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- Using a meshless method to assess the effect of mechanical loading in angiogenesisPublication . Guerra, Ana; Belinha, Jorge; Natal Jorge, RenatoAlthough it is known that blood vessels can be found in mechanically active environments, less is known about the effect of mechanical stimulus in angiogenesis. Therefore, understanding how endothelial cells respond to a mechanical stimulus is essential to improve tissue vascularization and to promote wound healing and tissue engineering development. In this work, a meshless method is used to combine an elasticity formulation with a capillary growth algorithm. The final numerical model is capable to simulate the effect of compressive loading in angiogenesis, using three strain magnitudes (5, 10 and 30% strain). In this proposed model, the vascular endothelial growth factor gradient regulates the endothelial cell migration and the compressive loading affects the branching process. The numerical results showed that all the compressive loadings tested increased the vascular network length and the number of branches, being 5% strain magnitude the most effective one. The capillary network obtained resembles the one presented in experimental assays and the obtained numerical results coincided to the experimental ones. Nevertheless, this study possesses some limitations since the viscoelastic properties of the tissue, the dynamic loading effect and the effect of the time variable were not considered. In the future, the combination of computational and experimental studies will be very useful to understand and to define which are the mechanical cues that promote angiogenesis, allowing to improve tissue vascularization and, consequently, the wound healing process.
- 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.