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Level set topology optimization with meshfree methods for design-dependent multiphysics problems

Neofytou, Andreas 2021. Level set topology optimization with meshfree methods for design-dependent multiphysics problems. PhD Thesis, Cardiff University.
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This thesis aims to develop computational tools for multiphysics problems in topology optimization with particular focus on design-dependent surface physics. This is a challenging class of problems governed by interface conditions and loadings. Fluid-structure interaction (FSI) is a typical example. Level set topology optimization (LSTO) possesses an advantage over traditional density-based methods since it provides clearly defined boundaries. However, maintaining this crisp boundary representation onto the computational model for the analysis is not straightforward especially with fixed grid methodologies. On the other hand, remeshing the structure at each iteration directly addresses the problem, it poses additional difficulties because of the need to ensure good quality meshes at each iteration. In this thesis a meshfree level set topology optimization methodology based on the reproducing kernel particle method (RKPM) is developed to ensure the well-defined geometrical representation of the structural boundary is transferred onto the computational domain by placing RKPM particles along the boundary. In this way, the difficulties associated with fixed grid LSTO methods and remeshing-based approaches are avoided. The methodology is first validated for purely hydrostatic pressure, which is a very simple case of design-dependent physics. The obtained results are validated through comparison with the literature. Different integration schemes, particle distributions and continuity orders are also explored to pin down the best balance between accuracy and efficiency. The development of the LSTO-RKPM methodology is later extended to fluidstructure interactions. To accomplish this, the LSTO-RKPM methodology is further combined with the modified immersed finite element method (mIFEM). The coupling of the different methods is illustrated through the analysis of transient FSI examples. For the optimization, the simplified case of steady-state FSI is assumed. The applicability of the methodology is illustrated through examples and compared with the literature. For the sensitivity analysis, a particle-based discrete adjoint methodology for the level set topology optimization method is presented. Additionally, an algorithm for identifying and removing free-floating volumes of solid material into the fluid domain is explained.

Item Type: Thesis (PhD)
Date Type: Acceptance
Status: Unpublished
Schools: Engineering
Uncontrolled Keywords: Level Set Topology Optimization, Reproducing Kernel Particle Method, Design-dependent, Fluid-Structure Interaction, Meshfree, Sensitivity Analysis
Date of First Compliant Deposit: 8 February 2022
Date of Acceptance: July 2021
Last Modified: 10 Jun 2023 01:59

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