Galerkin methods in time for semi‐discrete viscoelastodynamics
Galerkin methods in time for semi‐discrete viscoelastodynamics
复制标题
半离散粘弹动力学的及时伽辽金方法
DOI：
10.1002/pamm.200510175
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发表时间：
2005
期刊：
影响因子：
--
通讯作者：
Betsch P.
中科院分区：
文献类型：
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作者：
Groß M;Betsch P.
在半离散非线性弹性动力学中，高阶能量和动量守恒时间步进方案被证明非常适合计算长时间运动[1]。与标准ODE积分器相比，守恒格式表现出优越的稳定性，这在非线性问题中是至关重要的。元素框架。我们表明，守恒格式特别适合作为耗散动力系统的能量一致格式发展的起点。特别是，粘弹性材料的行为被考虑。能量一致方案的一个关键优势在于粘弹性系统的平衡状态可以确定地达到，而不受材料参数的影响。本文比较了半离散非线性粘弹性动力学时间离散的两种Galerkin方法：标准连续Galerkin （cG）方法和增强连续Galerkin （eG）方法。总能量平衡。（©2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim）
In semi‐discrete nonlinear elastodynamics, higher order energy and momentum conserving time stepping schemes turned out to be well suited for computing long time motions [1]. In comparison to standard ODE integrators, conserving schemes exhibit superior stability properties which are of utmost importance in a nonlinear .nite element framework. We show that conserving schemes are particularly well suited as starting point for the development of energy consistent schemes for dissipative dynamical systems. In particular, viscoelastic material behaviour is considered. A key advantage of energy consistent schemes lies in the fact that the equilibrium state of viscoelastic systems can be de.nitely reached, independent of the material parameters. In the paper, we compare two Galerkin methods for the temporal discretisation of semi‐discrete nonlinear viscoelastodynamics: the standard continuous Galerkin (cG) method and an enhanced continuous Galerkin (eG) method which ful.ls the total energy balance exactly. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)