The effect of a nanoplate buckling at a circular nanohole under the remote uniaxial tension is studied incorporating the surface energy in accordance with the Gurtin–Murdoch surface elasticity model. The hole surface within the framework of the plane problem and the faces of the plate within the framework of the Kirchhoff theory of the plate bending are characterized by both the surface elasticity properties and the residual surface tension. The full potential energy of the plate containing the surface tension with non-strain terms of the surface displacement gradient is derived. Based on the principle of virtual displacements, critical values of the load, corresponding symmetrical and asymmetrical forms of the buckling are found by the Ritz method. Numerical investigations reveal that allowing for the non-strain terms of the surface displacement gradient in the Gurtin–Murdoch constitutive relation leads to the essential increasing the rigidity of the plate and the critical Euler load. Two types of the size effect are detected. The nanoplate thickness and the ratio of the hole radius to the thickness influence independently the value of the critical load.

中文翻译：

---

具有结合表面能的纳米孔的拉伸纳米板的屈曲

根据 Gurtin-Murdoch 表面弹性模型，结合表面能，研究了远程单轴张力下圆形纳米孔处纳米板屈曲的影响。平面问题框架内的孔表面和基尔霍夫板弯曲理论框架内的板面均由表面弹性特性和残余表面张力来表征。导出了包含表面张力和表面位移梯度非应变项的板的全部势能。基于虚位移原理，利用Ritz法求出了载荷的临界值以及相应的对称和非对称屈曲形式。数值研究表明，在 Gurtin-Murdoch 本构关系中考虑表面位移梯度的非应变项会导致板的刚度和临界欧拉载荷显着增加。检测到两种类型的尺寸效应。纳米板的厚度和孔半径与厚度的比率独立地影响临界载荷的值。