Isogeometric couple stress continuum-based linear and nonlinear flexural responses of functionally graded composite microplates with variable thickness

Abstract

The proposed study scrutinizes the small scale-dependent geometrical nonlinear flexural response of arbitrary-shaped microplates having variable thickness made of functional graded (FG) composites. Accordingly, the modified couple stress continuum elasticity incorporating the von Karman large deflection supposition is established within a quasi-three dimensional (quasi-3D) plate framework in which the transverse shear deformation and normal deflection are assumed to be distributed in and trigonometric schemes. The thickness variation of microplates are assumed in linear, convex and concave patterns. Next, to resolve the couple stress-based nonlinear bending problem, the isogeometric technique incorporating non-uniform B-spline functions is taken into consideration to implement the both discretized-based estimation and accurate geometric description. The gradient of rotation associated with the couple stress type of size dependency causes a stiffening phenomenon in the both linear and nonlinear flexural responses. Also, through considering a change in the thickness variation pattern firstly from the convex kind to the linear one, thereafter from the linear kind to concave one, the role of couple stress size dependency becomes a bit more pronounced. In addition, it is deduced that the gap between nonlinear flexural curves associated with the convex, linear and concave patterns of thickness variation gets larger by changing the boundary conditions of the FG composite arbitrary-shaped microplates from clamped ones to simply supported ones.