A smooth boundary scheme-based topology optimization for functionally graded structures with discontinuities

This paper presents a novel implicit level set method for topology optimization of functionally graded (FG) structures with pre-existing discontinuities (pre-cracks) using radial basis functions (RBF). The mathematical formulation of the optimization problem is developed by incorporating RBF-based nodal densities as design variables and minimizing compliance as the objective function. To accurately capture crack-tip behavior, crack-tip enrichment functions are introduced, and an eXtended Finite Element Method (X-FEM) is employed for analyzing the mechanical response of FG structures with strong discontinuities. The enforcement of boundary conditions is achieved using the Hamilton-Jacobi method. The study provides detailed mathematical expressions for topology optimization of systems with defects using FG materials. Numerical examples are presented to demonstrate the efficiency and reliability of the proposed methodology.

Automated summary

This paper presents a novel implicit level set method using radial basis functions (RBF) for topology optimization of functionally graded (FG) structures with pre-existing discontinuities. The mathematical formulation incorporates RBF-based nodal densities as design variables and minimizes compliance as the objective function. Crack-tip enrichment functions are introduced to accurately capture crack-tip behavior and an eXtended Finite Element Method (X-FEM) is employed for mechanical analysis. The Hamilton-Jacobi method is used for enforcing boundary conditions. The study provides mathematical expressions for topology optimization of systems with defects using FG materials and numerical examples are presented to demonstrate the proposed methodology's efficiency and reliability.