Topology Optimization of General Structures with Anisotropic Fatigue Constraints
Translated title
Topologioptimering af generelle strukturer med anisotrope udmattelsesbibetingelser
Authors
Olesen, Asbjørn Malte ; Hermansen, Sebastian Malte
Term
4. term
Education
Publication year
2020
Submitted on
2020-06-03
Pages
24
Abstract
Additivt fremstillede (3D‑printede) metaller opfører sig næsten ens i alle retninger, når man ser på stivhed og statisk (enkeltbelastnings) styrke. Ved gentagne belastninger (udmattelse) afhænger ydeevnen derimod af retningen, og den samlede udmattelsesstyrke er lavere. Det gør det udfordrende at designe pålidelige letvægtskomponenter. Topologioptimering er en beregningsmetode, der bestemmer, hvor materialet skal placeres for at opnå stærke og lette konstruktioner. Tidligere blev de meget komplekse former ofte kun brugt som inspiration, fordi de var svære at fremstille. Med additiv fremstilling kan disse former nu produceres, hvilket flytter fokus til design til fremstilling. Afhandlingen præsenterer en ny udglatningsmetode, der omsætter grove topologioptimerede layouts til glatte, fremstillingsklare geometrier. Under antagelse af isotrop stivhed og statisk styrke formuleres optimeringen som en udvidelse af eksisterende udmattelsesbegrænsninger i densitetsbaseret topologioptimering, hvor materialet beskrives som et kontinuert tæthedsfelt. Der foreslås en forbedret formulering af udmattelsesskade, som sigter mod en bedre balance mellem nøjagtighed og beregningstid—en kendt udfordring i tidligere arbejder. Metoden demonstreres på to- og tredimensionale problemer, og de resulterende design verificeres med kommerciel finit element-software.
Additively manufactured (3D‑printed) metals behave almost the same in all directions in terms of stiffness and static (single‑load) strength. Under repeated loading (fatigue), however, their performance depends on direction and overall fatigue strength is reduced. This makes it challenging to design reliable lightweight parts. Topology optimization is a computational method that finds where to place material to achieve strong, lightweight designs. In the past, the highly complex shapes it produced were often used only as inspiration because they were difficult to manufacture. With additive manufacturing, these complex shapes can now be produced, which shifts the emphasis to design for manufacture. This thesis introduces a novel smoothing approach that turns rough topology‑optimized layouts into smooth, manufacturable geometries. Assuming isotropic stiffness and static strength, the optimization is formulated as an extension of existing fatigue constraint functions within density‑based topology optimization, where material is represented by a continuous density field. An improved formulation of fatigue damage is proposed to better balance accuracy and computational cost—a trade‑off that has been difficult in earlier studies. The approach is demonstrated on two‑ and three‑dimensional problems, and the resulting designs are validated using commercial finite element software.
[This abstract was generated with the help of AI]
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