An Energy Balanced Splitting Factor Calculation Method for Nonconforming Generalized Mixed Finite Elements with Distorted Meshes

This paper presents an Energy-Balanced Splitting Factor Method (EBSFM) for nonconforming generalized mixed finite elements to enhance accuracy and stability under mesh distortion. The splitting factor significantly influences the numerical solutions. Traditional approaches employ a uniform splitting factor for all elements, neglecting their distinct characteristics and boundary conditions. Wang's geometry-based Stiffness–Compliance Splitting Factor Method (SCSFM) is adopted to obtain element-wise initial values. Building upon SCSFM, the proposed EBSFM optimizes the splitting factor through an energy balance criterion that minimizes the deviation between mixed energy and generalized strain energy, thereby improving the physical consistency of the finite element model. The method establishes an approximate mapping relationship between unknown variables and splitting factors via matrix decomposition and reconstruction techniques, enabling element-wise adaptive optimization. The EBSFM demonstrates consistent superiority in terms of displacement accuracy, stress accuracy, and energy balance.