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- Topology optimization using a natural neighbour meshless method combined with a bi-directional evolutionary algorithmPublication . Gonçalves, D.C.; Lopes, Joel; Campilho, R.D.S.G.; Belinha, JorgeDue to recent developments in the additive manufacturing industry, topology optimization is nowadays a powerful computational tool that allows to design feasible lightweight components. Although the Finite Element Method (FEM) is the most applied discretization technique, meshless methods are currently established as accurate numerical methods with relevant advantages in several engineering fields. Nonetheless, the state-of-the-art of meshless methods in topology optimization is still scarce. This work develops the combination of a bi-direction structural optimization (BESO) algorithm with the Natural Neighbour Radial Point Interpolation Method (NNRPIM), a meshless method combining the natural neighbours geometric concept with the RPI shape functions. First, several benchmark examples are solved to evaluate the algorithm capability under several algorithm parameters. The proposed methodology is then implemented to design new automotive lightweight components. The results from the numerical applications demonstrate that the NNRPIM is a solid technique to be incorporated in optimization algorithms. Additionally, innovative automotive industry designs for additive manufacturing can be obtained using the presented approach.
- Topology optimization of light structures using the natural neighbour radial point interpolation methodPublication . Gonçalves, D. C.; Lopes, Joel; Campilho, R.D.S.G.; Belinha, JorgeIn this work, a bi-directional evolutionary topology optimization algorithm capable of reinforcing the structure at critical high stress regions is combined with the Natural Neighbour Radial Point Interpolation Method (NNRPIM). The NNRPIM uses the Voronoï diagram and natural neighbour concept to establish the background integration points, enforce the nodal connectivity, and construct the RPI shape functions. State-of-the-art of meshless methods in topology optimization is limited when compared with the classic Finite Element Method. Hence, this work originally introduces an accurate truly meshless method, the NNRPIM, to the topology optimization field. The proposed algorithm is validated by solving several benchmark topology optimization problems. A parametric study on algorithm parameters and mesh influence is performed, and the computational processing time is also evaluated Finally, the proposed calibrated method is extended to design lightweight aircraft industry components.
- The Radial Point Interpolation Method combined with a bi-directional structural topology optimization algorithmPublication . Gonçalves, D. C.; Lopes, Joel; Campilho, R.D.S.G.; Belinha, JorgeProjecting reduced-weight components with increased performance is a continuous engineering challenge, especially in the aircraft industry, where fuel consumption, emissions, and performance are highly dependent on structure weight. Nowadays, topology optimization is a growing computational technique capable of calculating optimal material configurations within a design domain and boundary conditions. Although the Finite Element Method (FEM) is the most disseminated discretization technique in engineering, meshless methods emerged as efficient alternatives to mesh-based methods. In meshless methods, the problem domain is discretized by an unstructured nodal distribution with no predetermined connectivity. Additionally, accurate and smooth stress fields can be obtained as a result of the elaborate shape functions and deep nodal connectivity allowed by meshless techniques. Despite, meshless methods application to topology optimization is still limited. In this work, an improved evolutionary topology optimization algorithm is combined with the Radial Point Interpolation Method (RPIM), a meshless technique. First, the proposed method was validated by solving two benchmark topology optimization problems, for which the developed algorithm efficiently achieved the optimal material configuration. Then, the capability of the topology optimization algorithm is demonstrated by extending the methodology to practical aircraft applications.