Nonlinear thermoelastic fractional-order model of nonlocal plates: Application to postbuckling and bending response

Abstract

This study presents a comprehensive frame-invariant fractional-order framework for the geometrically nonlinear bending and postbuckling analysis of nonlocal plates subject to combined thermal and mechanical loads. The fractional-order kinematic framework, unlike classical nonlocal formulations based on integer-order mechanics, is positive-definite and thermodynamically consistent. The positive-definite nature enables the application of variational principles to derive well-posed thermomechanical governing equations. A direct advantage of these theoretical advancements is reflected in the ability of the fractional-order approach to enable an energy-based asymptotic method obtained by extending the classical (local) Koiter’s approach. This method allows the analytical assessment of the impact of nonlocal interactions on the nature of the bifurcation and post-critical response of slender structures when subject to compressive loads. Further, the positive-definite nature of the fractional-order approach allows the development of an accurate fractional-order finite element method enabling the simulation of nonlocal structures subject to any combination of thermomechanical loads and boundary conditions. The above stated advantages are particularly important for a comprehensive and consistent analysis of nonlocal structures in the postbuckling regime. The theoretical framework is used to provide analytical and numerical insights on the effect of combined thermal and mechanical loads on the nonlinear response of nonlocal plates. Numerical results also demonstrate the high-level consistency of the framework when applied to the nonlinear thermoelastic analysis of nonlocal plates under different loading and boundary conditions.