Static analysis of ultra-thin beams based on a semi-continuum model  

作　　者：Cheng Li Zhi-Jun Zheng Ji-Lin Yu C.W. Lim 

机构地区：[1]CAS Key Laboratory of Mechanical Behaviorand Design of Materials,University of Science and Technology of China,230027 Hefei, China [2]Department of Building and Construction,City University of Hong Kong,Tat Chee Avenue, Kowloon,Hong Kong SAR, China

出　　处：《Acta Mechanica Sinica》2011年第5期713-719,共7页力学学报（英文版）

基　　金：supported by a collaboration scheme from University of Science and Technology of China-City University of Hong Kong Joint Advanced Research Institute,City University of HongKong (7002472 (BC));the National Natural Science Founda-tion of China (10932011)

摘　　要：A linear semi-continuum model with discrete atomic layers in the thickness direction was developed to investigate the bending behaviors of ultra-thin beams with nanoscale thickness.The theoretical results show that the deflection of an ultra-thin beam may be enhanced or reduced due to different relaxation coefficients.If the relaxation coefficient is greater/less than one,the deflection of micro/nano-scale structures is enhanced/reduced in comparison with macro-scale structures.So,two opposite types of size-dependent behaviors are observed and they are mainly caused by the relaxation coefficients.Comparisons with the classical continuum model,exact nonlocal stress model and finite element model （FEM） verify the validity of the present semi-continuum model.In particular,an explanation is proposed in the debate whether the bending stiffness of a micro/nano-scale beam should be greater or weaker as compared with the macro-scale structures.The characteristics of bending stiffness are proved to be associated with the relaxation coefficients.A linear semi-continuum model with discrete atomic layers in the thickness direction was developed to investigate the bending behaviors of ultra-thin beams with nanoscale thickness.The theoretical results show that the deflection of an ultra-thin beam may be enhanced or reduced due to different relaxation coefficients.If the relaxation coefficient is greater/less than one,the deflection of micro/nano-scale structures is enhanced/reduced in comparison with macro-scale structures.So,two opposite types of size-dependent behaviors are observed and they are mainly caused by the relaxation coefficients.Comparisons with the classical continuum model,exact nonlocal stress model and finite element model （FEM） verify the validity of the present semi-continuum model.In particular,an explanation is proposed in the debate whether the bending stiffness of a micro/nano-scale beam should be greater or weaker as compared with the macro-scale structures.The characteristics of bending stiffness are proved to be associated with the relaxation coefficients.

关 键 词：Bending stiffness · MEMS/NEMS · Relaxation coefficient · Semi-continuum model · Size-dependence 

分 类 号：TU375.1[建筑科学—结构工程] TP273.5[自动化与计算机技术—检测技术与自动化装置]