Topology optimization of coated structures and material interface problems

Abstract

This paper presents a novel method for including coated structures and prescribed material interface properties into the minimum compliance topology optimization problem. Several elements of the method are applicable to a broader range of interface problems. The approach extends the standard SIMP method by including the normalized norm of the spatial gradient of the design field into the material interpolation function, enforcing coating material at interfaces by attributing particular properties. The length scales of the base structure and the coating are separated by introducing a two-step filtering/projection approach. The modeled coating thickness is derived analytically, and the coating is shown to be accurately controlled and applied in a highly uniform manner over the structure. An alternative interpretation of the model is to perform single-material design for additive manufacturing. Infill is assumed to be constituted of an isotropic porous microstructure satisfying the Hashin-Shtrikman bounds and is modeled using the homogenized material properties. A range of numerical results illustrate the effectiveness of the approach.

Homogenization‐based topology optimization for high‐resolution manufacturable microstructures

“…porous structures that, apart from weight saving, also may increase buckling stability of topology optimized structures, c.f. [9,10].…”

Length scale and manufacturability in density-based topology optimization

“…The first one is resolving the thin wall and the internal porous structure and the second is parametrization of the different parts of detail during the optimization process. A parametrization based on the standard three field representation combined with an additional field utilizing the gradient of the physical density is presented in [34]. In such a parametrization the filling material can be realized using uniform material microstructure, thus avoiding the requirement for detailed modeling inside the design.…”

“…length scale between the inclusions and on the inclusion [69], [63] Minimum length scale ρ ρ {e ρ, ∇e ρ} b e ρ black and white design with length scale on both phases [166] Coating projection ρ, ∇ e ρ ρ e ρ b e ρ e ρ ∇ e ρ length scale on the coating [34] ing the mesh. This often results in lack of manufacturability, extremely sensitive performance due to manufacturing and exploitation uncertainties, stress concentration, etc.…”

“…Another recent extension [34] of the three field representation utilizes the gradient of the projected density field ρ for optimizing structures with a coating layer. The boundary of the solid phase can be identified by using the gradients of the density.…”

Topology optimization of piezo modal transducers with null-polarity phases

“…It is important to notice that this issue should be taken into account not only for designing piezo modal transducers, but also piezo transducers in general presenting regions with opposite polarities in contact. In order to enforce a new material-phase between two given phases we use the scheme recently suggested by Clausen et al (2015). In this research, a coating material (which plays the role of the gap-phase in our problem) is enforced in a base structure made from a porous material and void.…”