Application of a p-version curved C^(1)finite element based on the nonlocal Kirchhoff plate theory to the vibration analysis of irregularly shaped nanoplates  

作　　者：XIANG Wei NI Hua TIAN YiFeng WU Yang LIU Bo 

机构地区：[1]School of Mechanical Engineering,Southwest Jiaotong University,Chengdu 610031,China [2]Technology and Equipment of Rail Transit Operation and Maintenance Key Laboratory of Sichuan Province,Chengdu 610031,China [3]Southwest China Research Institute of Electronic Equipment,Chengdu 610036,China [4]CAEP Software Center for High Performance Numerical Simulation,Beijing 100088,China [5]Institute of Applied Physics and Computational Mathematics,Beijing 100088,China [6]The Solid Mechanics Research Centre,Beihang University(BUAA),Beijing 100191,China

出　　处：《Science China(Technological Sciences)》2023年第10期3025-3047,共23页中国科学（技术科学英文版）

基　　金：the National Major Science and Technology Projects of China(Grant No.J2019-VI-0001-0114);the National Natural Science Foundation of China(Grant Nos.11972004,11772031,11402015)。

摘　　要：Nanoplates have been widely used as elementary components for ultrasensitive and ultrafine resolution applications in the field of nano-electro-mechanical systems because of their potentially remarkable mechanical properties.The accurate analysis of their mechanical behavior is currently of particular interest in the function design and reliability analysis of nano-scaled devices.To examine the size-dependent bending and vibration behavior of nanoplates with curvilinear and irregular shapes,a new p-version curved C^(1)finite element is formulated in the framework of the nonlocal Kirchhoff plate model.This newly developed element not only enables an accurate geometry representation and easy mesh generation of curvilinear domains but also overcomes the difficulty of imposing C^(1)conformity required by the nonlocal Kirchhoff plate model,particularly on the curvilinear inter-element boundaries.Numerical examples show that this element can produce an exponential rate of convergence even when curved elements are used in the domain discretization.Vast numerical results are presented for nanoplates with various geometric shapes,including rectangular,circular,elliptic,annular,and sectorial.The high accuracy of the present element is verified by comparing the obtained results with analytical and numerical results in the literature.Additionally,a comprehensive parametric analysis is conducted to investigate the influences of nonlocal parameters,plate dimensions,and boundary conditions on the nonlocal behavior of nanoplates.The present element can be envisaged to allow large-scale mechanical simulations of nanoplates,with a guarantee of accuracy and efficiency.

关 键 词：NANOPLATES nonlocal theory p-version finite element method C^(1)conformity irregular shape 

分 类 号：TB383.1[一般工业技术—材料科学与工程] TB115[理学—数学] TB534.1[理学—应用数学]