Stability analysis of nanoscale non-uniform sandwich I-section beams with AFG core and two metal face-sheets under flexural loadings

Abstract

This work purposes to familiarize a novel, straightforward, and low-cost technique to accurately evaluate the sustainable lateral buckling load of non-uniform sandwich I-shaped nanobeam subjected to flexural loading. The weak form governing differential equations of the problem, which includes both lateral displacement and twisting angle, originates in the context of Eringen's non-local elasticity theory and Vlasov's model for non-uniform torsion, along with the classical laminated plate theory. From the mathematical viewpoint, the resulting variational formula is rewritten solitary based on the twisting angle. Finally, the Ritz technique is used to solve the equations and estimate the endurable lateral buckling load. The most crucial advantageous specification of the developed formula is the simplification of the fundamental computational complexities for calculating the endurable transverse buckling load of nanoscale non-uniform three-layered I-section beam elements. After checking the accuracy and reliability of the proposed analytical methodology, comprehensive parameterization research is conducted to investigate the sensitivity of lateral buckling resistance to the tapering parameter, non-local parameter, end moment ratio, volume fraction exponent, and thickness ratio. Numerical outcomes represent that in most cases, the extracted formula not only achieves the endurable buckling capacity precisely but also requires far less central processing unit time.