A Rigorous Application of the Method of Vertical Lines to Coupled Systems in Finite Element Analysis
A Rigorous Application of the Method of Vertical Lines to Coupled Systems in Finite Element Analysis
复制标题
垂直线法在耦合系统有限元分析中的严格应用
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
S. Rothe
中科院分区：
文献类型：
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作者：
S. Hartmann;S. Rothe
本文研究了垂直线法的严格应用，即对动态和准静态系统进行连续的时空离散化。一个特别的焦点在于固体力学领域，其中进化型本构模型是基本的兴趣。根据其结果方程的结构，研究了各种耦合系统，即热-机械、电热或电热-机械耦合问题，通常在空间离散步骤后导致常微分方程系统或微分-代数方程系统。对于热-机械问题和电热问题，采用了精确对角隐式龙格-库塔方法。
In this essay the rigorous application of the method of vertical lines, i.e. performing the successive steps of spatial and temporal discretization is investigated for dynamical and quasi-statical systems. A particular focus lies in the field of solid mechanics where constitutive models of evolutionary-type are of basic interest. Various coupled systems, i.e. thermo-mechanical, electro-thermal or electro-thermo-mechanical coupled problems are investigated in view of the structure of their resulting equations, commonly, leading to systems of ordinary differential equations or systems of differential-algebraic equations after the spatial discretization step. For the case of a thermo-mechanical and an electro-thermal problem stiffly accurate diagonally-implicit Runge-Kutta methods are applied.