Nonlocal and couple stress tensors in three-dimensional nonlinear dynamical stability behavior of microshells manufactured by smart materials

Abstract

By taking simultaneously the nonlocal stress and couple stress tensors into account, the nonlinear three-dimensional dynamical stability of smart microshells manufactured from functionally graded (FG) piezoelectric under a combination of axial compression, electric actuation, and temperature change is examined. In this regard, a unified three-dimensional small-scale-dependent shell model within the framework of the nonlocal couple stress continuum elasticity is originated to implement the unconventional stress tensors in conjunction with the influence of the geometrical nonlinearity. Through setting up an efficient numerical strategy via the generalized differential quadrature technique and pseudo-arc-length continuation method, the derived size-dependent nonlinear three-dimensional differential equations together with different employed boundary conditions are discretized and solved to trace the size-dependent dynamic stability paths of FG piezoelectric microshells. It is demonstrated that by changing the sign of the applied external electric voltage as well as the temperature change from negative to positive, the softening character associated with the nonlocal stress tensor and stiffening character associated with the couple stress tensor become more significant within both the postbuckling and prebuckling regime. Also, it is observed that through combination of the axial compression with an actuation via a positive electric voltage, the bifurcation point shifts to a lower applied compression as well as it causes to reduce the linear frequency within the prebuckling domain, and the nonlinear frequency ratio within the postbuckling regime.