates under various conditions, in which both the buckling, the snap-through and tristability behaviors are studied. Moreover, variable angle fiber shells provide more design possibilities than straight fiber shells. By opportunely varying the fibers angle of each lamina, it is possible to control the stable states as well as to obtain multiple stable configurations (bi- and tri-stability).