On well-posedness of two-phase nonlocal integral models for higher-order refined shear deformation beams

Abstract Due to the conflict between equilibrium and constitutive requirements, Eringen’s strain-driven nonlocal integral model is not applicable nanostructures of engineering interest. As an alternative, stress-driven has been recently developed. In this paper, for higher-order shear deformation beams, ill-posed issue (i.e., excessive mandatory boundary conditions (BCs) cannot be met simultaneously) exists only in models but also ones. The well-posedness both strain- two-phase (TPN-StrainD TPN-StressD) pertinently evidenced by formulating static bending curved beams made functionally graded (FG) materials. relation equivalent a differential law equipped with two restriction conditions. By using generalized quadrature method (GDQM), coupling governing equations are solved numerically. results show that can predict consistent scale-effects under different supported loading