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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.
- Introductory application of a natural neighbour meshless elastic formulation to double-lap adhesive jointsPublication . Gonçalves, Diogo C.; Sánchez-Arce, Isidro J.; Ramalho, Luís D. C.; Campilho, Raul; Belinha, JorgeNowadays, adhesive bonding is an essential joining technique in top-end sectors, such as aircraft, automotive, and construction industries. Due to their advantages over traditional joining methods, adhesive joints research has been under huge developments in recent years, being the development of accurate and efficient numerical techniques a leading challenge in adhesive joint design. Although the finite element method (FEM) is an established discretisation technique, meshless methods emerged as alternative discretisation methods to evaluate adhesive joints. Nonetheless, meshless techniques still require deeper research in adhesive joint simulations, where strength prediction is hindered by intricate stress states and material behaviour. This paper aims to evaluate the natural neighbours radial point interpolation method (NNRPIM) in the linear analysis of adhesive joints. The capability of the method was addressed by comparing it with analytical models, the FEM and experimental data. As the applications of meshless methods to analyse adhesive joints are scarce, this work evaluates the behaviour of double-lap joints (DLJ) considering distinct overlap lengths and adhesive materials. DLJ has a different behaviour than single-lap joints, which are more commonly analysed. Thus, this work provides a preliminary linear analysis, which could be the basis for further analyses of adhesive joints combining the NNRPIM with elastic–plastic, hyper-elastic, and large deformations formulations. Although it is remarked that elastic formulations underpredict joint strength, the NNRPIM shows similar results to the FEM, which supports the extension of the NNRPIM to more representative mathematical formulations and complex joint designs.
- Fracture Toughness Determination on an SCB Specimen by Meshless MethodsPublication . Mehri Sofiani, Farid; Farahani, Behzad V.; Belinha, JorgeThis work investigates fracture characteristics of a marble semi-circular bend (SCB) specimen with a pre-defined crack under a compressive loading condition. It aims at evaluating how the fracture toughness can be affected by the crack and span length variation. Numerically, the model is solved using meshless methods, extended to the linear elastic fracture mechanics (LEFM), resorting to radial point interpolation method (RPIM) and its natural neighbor versions (NNRPIMv1 and NNRPIMv2). Alternatively, to validate the meshless method results, the problem is resolved following the finite element method (FEM) model based on the standard 2D constant strain triangle elements. As a result, fracture toughness and the critical strain energy release rate are characterized following the testing method on the cracked straight through semi-circular bend specimen (CSTSCB). A comparison is drawn amongst the theoretical, meshless methods and FEM results to evaluate the capability of advanced numerical methods. Encouraging results have been accomplished leading to validate the supporting numerical methodologies.