东南大学学报（英文版）2019，Vol.35Issue(4)：453-463,11.DOI:10.3969/j.issn.1003-7985.2019.04.008
基于非局部应变梯度理论的轴向功能梯度微梁尺度相关弯曲行为研究
Study on size-dependent bending behavior of axially functionally graded microbeams via nonlocal strain gradient theory
摘要
Abstract
Based on the nonlocal strain gradient theory (NSGT),the static bending behaviors of an axially functionally graded (AFG) Bemoulli-Euler microbeam subjected to concentrated and distributed loads are studied.The material property of the AFG microbeam changes continuously along the longitudinal direction.On the basis of the minimum potential energy principle,the equations of motion and associated classical and non-classical boundary conditions are derived.Then,Galerkin's weighted residual method in conjunction with the normalization technique are utilized to solve the governing differential equations.The transverse deformations of the AFG microbeam suffering the sinusoidal distributed load within the framework of NSGT,nonlocal elasticity theory (NET),strain gradient theory (SGT) and classical elasticity theory (CET) are compared.It is observed that the bending flexibility of the microbeam decreases with the increase in the ratio of the material length scale parameter to the beam height.However,the bending flexibility increases with the increase in the material nonlocal parameter.The functionally graded parameter plays an important role in controlling the transverse deformation.This study provides a theoretical basis and a technical reference for the design and analysis of AFG micro-beams in the related regions.关键词
轴向功能梯度微梁/非局部应变梯度理论/弯曲/Galerkin法/归一化方法Key words
axially functionally graded microbeam/nonlocal strain gradient theory/bending/Galerkin method/normalization method分类
数理科学引用本文复制引用
康泽天,王志勇,周博,薛世峰..基于非局部应变梯度理论的轴向功能梯度微梁尺度相关弯曲行为研究[J].东南大学学报（英文版）,2019,35(4):453-463,11.基金项目
The National Key Research and Development Program of China (No.2017YFC0307604),the Talent Foundation of China University of Petroleum (No.Y1215042). （No.2017YFC0307604）
