Automatic reconstruction of beam structures from 3D topology optimization results

This paper presents a fully-automated reconstruction of beam-like CAD solid structures from 3D topology optimization (TO) results. Raw TO results are first processed to generate a triangulation that represents boundaries of the optimal shape derived. This triangulation is then smoothed and a curve skeletonization procedure is carried out to recover meaningful characteristics of this smoothed triangulation. The resulting skeleton, made with curvilinear geometry, is transformed into straight lines through a normalization process. These straight lines are used to generate a 3D beam structure. Thus, following these steps, a 3D beam structure is automatically derived from TO results. This 3D beam structure is meshed with beam finite elements and since TO non-design material is represented by 3D solid geometry, which is meshed using tetrahedron, the FEA beam structure needs to be rigidly connected with these tetrahedrons. Rigid connections between beam elements and 3D solid elements are ensured using specific FEA beam elements referred to as mini-beams. This results in a mixed-dimensional FEA model with beam and solid finite elements. Results obtained with this mixed-dimensional FEA model allow validating the beam structure obtained from TO results. Performance of the approach is demonstrated on several TO examples

Adaptation et transformation automatiques des résultats d’optimisation topologique en modèles CAO de structures de poutres

Les méthodes d’optimisation topologique sont de nos jours très populaires et intégrées dans plusieurs logiciels de conception. Elles munissent le concepteur d’un outil de choix pour l’obtention des formes optimisées en phase de conception. Cependant, l’une des principales limites de ces méthodes est l’interprétation du résultat de l’optimisation en un modèle facilement exploitable dans la suite du processus de conception. En effet, seulement un nombre limité d’approches ont été développées en vue de transformer un modèle optimisé en un modèle de CAO (Conception Assistée par Ordinateur). Bien qu’elles soient probantes à bien des égards, elles sont pour la plupart encore limitées aux modèles en 2D et sont semi ou non automatiques, ce qui fait que le concepteur est beaucoup mis à contribution durant l’interprétation du modèle optimisé. Dans cette recherche, une méthodologie d’interprétation d’un résultat d’optimisation topologique est proposée. La méthode d’optimisation utilisée est la méthode SIMP (Solid Isotropic Material with Penalization) qui donne comme résultat une répartition optimale de la matière dans le modèle. En considérant un résultat de la méthode SIMP qui s’oriente vers des structures composées de poutres, l’approche proposée compte deux étapes importantes que sont l’amélioration de la qualité du résultat de l’optimisation et la conversion en modèle CAO du modèle optimisé adapté qui en découle. Le produit est donc un modèle CAO plus facile à exploiter et à fabriquer. Ce dernier est finalement validé par une analyse multidimensionnelle par éléments finis. En plus d’être automatique, l’approche développée retourne des modèles CAO qui représentent bien la forme telle qu’optimisée. Nowadays, topology optimization methods are very popular and integrated into several computer-aided design (CAD) software. They provide the designer with a tool allowing to obtain optimized shapes in the design phase. However, one of the main limitations of these methods is the interpretation of optimization results into CAD models that can be easily used in subsequent design phases. Indeed, only a limited number of approaches have been developed in order to interpret raw optimization results into CAD models. Even if good results can be obtained with some of these methods, it is still limited to 2D models and these methods are semi- or non-automatic. Consequently, the interpretation process requires the designer’s intervention. In this work, a methodology for automatically interpreting three-dimensional topology optimization result into CAD models is proposed. The optimization method used is the SIMP (Solid Isotropic Material with Penalization) method, which results in an optimized distribution of material inside a given volume. Considering results of the SIMP method that tend towards beam-like structures, the proposed approach involves two main stages, which are quality improvement of the optimized result and conversion of the improved optimized shape into a CAD model of beam structure. Therefore, the outcome of this approach is a CAD model that is easier to use and to manufacture. The converted model is finally validated through a multidimensional finite element analysis (FEA). More than being fully automatic, the proposed method also produces CAD models that are good approximations of optimized shapes generated by the SIMP method

