Sadeghian Mostafa, Palevicius Arvydas, Janusas Giedrius
Faculty of Mechanical Engineering and Design, Kaunas University of Technology, Studentu 56, 51424 Kaunas, Lithuania.
Micromachines (Basel). 2023 Sep 19;14(9):1790. doi: 10.3390/mi14091790.
This article presents the nonlinear investigation of the thermal and mechanical buckling of orthotropic annular/circular single-layer/bilayer nanoplate with the Pasternak and Winkler elastic foundations based on the nonlocal strain gradient theory. The stability equations of the graphene plate are derived using higher-order shear deformation theory (HSDT) and first-order shear deformation theory (FSDT) considering nonlinear von Karman strains. Furthermore, this paper analyses the nonlinear thermal and mechanical buckling of the orthotropic bilayer annular/circular nanoplate. HSDT provides an appropriate distribution for shear stress in the thickness direction, removes the limitation of the FSDT, and provides proper precision without using a shear correction coefficient. To solve the stability equations, the differential quadratic method (DQM) is employed. Additionally, for validation, the results are checked with available papers. The effects of strain gradient coefficient, nonlocal parameter, boundary conditions, elastic foundations, and geometric dimensions are studied on the results of the nondimensional buckling loads. Finally, an equation is proposed in which the thermal buckling results can be obtained from mechanical results (or vice versa).
本文基于非局部应变梯度理论，对具有帕斯特纳克和温克勒弹性地基的正交各向异性环形/圆形单层/双层纳米板的热屈曲和机械屈曲进行了非线性研究。考虑非线性冯·卡门应变，采用高阶剪切变形理论（HSDT）和一阶剪切变形理论（FSDT）推导了石墨烯板的稳定性方程。此外，本文分析了正交各向异性双层环形/圆形纳米板的非线性热屈曲和机械屈曲。高阶剪切变形理论为厚度方向的剪应力提供了合适的分布，消除了一阶剪切变形理论的局限性，并且无需使用剪切修正系数就能提供适当的精度。为求解稳定性方程，采用了微分求积法（DQM）。此外，为进行验证，将结果与现有文献进行了核对。研究了应变梯度系数、非局部参数、边界条件、弹性地基和几何尺寸对无量纲屈曲载荷结果的影响。最后，提出了一个方程，通过该方程可以从机械结果中得到热屈曲结果（反之亦然）。
