THE DUAL MORTAR FINITE ELEMENT METHOD BASED ON THREE-FIELD VARIATIONAL PRINCIPLE
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摘要: 通过引入独立媒介面，将mortar有限元法由二场变分原理推广到三场变分原理。通过采用满足双正交性条件的对偶基函数离散Lagrange乘子空间，实现了Lagrange乘子的凝聚，由此提出了基于三场变分原理的对偶mortar有限元法。提出的新方法同时解决了常规mortar元的约束交叉、主从偏见及求解效率等问题。自主编制了相应的计算程序，并采用两个三维数值算例对新方法进行了验证。研究结果表明：基于三场变分原理的对偶mortar方法对界面连续性条件的求解精度高，可有效用于含约束交叉的非协调网格计算，所支持的复杂子区域划分使得有限元分析更为灵活。Abstract: An independent medium surface is introduced to extend the mortar method from a two-field variational principle to a three-field version. The Lagrange multipliers are discretized by using dual basis functions. The dual basis fulfills bi-orthogonal conditions, resulting in the static condensation of the Lagrange multipliers. The dual mortar finite element method using the three-field variational principle is then proposed. This method overcomes the well-known deficiencies of the conventional mortar method, such as the cross-point constraint problem, the master-slave biased problem and the efficiency problem associated with large-scale computations. An in-house code is developed correspondingly and then used to validate the proposed method by two three-dimensional numerical examples. The method achieves high accuracy for interfacial continuous conditions. It can be applied to treat the nonconforming mesh even involving cross-point constraints. The resultant support for the complex subdomain division introduces significant flexibilities to the finite element analysis.
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