功能梯度材料Euler-Bernoulli梁单元模态应变能对损伤参数的灵敏度分析  

Sensitivity analysis of elemental modal strain energy with respect to damage parameters of functionally graded Euler-Bernoulli beam

作　　者：黄立新[1] 韦琦 胡中明 岳世燕 HUANG Li-xin;WEI Qi;HU Zhong-ming;YUE Shi-yan(School of Civil Engineering and Architecture,Guangxi University,Nanning 530004,China;School of Naval Architecture,Ocean and Civil Engineering,Shanghai Jiaotong University,Shanghai 200240,China;Department of Resources Exploration and Civil Engineering,Engineering&Technical College of Chengdu University of Technology,Leshan 641000,China)

机构地区：[1]广西大学土木建筑工程学院,南宁530004 [2]上海交通大学船舶海洋与建筑工程学院,上海200240 [3]成都理工大学工程技术学院资源勘查与土木工程系,四川乐山641000

出　　处：《桂林理工大学学报》2021年第3期533-539,共7页Journal of Guilin University of Technology

基　　金：国家自然科学基金项目(11262002)。

摘　　要：基于2节点6自由度的梁单元,采用Euler-Bernoulli梁理论和梁的应变能公式,导出单元模态应变能公式。在此基础上推导出功能梯度材料Euler-Bernoulli梁的单元模态应变能一阶灵敏度表达式。选取功能梯度材料Euler-Bernoulli梁横截面顶部弹性模量E_(U)、底部弹性模量E_(L)和梯度指数k作为损伤参数,进行了单元模态应变能对损伤参数的灵敏度分析。数值算例表明,单元模态应变能对损伤参数k的灵敏度数值要比损伤参数E_(U)和E_(L)的灵敏度数值大很多个数量级,并且高阶模态单元模态应变能的灵敏度数值均大于低阶模态单元模态应变能的对应灵敏度数值。通过数值算例进一步探究了损伤参数k、E_(U)和E_(L)的变化对单元模态应变能灵敏度的影响,这为功能梯度材料Euler-Bernoulli梁结构损伤识别的研究提供了基础。Based on the beam element with two nodes and six degrees of freedom,Euler-Bernoulli beam theory and strain energy formula,the elemental modal strain energy(EMSE)formula was derived.Thus first-order sensitivity expression of EMSE was developed for the FG Euler-Bernoulli beam.Upper elastic modulus E_(U) and lower elastic modulus E_(L) of cross section and the gradient index k of the beam were selected as the damage parameters.Sensitivity analysis of EMSE was carried out with respect to the damage parameters.Numerical examples showed that the sensitivity values of EMSE with respect to k were many orders of magnitude larger than the ones of EMSE with respect to E_(U) and E_(L).The sensitivity values of EMSE with high order modal were all greater than the corresponding ones of EMSE with low order modal.The influence of variation in E_(U),E_(L) and k on the sensitivity of EMSE was investigated by a further numerical example.The sensitivity analysis of EMSE provides reference for the damage identification of FG Euler-Bernoulli beam.

关 键 词：功能梯度材料 EULER-BERNOULLI梁 单元模态应变能 灵敏度分析 

分 类 号：TB332[一般工业技术—材料科学与工程] O346.5[理学—固体力学]