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Análise estrutural de um quadro tubular de um veículo de Fórmula SAE recorrendo ao método dos elementos finitos
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Nas competições de Formula Student, não basta a equipa construir um quadro tubular
seguro, é obrigatório prová-lo matematicamente. O regulamento exige a submissão de uma
Structural Equivalency Spreadsheet (SES), um documento onde a equipa deve demonstrar,
através de cálculo estrutural, que o seu chassis iguala ou supera a rigidez e resistência de
uma estrutura de referência definida pelo regulamento, sob pena de reprovação técnica antes
mesmo do carro chegar à pista. Este contexto é precisamente onde a análise estrutural deixa
de ser uma boa prática para se tornar um requisito de admissão à competição, que o Método
dos Elementos Finitos (MEF) se torna indispensável. Só através da simulação numérica é
possível prever, com rigor suficiente, o comportamento de uma estrutura tubular irregular
sujeita a carregamentos combinados de impacto, torção e flexão.
Este trabalho desenvolve-se ao longo de duas vertentes complementares. A primeira consiste
numa revisão estruturada do estado da arte dos métodos numéricos de análise estrutural
não linear aplicada a estruturas tubulares, abrangendo formulações incrementais-iterativas,
não linearidade geométrica, não linearidade material e fenómenos de instabilidade estrutural.
A segunda frente consiste na aplicação prática destes conceitos à análise e otimização de
um chassis tubular para um protótipo Formula Student Eléctrico, através de simulação por
elementos finitos utilizando o software SolidWorks Simulation. O modelo foi discretizado
com elementos de viga e sujeito a um estudo de convergência de malha, fixando o tamanho
global do elemento em 10 mm como um compromisso entre precisão e custo computacional.
Foram realizadas análises estáticas de impactos frontal e lateral, análises de rigidez torcional
nos eixos dianteiro e traseiro, e análises modais com o chassis livre e carregado.
O chassis original, com um peso de 56 kg, demonstrou estar estruturalmente sobredimensionado
em todos os cenários de carga analisados, com valores de tensão combinada máxima
muito abaixo do limite de cedência do material, apresentando níveis de tensão muito baixos
nos seus membros. Consequentemente, foi realizada uma otimização geométrica da estrutura,
resultando numa redução de massa de 16 kg em comparação com o chassis original.
Isto foi alcançado sem comprometer a integridade estrutural do chassis e sem modi car a
triangulação. Embora se tenha observado uma diminuição na rigidez torcional, o seu valor
continua a ser considerado ótimo pela literatura.
In Formula Student competitions, it is not enough for a team to build a safe tubular frame, they are required to prove it mathematically. The regulations mandate the submission of a Structural Equivalency Spreadsheet (SES), a document in which the team must demonstrate, through structural calculation, that its chassis matches or exceeds the sti ness and strength of a reference structure de ned by the rulebook, under penalty of technical rejection before the car even reaches the track. It is precisely in this context, where structural analysis ceases to be good practice and becomes a requirement for admission to the competition, that the Finite Element Method (FEM) becomes indispensable. Only through numerical simulation is it possible to predict, with su cient accuracy, the behavior of an irregular tubular structure subjected to combined loading from impact, torsion, and bending. This work is developed along two complementary fronts. The rst consists of a structured review of the state of the art of numerical methods for non-linear structural analysis applied to tubular structures, encompassing incremental-iterative formulations, geometric non-linearity, material non-linearity, and structural instability phenomena. The second front consists of the practical application of these concepts to the analysis and optimization of a tubular frame for a Formula Student Electric prototype, through nite element simulation using SolidWorks Simulation software. The model was discretized with beam elements and subjected to a mesh convergence study, xing the global element size at 10 mm as a compromise between accuracy and computational cost. Static analyses of frontal and lateral impacts, torsional sti ness analyses on the front and rear axles, and modal analyses with both free and loaded frames were performed. The original frame, weighing 56 kg, proved to be structurally oversized in all analyzed load scenarios, with maximum combined stress values well below the material's yield strength, showing very low stress levels in its members. Consequently, a geometry optimization of the structure was carried out, resulting in a mass reduction of 16 kg compared to the original frame. This was achieved without compromising the structural integrity of the chassis and without modifying the triangulation. Although a decrease in torsional sti ness was observed, its value is still considered optimal by the literature.
In Formula Student competitions, it is not enough for a team to build a safe tubular frame, they are required to prove it mathematically. The regulations mandate the submission of a Structural Equivalency Spreadsheet (SES), a document in which the team must demonstrate, through structural calculation, that its chassis matches or exceeds the sti ness and strength of a reference structure de ned by the rulebook, under penalty of technical rejection before the car even reaches the track. It is precisely in this context, where structural analysis ceases to be good practice and becomes a requirement for admission to the competition, that the Finite Element Method (FEM) becomes indispensable. Only through numerical simulation is it possible to predict, with su cient accuracy, the behavior of an irregular tubular structure subjected to combined loading from impact, torsion, and bending. This work is developed along two complementary fronts. The rst consists of a structured review of the state of the art of numerical methods for non-linear structural analysis applied to tubular structures, encompassing incremental-iterative formulations, geometric non-linearity, material non-linearity, and structural instability phenomena. The second front consists of the practical application of these concepts to the analysis and optimization of a tubular frame for a Formula Student Electric prototype, through nite element simulation using SolidWorks Simulation software. The model was discretized with beam elements and subjected to a mesh convergence study, xing the global element size at 10 mm as a compromise between accuracy and computational cost. Static analyses of frontal and lateral impacts, torsional sti ness analyses on the front and rear axles, and modal analyses with both free and loaded frames were performed. The original frame, weighing 56 kg, proved to be structurally oversized in all analyzed load scenarios, with maximum combined stress values well below the material's yield strength, showing very low stress levels in its members. Consequently, a geometry optimization of the structure was carried out, resulting in a mass reduction of 16 kg compared to the original frame. This was achieved without compromising the structural integrity of the chassis and without modifying the triangulation. Although a decrease in torsional sti ness was observed, its value is still considered optimal by the literature.
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Palavras-chave
Métodos de Elementos Finitos Análise não Linear Não Linearidade Geomética e Material Quadros Tubulares Treliças Espaciais Otimização Estrutural Finite Element Method Nonlinear Analysis Geometric and Material Nonlinearity Tubular Frames Space Trusses Structural Optimization