Mixed-mode thermal stress intensity factors from the finite element discretized symplectic method
Mixed-mode thermal stress intensity factors from the finite element discretized symplectic method
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DOI：
10.1016/j.ijsolstr.2014.07.016
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发表时间：
2014-10
影响因子：
3.6
通讯作者：
Zhenhuan Zhou;A. Leung;Xinsheng Xu;X. Luo
中科院分区：
文献类型：
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作者：
Zhenhuan Zhou;A. Leung;Xinsheng Xu;X. Luo
采用有限元离散辛方法，通过辛展开求解稳态热载荷作用下的热应力强度因子。裂纹体采用常规有限元法模拟，分为近场和远场两个区域。在近场，分别建立了热传导和热弹性问题的哈密顿体系。在极坐标系下，温度和位移函数用辛本征解表示。结合解析辛级数和任意边界条件下的经典有限元，主要未知量不再是节点温度和位移，而是矩阵变换后的辛级数系数。同时得到了奇异区域的应力强度因子、温度、位移和应力，无需任何后处理。给出了一些数值例子和收敛性研究，并与现有的解决方案是在良好的协议。
A finite element discretized symplectic method is introduced to find the thermal stress intensity factors (TSIFs) under steady-state thermal loading by symplectic expansion. The cracked body is modeled by the conventional finite elements and divided into two regions: near and far fields. In the near field, Hamiltonian systems are established for the heat conduction and thermoelasticity problems respectively. Closed form temperature and displacement functions are expressed by symplectic eigen-solutions in polar coordinates. Combined with the analytic symplectic series and the classical finite elements for arbitrary boundary conditions, the main unknowns are no longer the nodal temperature and displacements but are the coefficients of the symplectic series after matrix transformation. The TSIFs, temperatures, displacements and stresses at the singular region are obtained simultaneously without any post-processing. A number of numerical examples as well as convergence studies are given and are found to be in good agreement with the existing solutions.