Application of Q4 Strain Gradient Notation Finite Element Method (SGN-FEM) in Level Set Optimization Using Radial Basis Functions

Resumo

The Strain Gradient Notation Finite Element Method (SGN-FEM) employs physically interpretable polynomials in the development of finite elements, allowing for the precise identification and subsequent elimination of parasitic shear sources, which cause shear locking. The element is corrected a priori, during development, by simply removing the spurious terms from the shear strain polynomials.
The Level Set Method (LVM) is an optimization technique widely employed in topology optimization to minimize the compliance of structures. This method consistently provides clear boundary and geometry information during the optimization process, giving it inherent advantages in solving boundary and geometry-related problems.
While numerous studies investigate different approaches to calculate level set optimization, there are fewer studies evaluating how the finite element technique contributes to the analysis. Considering this, this paper presents the application of Q4 SGN-FEM in optimization studies using LVM to minimize the compliance of a two-dimensional linear elastic structure. The differences obtained when using the SGN-FEM model are investigated. The parametrized level set method, as defined in Wei et al. (2018), is utilized alongside SGN-FEM to conduct the study. The model is validated through comparison with other studies, demonstrating that SGN-FEM proves to be a viable alternative for conducting optimization studies using the level set method.