In this work, a methodology for the optimization of offshore wind turbine substructures (jacket type) is presented. The use of a coupled model allows for capturing the full dynamic interaction between all the elements. The structural analysis is carried out in the time-domain. A non-linear integration scheme is necessarily applied due to the effects of the rotation of the blades. Environmental actions, such as wind and waves, are considered as loading conditions. Fatigue damage at the welds of the joints is taken into account. The objective function to be minimized is the weight of the structure. The shape and sizing optimization model is stated in terms of two variables that define the overall shape of the jacket, along with the dimensions of the cross-sections of the structural members. The model is subjected to Ultimate Limit Stress (ULS), Fatigue Limit State and natural frequency constraints. The time-dependent ULS constraints are efficiently treated by means of a new formulation that is based on constraint aggregation. Fatigue accumulation during the whole design life of the structure is accurately assessed, without the need for excessively costly numerical simulations. The optimization problem is solved by means of Sequential Linear Programming, what requires a full first order sensitivity analysis to be performed. The efficiency, reliability and robustness of the proposed methodology is demonstrated by optimizing a real jacket design.

In this work we present a $\delta$-Smoothed Particle Hydrodynamics (SPH) scheme for weakly compressible flows with automatic adaptive numerical dissipation. The resulting scheme is a meshless self-adaptive method, in which the introduced artificial dissipation is designed to increase the dissipation in zones where the flow is under-resolved by the numerical scheme, and to decrease it where dissipation is not required. The accuracy and robustness of the proposed methodology is tested by solving several numerical examples. Using the proposed scheme, we are able to recover the theoretical decay of kinetic energy, even where the flow is under-resolved in very coarse particle discretizations. Moreover, compared with the original $\delta$-SPH scheme, the proposed method reduces the number of problem-dependent parameters.

In this study, a historical review of the Finite Element Method (FEM) and Molecular Dynamics (MD), widely used at the macro and nanoscale respectively is presented, emphasizing the actual parallelisms between their development and applications. After this historical introduction, where certain similarities between both methods are pointed out, different FEM-like methods are analyzed and compared as for first order analysis of structures at the nanoscale. Firstly, the Structural Mechanics (SM) approach is analyzed, where it is assumed that the use of Euler Bernoulli beam elements is equivalent to working directly from the force field. On the other hand, the Molecular Element Method (MEM), which provides the stiffness matrices directly from the potentials, is analyzed. Several analytical static cases are studied for the validation and comparison of both methods. Finally, it is shown that, other branch of methods such as Elastic Network Models (ENM) can be viewed as a particular sub-case of the MEM, or as truss-type finite elements. As an example, the analysis of SARS-CoV2 spikes vibrations is included, comparing with both experimental results and continuous models.