Finite-Element Modeling of Circular Nanoplates

被引：14

作者：

Sapsathiarn, Y. ^{[1
]}

Rajapakse, R. K. N. D. ^{[1
]}

机构：

[1] Simon Fraser Univ, Fac Sci Appl, Burnaby, BC V5A 1S6, Canada

来源：

JOURNAL OF NANOMECHANICS AND MICROMECHANICS | 2013年 / 3卷 / 03期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Nanotechnology; Plates; Residual stress; Finite-element method; Deflection; Natural frequency;

D O I：

10.1061/(ASCE)NM.2153-5477.0000056

中图分类号：

TB3 [工程材料学];

学科分类号：

0805 ; 080502 ;

摘要：

A finite-element method for static and free vibration analysis of axisymmetric circular nanoscale plates is presented based on the Gurtin-Murdoch continuum theory accounting for surface energy. Explicit solutions for stiffness and mass matrices and the load vector of a two-node plate finite element are derived by using a weighted residual formulation. The accuracy of the present finite-element model is verified by comparing with a set of analytical solutions for nanoplates. Simply supported plates show more influence of the surface energy effect compared with clamped plates. The first natural frequency is also affected, but higher natural frequencies as well as all mode shapes show minor influence of surface energy effects. The surface residual stress is found to be the key parameter that influences the deflections and natural frequencies. The current solutions clearly show the size-dependent response of nanoplates. (C) 2013 American Society of Civil Engineers.

引用

页码：59 / 66

页数：8

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