Integration of Strain Gradient Notation Finite Elements into SIMP-Based Topology Optimization

Resumo

The Strain Gradient Notation Finite Element Method (SGN-FEM) introduces a physically consistent formulation for Q4 elements by eliminating spurious shear strain terms responsible for shear locking. This technique enhances numerical precision in structural analysis and optimization, especially when dealing with fine mesh discretization. Multiscale topology optimization aims to integrate microstructural characteristics into the macrostructural design process. In this context, effective material properties are derived from representative volume elements (RVEs) via homogenization and incorporated into the macrostructure through a FE²-type coupling scheme. This work presents a preliminary implementation of SGN-FEM within a multiscale optimization framework. The Solid Isotropic Material with Penalization (SIMP) method is used in the macro-level optimization, while the effective constitutive tensor Ceff is computed from microstructural models defined by varying density values. The coupling between scales is handled iteratively, enabling the macrostructure to evolve based on microstructural response. Initial numerical results from classical benchmark problems are performed to demonstrate the potential of SGN-FEM in capturing fine-scale effects while maintaining mechanical consistency. The proposed framework offers a promising path for material design strategies where microstructural control plays a key role in structural performance.