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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.
- Elasto-plastic adhesive joint design approach by a radial point interpolation meshless methodPublication . Resende, R.F.P.; Resende, B.F.P.; Sanchez Arce, I.J.; Ramalho, L.D.C.; Campilho, R.D.S.G.; Belinha, JorgeFor efficient use of adhesive joints, reliable prediction techniques should be made available to the designer. Simulation of these joints’ behaviour is usually performed using the Finite Element Method (FEM). However, it is known that, in adhesive joints, the adhesive thickness (tA) is much smaller than the adherend thickness (tP), thus requiring a highly refined mesh to produce good results. Linked to this, the adhesive has to withstand high strains, causing mesh distortion and hindering the resolution. In these cases, meshless methods can be a good alternative. This work aims to implement the von Mises (vM) and Exponent Drucker-Prager (EDP) criteria combined with a meshless formulation based on the Radial Point Interpolation Method (RPIM), for the strength prediction of adhesively-bonded single-lap joints (SLJ). Validation with experiments is undertaken for joints with brittle to ductile adhesives, with varying overlap lengths (LO). Stress and strain distributions were plotted in the adhesive layer, and the failure load (Pm) was assessed by strength of materials failure criteria. Significant adhesive and LO effects were found on Pm. The RPIM proved to be a promising tool to predict the behaviour of bonded joints, although some limitations were found by using strength of materials criteria.
- 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.
- Analysis of stress singularity in adhesive joints using meshless methodsPublication . Ramalho, L.D.C.; Dionísio, J.M.M.; Sánchez-Arce, I.J.; Campilho, R.D.S.G.; Belinha, JorgeRecent years saw a rise in the application of bonding techniques in the engineering industry. This fact is due to the various advantages of this technique when compared to traditional joining methods, such as riveting or bolting. The growth of bonding methods demands faster and more powerful tools to analyze the behavior of products. For that reason, adhesive joints have been the subject of intensive investigation over the past few years. Recently, a fracture mechanics based approach emerged with great potential to evaluate joint behavior, called Intesity of Singular Stress Fields (ISSF), similar to the Stress Intensity Factor (SIF) concept. However, it allows the study of multi-material corners and does not require an initial crack. This approach was not yet tested with meshless methods. The present work intends to fill this gap, resorting to the Radial Point Interpolation Method (RPIM). With this purpose, adhesive joints with four different overlap lengths (LO) bonded with a brittle adhesive were studied. The interface corner's stresses were also evaluated. The predicted strengths were compared with the experimental data to assess the accuracy of the applied methods. In conclusion, the ISSF criterion proved to be applicable to meshless methods, namely the RPIM.
- Hyperelasticity and the radial point interpolation method via the Ogden modelPublication . Sánchez-Arce, I.J.; Ramalho, L.D.C.; Gonçalves, D.C.; Campilho, R.D.S.G.; Belinha, JorgeRubber-like and biological materials could show a hyperelastic behaviour, often studied using the Finite Element Method (FEM), limitations still exist due to the large deformations that this type of material experiment. Conversely, meshless methods are suitable for large deformations. The Ogden hyperelastic model can also represent the Neo-Hookean and Mooney–Rivlin models with ease, making it versatile but its implementation into meshless methods is yet to be done. In this work, the Ogden model was implemented into the Radial Point Interpolation Method (RPIM), a robust and accurate meshless method, within its iterative process allowing for future simulation of multi-material domains. Then, the implementation was tested with small deformations cases. The implementation was validated using three examples and a different hyperelastic model was used for each example, Mooney–Rivlin, Neo-Hookean, and Ogden, whilst their material properties were taken from the literature. The results were compared to FEM solutions and the literature, a good agreement was achieved with differences below 2%, indicating a successful implementation. This is the first implementation of the Ogden model into the RPIM. The ability to model hyperelastic structures together with the inherent advantages of meshless methods provides a good alternative for the analysis of industrial and biological structures.
- 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.
- Numerical analysis of the dynamic behaviour of adhesive joints: A reviewPublication . Ramalho, L.D.C.; Sánchez-Arce, Isidro J.; Gonçalves, Diogo C.; Belinha, Jorge; Campilho, R.D.S.G.Adhesive joints are being increasingly used in various industries, including the automotive or the wind turbines industries. Such increasing interest is a direct result of its high structural efficiency and also the product of its related scientific research. Therefore, the state-of-the-art on adhesive joints is significantly expanding. The current work aims to discuss the most recent works dedicated to the numerical analysis of the dynamic behaviour of adhesive joints. Dynamic behaviour was divided into three separate fields: fatigue, variable strain rate and impact, and modal analysis. It was found that Cohesive Zone Models are a popular approach to study fatigue, variable strain rates and impact. Additionally, the available literature focused on fatigue and impact is more extensive than the one focused on modal analysis. Overall, it was found that the available research on the numerical analysis of the dynamic behaviour of adhesive joints is increasing at a solid rate, and many geometrical and material variations have been tested numerically. With this review designers and researchers of adhesive joints should be able to choose the most suitable numerical technique for their specific dynamic analysis.
- Meshless analysis of the stress singularity in composite adhesive jointsPublication . Ramalho, L.D.C.; Dionísio, J.M.M.; Sánchez-Arce, I.J.; Campilho, R.D.S.G.; Belinha, JorgeAdhesives are an exceptionally well-suited method for joining composites. Unlike other methods, such as bolting or riveting, adhesives do not introduce holes in their joining material. This is a significant advantage in the case of composites because the holes required by bolting or riveting induce stress concentrations and can also lead to tears, burrs or delamination. A point of concern in adhesive joints is the adhesive/adherend interface corner where a stress singularity occurs, and failure usually initiates. Thus, it is crucial to study this stress singularity to better understand adhesive joints’ mechanical behaviour. The goal of this work is to validate the application of the Intensity of Singular Stress Fields (ISSF) criterion to meshless methods, in this case, the Radial Point Interpolation Method (RPIM). With this purpose, eight overlap lengths (LO) in single-lap joints (SLJ) composed of Carbon Fibre Reinforced Polymer (CFRP) and bonded with a brittle adhesive were experimentally and numerically tested. Furthermore, an extrapolation based method is implemented to determine the critical stress singularity components (Hc) necessary for the strength predictions. In the end, the experimental and numerical results are compared to assess the suitability of the method. It was found that the ISSF criterion can be accurately applied to meshless methods and composite materials successfully, given the simplicity of the method applied.
- Fracture propagation based on meshless method and energy release rate criterion extended to the Double Cantilever Beam adhesive joint testPublication . Gonçalves, D.C.; Sánchez-Arce, I.J.; Ramalho, L.D.C.; Campilho, R.D.S.G.; Belinha, JorgeIn this work, a numerical methodology based on a meshless technique is proposed to predict the fracture propagation in Double Cantilever Beam (DCB) adhesive joints. The Radial Point Interpolation Method (RPIM) is used to approximate the field variable at each crack increment step. The meshless method permits a flexible discretization of the problem domain in a set of unstructured field nodes and eases the implementation of the geometric crack propagation algorithm. Regarding the fracture propagation algorithm, a recent adaptative remeshing technique is used combined with the RPIM. The crack tip is explicitly propagated by locally remeshing the field nodes and triangular integration cells in the crack tip vicinity. To predict the crack initiation, a fracture mechanics criterion based on the energy release rate in DCB is implemented. The proposed numerical methodology is validated with experimental data.