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Nonlinear buckling mode transition analysis of axial-thermal-electrical‑loaded FG piezoelectric nanopanels incorporating nonlocal and couple stress tensors

Rao Rui, Ye Zijie, Yang Zhicheng, Sahmani Saeid, Safaei Babak

Archives of Civil and Mechanical Engineering

2022

Vol. 22, no. 3

art. no. e125

Piezoelectric nanostructures are one of the essential components in the design of electromechanical systems and devices at nanoscale. In the present exploration, a size-dependent panel model accommodating the both softening and stiffening features is introduced for nonlinear stability characteristics of functionally graded (FG) piezoelectric cylindrical nanopanels under combinations of axial mechanical load with external electric actuation and temperature change. In accordance with this objective, an efficient numerical strategy based upon the moving Kriging meshfree (MKM) technique is employed within the framework of the nonlocal couple stress (NCS) continuum elasticity. The established NCS-based numerical model has the capability to incorporate the buckling mode transition phenomenon as well as satisfying the function property of Kronecker delta via imposing essential boundary conditions with no use of predefined mesh and directly at the associated nodes. The NCS-based nonlinear equilibrium curves are traced including the modal transition corresponding to various parameter investigations of FG piezoelectric nanopanels. It is deduced that the nonlocal stress tensor leads to increase the difference between the minimum postbuckling loads associated with the first and second buckling modes, while the couple stress tensor causes to reduce it. It is also demonstrated that by changing the sign of electric actuation from negative to positive, the softening character of nonlocality as well as the strengthening character associated with the couple stress size dependency become a bit more significant. Furthermore, the roles of both unconventional stress tensors are more prominent in the value of the second bifurcation point in comparison with the first one.

Isogeometric nonlinear bending analysis of porous FG composite microplates with a central cutout modeled by the couple stress continuum quasi-3D plate theory

Rao Rui, Sahmani Saeid, Safaei Babak

Archives of Civil and Mechanical Engineering

2021

Vol. 21, no. 3

214--230

In the present investigation, by putting the isogeometric finite element methodology to use, the nonlinear flexural response of composite rectangular microplates having functionally graded (FG) porosity is predicted incorporating couple stress type of small scale effect. To accomplish this analysis, a non-uniform kind of rational B-spline functions are employed for an accurate geometrical description of cutouts with various shapes located at the center of microplates. The modified couple stress continuum elasticity is implemented within the framework of a new quasi-three-dimensional (quasi-3D) plate theory incorporating normal deflections with only four variables. By refining the power-law function, the porosity dependency in conjunction with the material gradient are taken into consideration in a simultaneous scheme. The couple stress-based nonlinear flexural curves are achieved numerically based upon a parametrical study. It is demonstrated that for a larger plate deflection, the role of couple stress type of small scale effect on the nonlinear bending curves of porous FG composite microplates is highlighted. It is seen that the gap between nonlinear flexural responses associated with different through-thickness porosity distribution schemes is somehow higher by taking the couple stress effect into account. Also, it is observed that the existence of a cutout at the center of composite microplates makes a change in the slope of their nonlinear flexural curve.