Isogeometric analysis of FG-CNTRC plates in combination with hybrid type higher-order shear deformation theory

Abstract

Abstract Bezier extraction based isogeometric finite element analysis method coupled with a new hybrid type higher-order shear deformation theory (HSDT) is presented for the static bending and buckling analysis of functionally graded carbon nanotube reinforced composite (FG-CNTRC) plates. By mapping non-uniform rational B-spline basis functions to Bezier element in the forms of Bernstein polynomial basis via the Bezier extraction operator, the isogeometric analysis (IGA) can be implemented in the conventional finite element method (FEM) framework. This study focuses on the introduction of the Bezier extraction based IGA combined with the HSDT for the static analysis through the formulation and implementation of the second-order derivatives of the Bezier element basis functions, which has hardly been attempted in the open literature. Compared to the conventional FEM based on first-order shear deformation theory, the present IGA method based on the HSDT surmounts the shear locking without exploiting the shear correction factor. The proposed isogeometric approach is thus believed to be more accurate and effective and achieves higher convergence as the polynomial order increases. Performance accuracy of the Bezier extraction based isogeometric approach is first evidenced by comparing the computed results with the reference solutions, followed by the illustrative examples to further explore the flexural and buckling behavior of FG-CNTRC plates with various reinforcement patterns.