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

• 作者: Pei ZHANG Hai QING
• 来源期刊: 应用数学和力学（英文版）
• 年，卷（期）: 2021,（7）
• 页码范围: 931-950
• 页数: 20页
• 分类号: O342
• 语种: 英文

摘要

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.