Dimensionamento Mecânico de Reforço "Favo de Abelha" de Componentes pelo Método de Elementos Finitos, para a Indústria Automóvel

Na fabricação de peças de materiais de cariz polimérico, uma das metodologias empregues para melhorar as propriedades mecânicas de uma determinada zona, consiste em criar secções retas e finas de material, denominadas de frisos, que conferem uma maior rigidez na área aplicada. Isto é muito útil quando apenas uma porção pequena da peça se encontra a condições de trabalho mais exigentes, pois funciona como uma medida de reforço geométrico, a um custo relativamente reduzido. Ora, de maneira a poder-se reduzir ainda mais os custos de produção, é do interesse das empresas, otimizar o design destas geometrias, de forma a ser gasto a menor quantidade de matéria-prima possível, enquanto se mantêm as propriedades desejadas pelo cliente. A presente dissertação tem como objetivo a otimização do design destes mesmos frisos, em certos componentes de interior de automóveis da empresa Simoldes Plásticos®. Para se alcançar este objetivo desenvolveram-se scripts em Python que permitem fazer análises sequenciais e automáticas no software Simulia Abaqus®, através de simulações pelo Método de Elementos Finitos (MEF), onde as respetivas peças, com diferentes geometrias de reforço, foram submetidas a um ensaio de flexão, e os dados das respostas dos sistemas foram processados automaticamente, de maneira a determinar-se a combinação de características que melhor se adequa ao componente. Para o desenvolvimento do programa, as peças foram primeiro modeladas no software de CAD Cátia V5®, tendo-se depois recorrido à simplificação das mesmas, através da supressão de atributos irrelevantes para a simulação, e a implementação de superfícies médias. As peças simplificadas foram depois transferidas para o Simulia Abaqus® onde se fez uma simulação, sem que tenham sido aplicados frisos, de maneira a utilizar o código resultante, como base para a construção do modelo do script final. Com a base do programa feita, procedeu-se com a formulação do algoritmo responsável pelo desenho, e parametrização automática dos frisos, bem como as funções relativas ao pré-processamento, pós-processamento, desenvolvimento de um Graphical User Interface (GUI), envio de relatórios por correio eletrónico e alteração das prioridades dos programas presentes no sistema operativo. Com o software desenvolvido, correram-se as simulações, tendo-se obtidos os dados sobre a geometria dos frisos que permite satisfazer os requisitos do cliente, utilizandose a menor quantidade de material possível.In the manufacturing of polymeric parts, one of the methodologies used to improve the mechanical properties of a given area is to create straight and thin sections of material, called ribs, which provide greater rigidity to the applied area. This is very useful when only a small portion of the part is under more demanding working conditions, as it works as a geometrical reinforcement measure, at a relatively low cost. However, for companies whose production focus is on this type of components, it makes sense that they want to spend as little material as possible, while giving them the properties desired by the customer. This dissertation aims to optimize the design of these same ribs, in certain car interior components from Simoldes Plásticos®. To achieve this goal, Python scripts were developed that allow automatic sequential analysis in the Abaqus® software, using the Finite Element Method (FEM). Where different combinations of material and geometric properties of the ribs were tested, and the response of the components to a bending test was observed. With the data obtained, the best possible geometry was then selected. For the development of the software, the parts were first modelled in the CAD software Catia V5, having then resorted to their geometrical simplification, through the suppression of irrelevant attributes for the simulation, and the implementation of mid-planes. The simplified parts were then taken to Abaqus® where a simulation was carried out, without ribs having been applied, in order to use the resulting code as a constructor of the part in the final script. With the constructer completed, next came the coding of the function responsible for the parameterization of the friezes geometry, as well as the functions related to post-processing, development of a Graphical User Interface (GUI), sending reports via email and changing program priorities in the operating system. With the developed software, the simulations were run over a weekend, having obtained data on the best geometry for the friezes, and implemented these in the final piece