Buckling mode transition in nonlinear strain gradient-based stability behavior of axial-thermal-electrical loaded FG piezoelectric cylindrical panels at microscale

Abstract

In the current investigation, the microstructural-dependent nonlinear stability characteristics of functionally graded (FG) piezoelectric cylindrical micropanels under combinations of axial mechanical load with external electric actuation and temperature are studied. To this purpose, an efficient numerical strategy based upon the moving Kriging meshfree (MKM) technique is employed within the framework of the modified strain gradient continuum elasticity. The established unconventional formulations take the buckling mode transition phenomenon into consideration in the presence of microstructural size effects including rotation gradient, dilatation gradient, and deviatoric stretch gradient tensors, The derived microsize-dependent panel model has the capability to satisfy the function property of Kronecker delta via imposing essential boundary conditions with no use of predefined mesh and directly at the associated nodes. The unconventional nonlinear equilibrium curves are traced including the modal transition corresponding to different parametric change values. It is displayed that the microsize dependency leads to shift the minimum nonlinear stability loads associated with the first and second buckling modes to a lower panel deflection and a higher panel shortening. Also, it is revealed that the effects of all three microstructural gradient tensors on the second nonlinear stability load are higher than that on the first one, and the both cases are more prominent than the microsize dependencies on the critical buckling load. Also, it is observed that the value of property gradient index has a negligible role on the first and second critical shortenings as well as shell deflections at the first and second minimum nonlinear stability points.