CAJ | 학술논문

研究了远场作用反平面剪切载荷时含纳米椭圆孔正交异性材料问题。基于Gurtin-Murdoch表面/界面理论模型引入界面应力，利用复变弹性理论和保角映射方法，给出了考虑界面应力时含椭圆孔正交异性材料反平面问题的解析解答，获得了应力场的闭合解。研究表明：当椭圆孔在纳米量级时，正交异性材料内应力场受孔隙尺寸影响显著。随着椭圆孔尺寸的增大，界面效应对应力场的影响逐渐减弱，趋近于经典弹性理论的解答。界面效应对正交异性材料内应力场的影响随着材料弹性主方向比55/44的增大逐渐减弱。
연구료원장작용반평면전절재하시함납미타원공정교이성재료문제。기우Gurtin-Murdoch표면/계면이론모형인입계면응력，이용복변탄성이론화보각영사방법，급출료고필계면응력시함타원공정교이성재료반평면문제적해석해답，획득료응력장적폐합해。연구표명：당타원공재납미량급시，정교이성재료내응력장수공극척촌영향현저。수착타원공척촌적증대，계면효응대응력장적영향축점감약，추근우경전탄성이론적해답。계면효응대정교이성재료내응력장적영향수착재료탄성주방향비55/44적증대축점감약。
A theoretical study on the orthotropic materials containing nano elliptic cavity under anti-plane shear is reported. Interface stress is introduced based on the theory of Gurtin-Murdoch surface/interface model. A rigorous whole-field solution is presented by using the complex variable elasticity theory and the conformal mapping method, in terms of which closed-form solutions of the stress field is obtained. The results reveal that the stress fields in the orthotropic materials are size dependent when the size of the nano elliptic cavity is on the order of nanometer. The present solution approaches to the classical elasticity theory results with the increase of the nano elliptic cavity. The influence of the interfacial effects on the stress fields in the orthotropic materials decrease with the increase of the ratio of elastic main direction 55/ 44.