A nonlocal approach to graded surface modeling in topology optimization

Abstract

Additively manufactured structures often exhibit a correlation between their mechanical properties, such as stiffness, strength, and porosity, and their wall thickness. This correlation stems from the interplay between the manufacturing process and the properties of the filler material. In this study, we investigate the thickness-dependent effect on structural stiffness and propose a nonlocal integral model that introduces surface grading of Young's modulus to capture this phenomenon. We incorporate this model into topology optimization for designing structures with optimized compliance subject to a volume constraint. Notably, elastically degraded surfaces penalize excessively thin features, effectively eliminating them from the optimized design. We showcase the efficacy of our proposed framework by optimizing the design of a two-dimensional cantilever beam and a bridge.

Figures (8)

• Figure 1: A one-dimensional specimen of thickness $t$ under tension.
• Figure 2: The effective Young's modulus (Eq. \ref{['eq:effective_youngs_modulus_1d']}) for one-dimensional elastic bar, with $\delta=0.4mm$. The effective Young's modulus significantly degrades for thickness below 1mm.
• Figure 3: Spatial distribution of Young's modulus across the thickness of the one-dimensional specimen, as illustrated in Figure \ref{['fig:elastic_bar']}, showcasing variations corresponding to different specimen thickness values $t$.
• Figure 4: Geometrical setup of 2D cantilever beam (left) and bridge (right) structures.
• Figure 5: Final designs for the 2D cantilever beam and bridge structures, optimized with $\delta=0$ and $\delta=0.4mm$, and varying sizes of the design domain. For all designs, the Young's modulus and compliance values are computed in a postprocessing step where a volume preserving thresholding is performed and nonlocal material model is applied with $\delta=0.4mm$. Owing to the bridge's symmetry across the central vertical axis, only the right half of the structure is depicted.