基于样条无网格法的厚/薄压电功能梯度板动力分析
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摘要
在将板的挠度和剪切应变作为场变量的基础上增加考虑面内位移,采用样条无网格法建立了热环境下厚/薄压电功能梯度板动力分析新的计算格式。考虑功能梯度材料的物性参数随温度改变以及温度变化引起的面内力,讨论了压电FGM板在不同边界约束下材料梯度指数变化时,面内位移及面内力对热环境下压电功能梯度板的动力特性和动力响应的影响。分析结果表明,新建立的模型对厚/薄压电功能梯度板动力分析具有通用性和有效性,没有剪切闭锁现象,且计算效率和计算精度较高。
The in-place displacement of a plate was taken as field variable besides the plate's deflection and shear strain. By using the spline meshless method,a new dynamic analysis model for thick/thin piezoelectric functionally graded material( FGM) plates under thermal environment was established. Considering FGM physical parameters variation with temperature and in-plane force caused by different temperatures,the effects of in-plate displacement and in-plane force on the dynamic property and dynamic response of the FGM plate were investigated under different boundaries and gradients.Analysis results showed that the new model has the universality and effectiveness for dynamic analysis of thick/thin piezoelectric FGM plates,and has advantages of high efficiency,high precision and no shear locking problems.
The in-place displacement of a plate was taken as field variable besides the plate's deflection and shear strain. By using the spline meshless method,a new dynamic analysis model for thick/thin piezoelectric functionally graded material( FGM) plates under thermal environment was established. Considering FGM physical parameters variation with temperature and in-plane force caused by different temperatures,the effects of in-plate displacement and in-plane force on the dynamic property and dynamic response of the FGM plate were investigated under different boundaries and gradients.Analysis results showed that the new model has the universality and effectiveness for dynamic analysis of thick/thin piezoelectric FGM plates,and has advantages of high efficiency,high precision and no shear locking problems.
引文
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[2]FAKHARI V,OHADI A,YOUSEFIAN P.Nonlinear free and forced vibration behavior of functionally graded plate with piezoelectric layers in thermal environment[J].Composite Structures,2011,93(9):2310-2321.
[3]黄小林,沈惠申.热环境下贴压电层的功能梯度材料板的自由振动和动力响应[J].应用力学学报,2005,22(3):456-460.HUANG Xiaolin,SHEN Huishen.Free vibration and dynamic response of functionally graded plates with piezoelectric layers in thermal environments[J].Chinese Journal of Applied Mechanics,2005,22(3):456-460.
[4]黄君,莫春美,李双蓓.基于样条有限点法的压电功能梯度板的动力分析[J].广西大学学报(自然科学版),2015,40(1):127-137.HUANG Jun,MO Chunmei,LI Shuangbei.Dynamic analysis of piezoelectric FGM plate based on spline finite point method[J].Journal of Guangxi University(Natural Science),2015,40(1):127-137.
[5]FARSANGI M A A,SAIDI A R,BATRA R C.Analytical solution for free vibrations of moderately thick hybrid piezoelectric laminatedplates[J].Journal of Sound and Vibration,2013,332(22):5981–5998.
[6]腾兆春,蒲育.温度影响下FGM圆环板的面内自由振动分析[J].振动与冲击,2015,34(9):210-217.TENG Zhaochun,PU Yu.In-plane free vibration of FGM annular plates considering temperature effect[J].Journal of Vibration and Shock,2015,34(9):210-217.
[7]田娇,蔡永昌,田龙岗,等.含剪切自由度的厚薄通用三角形层合板单元[J].同济大学学报(自然科学版),2013,41(12):1781-1786.TIAN Jiao,CAI Yongchang,TIAN Longgang,et al.A new laminated plate element CDST-S6 for thin or thick plates[J].Journal of Tongji University(Natural Science),2013,41(12):1781-1786.
[8]李秀梅,吴锋,秦荣,等.厚/薄板振动分析的样条无单元法[J].振动与冲击,2010,29(2):107-110.LI Xiumei,WU Feng,QIN Rong,et al.Spline element-free method for thick/thin plate vibration analysis[J].Journal of Vibration and Shock,2010,29(2):107-110.
[9]尹硕辉,余天堂,刘鹏.基于等几何有限元法的功能梯度板自由振动分析[J].振动与冲击,2013,32(24):181-186.YIN Shuohui,YU Tiantang,LIU Peng.Free vibration analysis of functionally graded plates using isogeometric finite element method[J].Journal of Vibration and Shock,2013,32(24):181-186.
[10]LOJA M A R,MOTA SOARES C M,BARBOSA J I.Analysis of functionally graded sandwich plate structures with piezoelectric skins,using B-spline finite strip method[J].Composite Structures,2013,96(4):606-615.
[11]LI Shuangbei,HUANG Lixin,JIANG Linjie,et al.A bidirectional B-spline finite point method for the analysis of piezoelectric laminated composite plates and its application in material parameter identification[J].Composite Structures,2014,107(1):346-362.
[12]秦荣.计算结构力学[M].北京:科学出版社,2001:210-222.