Structural optimisation of the DEMO alternative divertor configurations based on FE and RBF mesh morphing.

The DEMO tokamak exhibits extraordinary complexity due to the constraints and requirements pertaining to different fields of physics and engineering. The multidisciplinary nature of the DEMO system makes its design phase extremely challenging since different and often opposite requirements need to be accounted for. Toroidal field (TF) coils generate the toroidal magnetic field required to magnetically confine the plasma particles and support at the same time the poloidal field coils. They must bear tremendous loads deriving from electromagnetic interactions between the coil currents and the generated magnetic field. An efficient tokamak design aims at minimizing the energy stored in its magnetic field and hence at reducing the toroidal volume within the TF coils whose shape would hence ideally mimic co-centrically the shape of the plasma. In order to bear the enormous forces a D-shape is most suitable for the TF coils as it allows them to resist the very large compression on the inner side and to carry the electro-magnetic (EM) pressure mainly by membrane stresses preventing large bending to occur on the outer side. At the same time the divertor structures must fit within the TF coils and this requires adaptations of the TF coil shape in the case of so-called advanced divertor configurations (ADCs), which require larger divertor structures. This article shows the TF coils adapted to ADCs using a structural optimisation procedure applied to the reference shape. The introduced strategy takes as structural optimum the iso-stress profile associated to each coil. A continuous transformation, based on radial basis functions mesh morphing, turns the baseline finite element (FE) model into its iso-stress counterpart, with a series of intermediate configurations available for electromagnetic and structural investigations as output. The adopted strategy allowed to determine, for each of the ADC cases, a candidate shape. Static membrane stress levels during magnetization could be reduced significantly from more than 700 MPa to below 450 MPa.

A Post-Processing Method Based on Radial Basis Functions for the Fast Retrieval of the Strain Field in Digital Image Correlation Methods.

Digital image correlation methods allow the determination of the displacement (and thus the strain) field of a target by picture comparisons, without the application of strain gauges or other invasive devices. Homologous sites are mapped from the undeformed to the deformed configuration, and displacements retrieved at a cloud of points in a scattered fashion. Radial basis functions (RBF) offer a rapid and reliable tool to post-process on-the-fly data from image correlation, in order to compute deformations directly without the need for generating a numerical grid over the measurement points. Displacements and associated strains can be computed only where desired, tracking automatically only the most reliable features for each image. In this work, a post-processing strain evaluation method for large displacement problems, based on RBF and the Green-Lagrange tensor, is presented and demonstrated for several test cases. At first, the proposed method is adopted on a set of artificially generated pictures, demonstrating a faster convergence with respect to FEM even when few points are used. Finally, the approach is applied to cases for which experimental results are available in the literature, exhibiting a good agreement.

An RBF Meshless Approach to Evaluate Strain Due to Large Displacements in Flexible Printed Circuit Boards.

Thin plates are very often employed in a context of large displacements and rotations, for example, whenever the extreme flexibility of a body can replace the use of complicated kinematic pairs. This is the case of the flexible Printed Circuit Boards (PCBs) used, for example, within last-generation foldable laptops and consumer electronics products. In these applications, the range of motion is generally known in advance, and a simple strategy of stress assessment leaving out nonlinear numerical calculations appears feasible other than desirable. In this paper, Radial Basis Functions (RBFs) are used to represent a generic transformation of a bi-dimensional plate, with all the derivate fields being analytically achieved without the need for a numerical grid for large-displacement applications. Strains due to bending are easily retrieved with this method and satisfactorily compared to analytical and shell-based Finite Element Method (FEM) benchmarks. On the other hand, the computational costs of the juxtaposed methods appear far different; with the machine being equal, the orders of magnitude of the time elapsed in computation are seconds for the RBF-based strategy versus minutes for the FEM approach.

A novel formulation for the study of the ascending aortic fluid dynamics with in vivo data.

Numerical simulations to evaluate thoracic aortic hemodynamics include a computational fluid dynamic (CFD) approach or fluid-structure interaction (FSI) approach. While CFD neglects the arterial deformation along the cardiac cycle by applying a rigid wall simplification, on the other side the FSI simulation requires a lot of assumptions for the material properties definition and high computational costs. The aim of this study is to investigate the feasibility of a new strategy, based on Radial Basis Functions (RBF) mesh morphing technique and transient simulations, able to introduce the patient-specific changes in aortic geometry during the cardiac cycle. Starting from medical images, aorta models at different phases of cardiac cycle were reconstructed and a transient shape deformation was obtained by proper activating incremental RBF solutions during the simulation process. The results, in terms of main hemodynamic parameters, were compared with two performed CFD simulations for the aortic model at minimum and maximum volume. Our implemented strategy copes the actual arterial variation during cardiac cycle with high accuracy, capturing the impact of geometrical variations on fluid dynamics, overcoming the complexity of a standard FSI approach.