Dynamic analysis of carbon nanotube reinforced composite plates by using Bezier extraction based isogeometric finite element combined with higher- order shear deformation theory

摘要

This study intends to explore the free vibration and dynamic transient response of carbon nanotube reinforced composite (CNTRC) plates by using the Bezier extraction based isogeometric analysis (IGA). Bezier extraction decomposes non-uniform rational B-spline (NURBS) basis functions into the linear combinations of Bernstein polynomial basis through the Bezier extraction operator, hence providing piecewise C-0-continuous Skier elements. The IGA can thus be implemented in the familiar fmite element method (FEM) framework. Higher-order shear deformation theory (HSDT) able to remedy the shear locking problem with no use of the shear correction factor is coupled with the variant IGA. The HSDT adopts a hybrid type shape function, and the governing equilibrium equations for the dynamic behavior are formulated by virtue of the Hamilton's principle. The validity of the Bezier extraction based isogeometric approach coupled with the HSDT in obtaining the solutions for the free vibration and dynamic transient response is first evidenced. Compared with the classical FEM based on the first-order shear deformation theory, the proposed IGA method combined with the HSDT is proved to be more accurate, effective and efficient. Illustrative parametric studies are also carried out to further scrutinize the dynamic behavior of CNTRC plates with various reinforcement schemes. The sinusoidally distributed transverse loads with different time-history patterns and harmonic excitation loading are applied for the dynamic transient analysis, and the damping effect on the temporal response is also examined through the Rayleigh damping model.