Level set topology optimization for design-dependent pressure loads using the reproducing kernel particle method

This paper presents a level set topology optimization method in combination with the reproducing kernel particle method (RKPM) for the design of structures subjected to design-dependent pressure loads. RKPM allows for arbitrary particle placement in discretization and approximation of unknowns. This attractive property in combination with the implicit boundary representation given by the level set method provides an effective framework to handle the design-dependent loads by moving the particles on the pressure boundary without the need of remeshing or special numerical treatments. Moreover, the reproducing kernel (RK) smooth approximation allows for the Young’s modulus to be interpolated using the RK shape functions. This is another advantage of the proposed method as it leads to a smooth Young’s modulus distribution for smooth boundary sensitivity calculation which yields a better convergence. Numerical results show good agreement with those in the literature

Topology Optimization Applications on Engineering Structures

Over the years, several optimization techniques were widely used to find the optimum shape and size of engineering structures (trusses, frames, etc.) under different constraints (stress, displacement, buckling instability, kinematic stability, and natural frequency). But, most of them require continuous data set where, on the other hand, topology optimization (TO) can handle also discrete ones. Topology optimization has also allowed radical changes in geometry which concludes better designs. So, many researchers have studied on topology optimization by developing/using different methodologies. This study aims to classify these studies considering used methods and present new emerging application areas. It is believed that researchers will easily find the related studies with their work

Structural Optimization Techniques Combined With Meshless Methods: A Review

Structural optimization has been growing in recent years, as it is an excellent tool to obtain reliable and high-performance products. In addition to reducing the waste of resources and emissions as well as the production cost, this can be applied in several areas from engineering to medicine. The numerical method most used in recent decades to obtain structurally optimized parts is the finite element method (FEM) and it is included in the group called mesh-based methods. However, the application of these methods in parts with complex geometries and in large deformation problems result in low accuracy and instable solutions. In order to solve this problem, in the last decades, methods that are independent of a mesh have been developed to obtain unknown variables, called meshless methods. Although meshless methods are still recent and there are few documentations, these have been showing good results compared to the mesh-based methods, proving to be a good alternative. Considering what has been said previously, this work has as main objective the study and analysis of parts subjected to structural optimization using mesh-based and meshless methods, in order to compare the results and verify the benefits of using a type of method instead of the other.A optimização estrutural tem vindo a crescer nos últimos anos, uma vez que é uma excelente ferramenta para a obtenção de produtos fiáveis e de alto desempenho. Para além de que reduz o gasto de recursos e emissões assim como o preço de produção das mesmas, esta pode ser aplicada em diversas áreas desde a engenharia à medicina. O método numérico mais utilizado nas últimas décadas para a obtenção de partes estruturalmente optimizadas é o método dos elementos finitos (MEF), o qual pode ser incluído no grupo denominado de métodos com malha. No entanto, a aplicação destes métodos em partes com geometrias complexas e em problemas com grandes deformações resultam em soluções com pouca precisão e de baixa estabilidade. De modo a solucionar este problema, nas últimas décadas, têm vindo a ser desenvolvidos métodos que são independentes de uma malha para a obtenção das varáveis desconhecidas, denominados de métodos sem malha. Apesar dos métodos sem malha ainda serem recentes e existir pouca documentação, estes têm vindo a mostrar bons resultados comparativamente aos métodos com malha provando ser uma boa alternativa. Tendo em conta o referido anteriormente, este trabalho tem como objectivo principal o estudo e análise de partes submetidas a optimização estrutural utilizando métodos com malha e sem malha, de modo a comparar os resultados e verificar os benefícios da utilização de um tipo de método relativamente ao outro