Christiansen, Asger Nyman

Form- og topologioptimering forsøger at beregne den optimale form og topologi af en struktur så en eller flere egenskaber, for eksempel stivhed, balance eller volumen, bliver forbedret. Målet med afhandlingen er at udvikle en metode til form- og topologioptimering som anvender Deformable Simplicial Complex (DSC) metoden. Denne afhandling præsenterer derfor en ny metode der kombinerer tidligere form- og topologioptimerings metoder. Metoden repræsenterer overfladen af strukturen eksplicit og diskretiserer strukturen i elementer der ikke overlapper. En eksplicit repræsentation af overfladen begrænser normalt optimeringen til små formændringer men DSC metoden, der andvender en enkelt eksplicit repræsentation, giver mulighed for store formændringer og endda topologiændringer. Den opnår dette ved konstant at anvende et sæt af mesh operationer samtidigt med at strukturen bliver deformeret. En eksplicit i stedet for en implicit repræsentation giver anledning til en række fordele, f.eks. er det ligetil at modellere overfladen, metoden skalerer bedre og optimering med flere materialer er muligt.Afhandlingen beskriver de væsentlige dele af den nye metode til kombineret form- og topologioptimering. Dette omfatter den strukturelle analyse i kapitel 2, optimeringen i kapitel 3 og Deformable Simplicial Complex metoden i kapitel 4. Derudover er fire anvendelser af denne nye metode præsenteret i de medfølgende artikler og sammenfattet i kapitel 5.Shape and topology optimization seeks to compute the optimal shape and topology of a structure such that one or more properties, for example stiffness, balance or volume, are improved. The goal of the thesis is to develop a method for shape and topology optimization which uses the Deformable Simplicial Complex (DSC) method. Consequently, we present a novel method which combines current shape and topology optimization methods. This method represents the surface of the structure explicitly and discretizes the structure into non-overlapping elements, i.e. a simplicial complex. An explicit surface representation usually limits the optimization to minor shape changes. However, the DSC method uses a single explicit representation and still allows for large shape and topology changes. It does so by constantly applying a set of mesh operations during deformations of the structure. Using an explicit instead of an implicit representation gives rise to several advantages including straightforward modeling of the surface, improved scalability and ability to optimize multiple materials. This dissertation describes the essential parts of the novel method for combined shape and topology optimization. This includes the structural analysis in Chapter 2, the optimization in Chapter 3 and the Deformable Simplicial Complex method in Chapter 4. Finally, four applications of the developed method are presented in the included papers and summarized in Chapter 5

Online Research Database In Technology

Combined Shape and Topology Optimization

http://orbit.dtu.dk/ws/files/107843261/phd350_Christiansen_AN.pdf

Combined Shape and Topology Optimization

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