本文以Eringen微極彈性理論(MET)為基礎，利用平面線性三角形元素，依照所推導之位移、微旋轉、應力及力偶應力之關係，以有限元素法撰寫Fortran 電腦語言程式，來分析微極彈性內凹型蜂巢結構結構之波桑比，並探討結構之幾何變化及微極彈性常數之變化對結構之波桑比之影響。 由數值分析結果得知，微極彈性內凹型蜂巢結構其內凹角度(幾何限制範圍內)在30度時具有較低，更甚有負值的波桑比值出現。 而在微極彈性常數之限制條件下，當改變微極彈性常數(α＝0、β＝0、γ、κ、λ、μ*)時，我們可以找到使結構之波桑比出現負值的各個常數範圍，並可依照所需條件去選擇材料。 Based on the Eringen's micropolar elasticity theory (MET), a two-dimensional triangular finite element formulation is desired using constant strain triangle (CST) element and a corresponding computer program is developed to investigate the relation between the value of Poisson’s ratio for the re-entrant honeycomb structure by the variation of micropolar elastic constants and structural geometry. According to our numerical results, the honeycomb structure can exhibit negative Poisson’s ratio with appropriate re-entrant angle. Under the restrictions on micropolar elastic constants, we find that the value of Poisson’s ratio varied when changing the micropolar elastic constants. The range of micropolar elastic constants when the Poisson’s ratio become negative is obtained.
