High-order FEMs for thermo-hyperelasticity at finite strains
High-order FEMs for thermo-hyperelasticity at finite strains
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DOI：
10.1016/j.camwa.2013.11.003
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发表时间：
2014-02
期刊：
影响因子：
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通讯作者：
Z. Yosibash;D. Weiss;S. Hartmann
中科院分区：
文献类型：
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作者：
Z. Yosibash;D. Weiss;S. Hartmann
有限应变下的热超弹性问题属于一类非线性耦合问题，其数值处理具有挑战性。我们提出了一个1-D耦合，固定，热超弹性系统的常数或温度依赖的材料属性的弱形式。耦合系统离散的“单片”高阶有限元法（p-FEM）的基础上分层形函数。为了验证的准确性和调查的p-FEM的非线性耦合问题的收敛速度，精确的解决方案推导出的数值结果进行比较。这些都证明了所应用的p-FEM的精度和效率。
Thermo-hyperelastic problems at finite strains belong to a category of non-linear coupled problems that impose challenges on their numerical treatment. We present the weak-form for a 1-D coupled, stationary, thermo-hyperelastic system with constant or temperature-dependent material properties. The coupled system is discretized by a ‘monolithic’high-order finite element method (p-FEM) based on hierarchical shape-functions. To verify the accuracy and to investigate the convergence rates of the p-FEM for the non-linear coupled problem, exact solutions are derived that are compared to the numerical results. These demonstrate the accuracy and efficiency of the applied p-FEMs.