Couple stress-based moving Kriging meshfree shell model for nonlinear free oscillations of random checkerboard reinforced microshells

Abstract

In the preset exploration, a numerical strategy based upon the moving Kriging meshfree formulations is proposed to analyze small scale-dependent nonlinear oscillations of random checkerboard reinforced cylindrical microshells. To accomplish this aim, the modified couple stress continuum mechanics is implemented in the third-order shear flexible shell theory. The microshells are made of composites containing graphene nanofillers dispersed in a random checkerboard pattern. The associated material characteristics are captured via a probabilistic-based micromechanical scheme together with the Monte-Carlo simulation. Afterwards, proper meshfree functions are implemented to enforce the essential boundary conditions at the considered nodding system accurately. It is revealed that that by considering the effects of rotation gradient tensor, the frequency ratio associated with a given maximum shell deflection reduces, while the value of linear frequency gets larger. This anticipation is related to stiffening characters of this microstructural gradient tensor. Moreover, it is demonstrated that an increment in the value of the nanofiller volume fraction or its aspect ratio leads to shift the peak of the frequency ratio to a lower value of the shell length to radius ratio.