Three-dimensional nonlinear stability analysis of axial-thermal-electrical loaded FG piezoelectric microshells via MKM strain gradient formulations

Abstract

The present study focuses on the moving Kriging meshfree (MKM) technique combined with the three-dimensional strain gradient continuum mechanics to analyze three-dimensional nonlinear stability response of thermo-electro-mechanical loaded functionally graded (FG) piezoelectric cylindrical microshells. The derived three-dimensional MKM model has the capability to present the transition of buckling mode containing different microsize-dependent gradient tensors. The microshells are made of a mixture containing PZT-4 and PZT-5H piezoelectric phases, the material properties of which vary continuously along the shell thickness and captured based on the power law composition scheme. With the aid of MKM strain gradient-based shell model, it is possible to satisfy the function property associated with Kronecker delta by putting the required boundary conditions directly at the associated nodes without any predefined mesh. The microsize-dependent nonlinear stability plots are obtained in the presence of modal transition relevant to various environment temperatures, external electric voltages, microstructural size dependency tensors, and power-law indexes. It is found that the stiffening character related to all three microstructural strain gradient tensors is more significant for the second nonlinear stability mechanical/electrical load in comparison with the first one. However, for the three-dimensional mechanical/electrical bifurcation load, the stiffening character of these gradient tensors becomes even lower than the first postbuckling load. Moreover, by applying an actuation via a positive voltage, the first three-dimensional critical buckling load and the associated end shortening reduce, while an actuation via a negative voltage results in to increase them. It is observed that by shifting to the postbuckling territory, the role of the electric actuation gets negligible.