Enhancing topology optimisation of elastic structures via mesh adaptation

Topology optimization aims to find the best layout of material within a design domain to obtain the best performance, according to specific criteria. In many applications, the objective functional depends on the solution of a partial differential equation (PDE), so these problems may be looked as a...

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Detalles Bibliográficos
Autor: Araya Matilla, Daniel Rolando
Tipo de recurso: tesis de maestría
Fecha de publicación:2023
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/385671
Acceso en línea:https://hdl.handle.net/2117/385671
Access Level:acceso abierto
Palabra clave:Differential equations
Numerical analysis
Equacions diferencials
Anàlisi numèrica
Classificació AMS::74 Mechanics of deformable solids
Classificació AMS::65 Numerical analysis
Àrees temàtiques de la UPC::Matemàtiques i estadística
Descripción
Sumario:Topology optimization aims to find the best layout of material within a design domain to obtain the best performance, according to specific criteria. In many applications, the objective functional depends on the solution of a partial differential equation (PDE), so these problems may be looked as a PDE-constrained optimization problem of a domain-dependent functional. A method based on a reaction-diffusion equation is presented and applied to the design of a linear elastic structure under a minimum compliance requirement. Topology optimization methods can be sensitive to the discretization of the design space, and suffer from mesh dependency issues. To overcome such drawbacks, this work proposes an anisotropic mesh adaptation technique for the reaction-diffusion based optimization method. Implementing the anisotropic mesh adaptation allows us to deliver a final layout characterized by a smooth contour while significantly reducing the computational cost. Several structural benchmarks are given to demonstrate the validity of the proposed approach. In addition, we perform a sensitivity analysis to some parameters, proving the robustness of the method. We also show that complex designs, characterized by a higher number of inner holes, are feasible with remarkable computational efficiency.