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- Title
On well-posedness of two-phase nonlocal integral models for higher-order refined shear deformation beams.
- Authors
Zhang, Pei; Qing, Hai
- Abstract
Due to the conflict between equilibrium and constitutive requirements, Eringen's strain-driven nonlocal integral model is not applicable to nanostructures of engineering interest. As an alternative, the stress-driven model has been recently developed. In this paper, for higher-order shear deformation beams, the ill-posed issue (i.e., excessive mandatory boundary conditions (BCs) cannot be met simultaneously) exists not only in strain-driven nonlocal models but also in stress-driven ones. The well-posedness of both the strain- and stress-driven two-phase nonlocal (TPN-StrainD and TPN-StressD) models is pertinently evidenced by formulating the static bending of curved beams made of functionally graded (FG) materials. The two-phase nonlocal integral constitutive relation is equivalent to a differential law equipped with two restriction conditions. By using the generalized differential quadrature method (GDQM), the coupling governing equations are solved numerically. The results show that the two-phase models can predict consistent scale-effects under different supported and loading conditions.
- Subjects
SHEAR (Mechanics); DIFFERENTIAL quadrature method; CURVED beams; INTEGRALS
- Publication
Applied Mathematics & Mechanics, 2021, Vol 42, Issue 7, p931
- ISSN
0253-4827
- Publication type
Article
- DOI
10.1007/s10483-021-2750-8