在奈米尺度下，材料與結構的力學性質呈現顯著的尺寸效應，主要的原因為表面力的影響所致。本文主要探討高階表/界面力對板結構挫曲和振動的影響，所使用的高階表面力模型，是傳統表面力模型之延伸，主要內容為在材料表面或交界處同時考慮薄膜應力與界面彎矩之合效應。本文將高階表面應力條件導入古典板理論的數學模式，以圓形與矩形板為例，求解簡支承及固定端等不同邊界條件下，平板結構的臨界挫屈力與共振頻率。比較高階界面模型、傳統界面應力模型與線彈性古典板三者之數值結果可發現，高階界面效應會導致臨界挫屈力與自然共振頻率提升，此趨勢隨著結構尺寸減少也變得更加明顯。本文目標希望所提出之理論架構，能更精準的評估奈米尺度下結構的力學行為。

A refined mathematical framework of high-order surface stresses, extended from the conventional surface stresses model, is implemented in the mathematical framework for the modeling of buckling load and resonance frequency of nanoplates. The high-order interface stresses are formulated following the proposition of non-uniform surface stress across the layer thickness, and thereby effectively inducing a membrane stress as well as surface moment. In the formulation the deformation of the thin interphase is approximated by the Kirchhoff-Love assumption of thin plate. In illustration, circular and rectangular nanoplates with simply supported or clamped boundary conditions are exemplified. Analytic for numerical solutions of the derived results are compared with the simplified solutions based on conventional surface stress model and on the classical results of linear elasticity. We aim to explore the scope of applicability that the refined continuum mechanics model could be a valid approach in the estimate of mechanical behavior of nanoplates.

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