An optimization method for the splitting factors of generalized mixed finite elements
摘要
Determining the optimal splitting factor is crucial for the efficient application of generalized mixed finite elements (GME). In GME, the splitting factor adjusts the proportion of strain and complementary energy in the functional, which directly affects the accuracy of the numerical solution. To improve the accuracy of distorted hexahedral elements in GME, an alternative method for optimizing the splitting factors is introduced. The deviation of the coefficient matrix between a distorted element and its corresponding standard element is quantified by the matrix norm. Accordingly, the splitting factor is obtained by minimizing the deviation. Rather than adopting a uniform splitting factor, the method determines individualized splitting factors for each element in the finite element model. Several representative examples with different geometric parameters, boundary conditions, and loads are used to validate the proposed method. Numerical examples demonstrate that, compared to adopting a uniform splitting factor of 0.75, the individualized splitting factors significantly improve the numerical accuracy of generalized mixed elements with distortion.