Multi-patch NURBS formulation for anisotropic variable angle tow composite plates

Abstract

Conventional methods result in sharp variation of stiffness in analysis of variable angle tow (VAT) composite plates, which can be enhanced using high-order continuity of non-uniform rational B-spline (NURBS). To this end, a Bézier extraction-based isogeometric (IGA) model based on the higher-order shear deformation theory (HSDT) is developed for the parametric instability study of anisotropic VAT composite plates. Bézier extraction-based IGA approach expresses exactly the orientation function of VAT composites for multi-patch geometries, which provides accurate solution for general-shape plates. The accuracy and convergence of the developed framework is compared with recently formulated methods. Primary results shows that the developed concept solves VAT problems with much lower number of equations than variable kinematic models. Further, response characteristics of analyzed anisotropic VAT plates are presented and discussed considering various fiber orientation functions, boundary conditions and multi-patch geometry. Based on results, Bézier control mesh is more accurate than the NURBS-based IGA solution due to considering the continuity of strain field along coupled boundaries. Anisotropic VAT plates have severe deformation couplings and the current concept accurately captures this feature even with courser meshes. The interaction between boundary conditions and fiber orientations along edges affects mainly the dynamic instability regions (DIR) of modeled VAT plates, dislike to straight fiber ones. The dynamic instability opening (DIO) of VAT plates relies on the fiber orientation functions and boundaries. In anisotropic VAT plates, maximum frequency case and maximum buckling force case would not necessarily be the same. Modes shapes are variable of external force intensity and therefore the Rayleigh-Ritz based methods are not appropriate for dynamic stability analysis of VAT plates. It is essential to change the NURBS control mesh to the Bézier type to offer the required accuracy for the multi-patch domains.