| In last fourty years, more and more works has been done to analyze the problem of nanoscale defects by applying the Gurtin-Murdoch surface model. But most scholars mostly ignored the surface energy caused by the surface effect, and the research about the surface effect of elliptical hole is much less. Taking an infinite elastic plane with nanopores as our model, we study the surface energy under surface effects in the elastic plane containing circular holes without external load, and the surface effects in elastic plane containing elliptical holes without external load. The thesis mainly includes two items as following:(1)Based on the Gurtin-Murdoch surface model, taking an infinite elastic plane with nanopores as our model, we solve the surface energy only caused by the surface effect. The surface energy caused by surface effects in the elastic plane with nanopores ultimately tends to be constant along with the increase of the circular radius, no matter what material the matrix is.Under the surface effect, there are two ways how the surface energy varies: dicontinuity points existing or being continuous. Finally the surface energy and displacement gradually tend to be constant with the increase of the circular radius.(2)We use the finite element software FEniCS to analyze the influence of surface effect on mechanical performance of materials via Python programming. Based on the complete Gurtin-Murdoch surface model, the Mises stress and displacement of an infinite plane contained a single elliptical hole without external load are studied. Based on the yield strength of the material, the correlation between the surface effect and the size ratio of the elliptic hole is analyzed. Results show that the Mises stress in the elliptical hole tip is negatively correlated to short-lo ng axis ratio of the ellipse hole because of the surface effect. Also the minimal curvature radius at the end point of the long axis in the is sloved ellipse hole is solved within the elastic range. |
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