不可压缩材料分析的界带有限元
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摘要
针对完全不可压缩材料系统(ν=0.5),提出流函数的概念,给出相应的变分原理,并进行数值分析.流函数的引入涉及到高阶微分,为此提出界带有限单元.该单元基于界带理论,能够很好地解决具有高阶微商的变分原理所带来的高阶近似问题.
A concept of the flow function and the corresponding variational principle were developed to deal with the absolute incompressible material system,and the numerical analysis was also presented.When the flow function was introduced,the higher order differential system was involved,which led to a new type of element,the inter-belt finite element,based on the belt theory.The belt finite element can overcome well the problem derived by the variational principle with the higher order differential.
A concept of the flow function and the corresponding variational principle were developed to deal with the absolute incompressible material system,and the numerical analysis was also presented.When the flow function was introduced,the higher order differential system was involved,which led to a new type of element,the inter-belt finite element,based on the belt theory.The belt finite element can overcome well the problem derived by the variational principle with the higher order differential.
引文
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[9]张洪武,姚征,钟万勰.界带分析的基本理论和计算方法[J].计算力学学报,2006,23(3):257-263.(ZHANG Hong-wu,YAO Zheng,ZHONG Wan-xie.Basic theory and algorithm for Inter-Belt analysis[J].Chinese Journal of Solid Mechanics,2006,23(3):257-263.(in Chinese))
[10]姚征,张洪武,王晋宝,钟万勰.基于界带模型的碳纳米管声子谱的辛分析[J].固体力学学报,2008,29(1):13-22.(YAO Zheng,ZHANG Hong-wu,WANG Jin-bao,ZHONG Wan-xie.A newmethod for tensile creep compliance of composite solid propellant[J].Chinese Journal of Solid Mechan-ics,2008,29(1):13-22.(in Chinese))
[11]姚征.辛体系算法在波的传播与振动问题中的应用[D].博士论文.大连:大连理工大学,2007.(YAO Zheng.Applications of symplectic algorithm in wave propagation and vibration problems[D].Ph D thesis.Dalian:Dalian University of Technology,2007.(in Chinese))
[12]钟万勰,高强.辛破茧[M].大连:大连理工大学出版社,2011.(ZHONG Wan-xie,GAO Qiang.Break the Limitations of Symplecticity[M].Dalian:Dalian University of Technology Press,2011.(inChinese))
[2]史守峡,白若阳.非线性不可压缩橡胶柱体的大变形罚有限元分析[J].世界地震工程,1998,14(1):51-58.(SHI Shou-xia,BAI Ruo-yang.A penalty finite elementapproach for large strains ofnearly incompressible rubber cylinder[J].World Information on Earthquake Engineering,1998,14(1):51-58.(in Chinese))
[3]Brenner S C.A nonconforming mixed multigrid method for the pur traction problem in planarlinear elas-ticity[J].Math Comp,1994,63:435-460.)
[4]Falk R S.Nonconforming finite element methods for the equations of linear elasticity[J].Math Comp,1991,57:529-550.
[5]Falk R S,Morley M E.Equivalence of finite element methods for problems in elasticity[J].SIAM JNumer Anal,1990,27(6):1486-1505.
[6]Kouhia R,Stenberg R.A linear nonconforming finite element method for nearly incompressible elastic-ity and Stokes flow[J].Comput Meths Appl Mech Engrg,1995,124(3):195-212.
[7]党发宁,荣廷玉,孙训方.用有限元广义混合法分析不可压缩或几乎不可压缩弹性体[J].力学季刊,2000,21(3):299-304.(DANG Fa-ning,RONG Ting-yu,SUN Xun-fang.Application of gener-alized mixed finite element method to research on incompressible and nearly incompressible elasticity[J].Chinese Quarterly of Mechanics,2000,21(3):299-304.(in Chinese))
[8]姚伟岸,钟万勰.辛弹性力学[M].高等教育出版社,2003.(YAO Wei-an,ZHONG Wan-xie.Symplectic Elasticity[M].Singapore:World Scientific,2009.)
[9]张洪武,姚征,钟万勰.界带分析的基本理论和计算方法[J].计算力学学报,2006,23(3):257-263.(ZHANG Hong-wu,YAO Zheng,ZHONG Wan-xie.Basic theory and algorithm for Inter-Belt analysis[J].Chinese Journal of Solid Mechanics,2006,23(3):257-263.(in Chinese))
[10]姚征,张洪武,王晋宝,钟万勰.基于界带模型的碳纳米管声子谱的辛分析[J].固体力学学报,2008,29(1):13-22.(YAO Zheng,ZHANG Hong-wu,WANG Jin-bao,ZHONG Wan-xie.A newmethod for tensile creep compliance of composite solid propellant[J].Chinese Journal of Solid Mechan-ics,2008,29(1):13-22.(in Chinese))
[11]姚征.辛体系算法在波的传播与振动问题中的应用[D].博士论文.大连:大连理工大学,2007.(YAO Zheng.Applications of symplectic algorithm in wave propagation and vibration problems[D].Ph D thesis.Dalian:Dalian University of Technology,2007.(in Chinese))
[12]钟万勰,高强.辛破茧[M].大连:大连理工大学出版社,2011.(ZHONG Wan-xie,GAO Qiang.Break the Limitations of Symplecticity[M].Dalian:Dalian University of Technology Press,2011.(inChinese))
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