An interface-enriched generalized finite element method for level set-based topology optimization

Abstract

During design optimization, a smooth description of the geometry is important, especially for problems that are sensitive to the way interfaces are resolved, e.g., wave propagation or fluid-structure interaction. A level set description of the boundary, when combined with an enriched finite element formulation, offers a smoother description of the design than traditional density-based methods. However, existing enriched methods have drawbacks, including ill-conditioning and difficulties in prescribing essential boundary conditions. In this work, we introduce a new enriched topology optimization methodology that overcomes the aforementioned drawbacks; boundaries are resolved accurately by means of the Interface-enriched Generalized Finite Element Method (IGFEM), coupled to a level set function constructed by radial basis functions. The enriched method used in this new approach to topology optimization has the same level of accuracy in the analysis as the standard finite element method with matching meshes, but without the need for remeshing. We derive the analytical sensitivities and we discuss the behavior of the optimization process in detail. We establish that IGFEM-based level set topology optimization generates correct topologies for well-known compliance minimization problems.

Edible mechanical metamaterials with designed fracture for mouthfeel control

“…In comparison with standard density-based TO methods, our approach can provide smooth and crisp designs without the need for post-processing. 30,34…”

“…The connection between high stresses and crack nucleation has been used elsewhere to predefine cracks at the beginning of topology optimization. 32,33 Our approach to topology optimization 30,34 uses a level set function j, whose zeroth value represents the interface between chocolate and void, an enriched finite element formulation to accurately determine the structural response, and the method of moving asymptotes (MMA) as the optimizer to update design variables. Noteworthy, energy release rates are computed at the locations of enriched nodes that are added to the finite element formulation to properly describe the discontinuous kinematics at void-solid interfaces.…”

“…In comparison with standard density-based TO methods, our approach can provide smooth and crisp designs without the need for postprocessing. 30,34 Fig. 6 shows the initial design containing four circular holes within the entire mechanical metamaterial cell (only one hole in our quarter optimization domain), where the ratio J 2 /J 1 = 1.…”

Edible meta-atoms

“…Our approach to topology optimization [28] uses a level set function φ, whose zeroth value represents the interface between chocolate and void, an enriched finite element formulation to accurately determine the structural response, and the method of moving asymptotes (MMA) as the optimizer to update the design variables. Noteworthy, energy release rates are computed at the locations of enriched nodes that are added to the finite element formulation to properly describe the discontinuous kinematics at void-solid interfaces.…”

“…Noteworthy, energy release rates are computed at the locations of enriched nodes that are added to the finite element formulation to properly describe the discontinuous kinematics at void-solid interfaces. In comparison with standard density-based TO methods, our approach can provide smooth and crisp designs without the need for postprocessing [28].…”