A node-based smoothed point interpolation method (NS-PIM) for thermoelastic problems with solution bounds
A node-based smoothed point interpolation method (NS-PIM) for thermoelastic problems with solution bounds
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DOI：
10.1016/j.ijheatmasstransfer.2008.09.001
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发表时间：
2009-02
影响因子：
5.2
通讯作者：
S. Wu;S. Wu;Guirong Liu;Guirong Liu;Haiou Zhang;Guiyong Zhang
中科院分区：
文献类型：
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作者：
S. Wu;S. Wu;Guirong Liu;Guirong Liu;Haiou Zhang;Guiyong Zhang
提出了一种基于节点的光滑点插值方法（NS-PIM），用于分析稳态热弹性问题。在这种方法中，形状函数构造使用点插值法（PIM），它允许直接执行的本质边界条件。光滑的Galerkin弱形式，然后使用基于节点构造的光滑域来构造离散化的系统方程。用一维和二维热弹性力学问题研究了该公式的边界性质、精度和收敛性。结果表明，计算得到的温度及其梯度与解析结果或有限元法计算得到的结果吻合得很好。与三节点三角形有限元法相比，在使用相同的线性三角形网格时，NS-PIM可以获得更好的精度和更高的能量范数收敛性。与有限元法一起，我们现在第一次有了一个简单的方法来获得热弹性问题精确解的上下界。
A node-based smoothed point interpolation method (NS-PIM) is formulated to analyze steady-state thermoelastic problems. In this approach, shape functions are constructed using the point interpolation method (PIM), which permits the straightforward enforcement of essential boundary conditions. The smoothed Galerkin weak form is then used to construct discretized system equations using smoothing domains constructed based on nodes. The bound property, accuracy and convergence of the present formulation are studied using 1D and 2D thermoelasticity problems. It is found that the computed temperature and its resulted gradient are in very good agreement with the analytical results or those obtained using the finite element method (FEM). Compared with the 3-node triangular FEM, the NS-PIM can achieve better accuracy and higher convergence in energy norm using the same linear triangular mesh. Together with the FEM, we now for the first time have a simple way to obtain both upper and lower bounds of the exact solution to thermoelasticity problems.