Radial Basis Functions Mesh Morphing Research Articles

Advancing Structural Optimization of an Electric Motor Rotor through Mesh Morphing Techniques

The electric motor has been one of the most important inventions of the last two centuries and has become increasingly important in the last 10 years thanks to its efficiency and its ability to reduce pollution. Given this increasing importance of electrical motors, an interest in design and optimization approaches for motor components is arising. Given the different physics involved in the transformation from electrical to mechanical energy, a valuable and reliable approach has to be applied in the optimization process. In past years, Mesh Morphing based on Radial Basis Functions (RBF) has largely proved its validity in generating shape modification for Finite Element Method (FEM) models. In this work, authors will demonstrate the advantages in applying two opposite approaches for shape optimization using RBF Mesh Morphing applied to electrical motors rotors. These components need to be accurately designed in order to guarantee an adequate life duration by reducing stresses in the rotating components. The two approaches that will be described are the parameter based one, in which a set of design parameters will be varied to generate shape modification used to feed a meta-model that will be used to identify an optimal configuration, and a parameter-less approach, in which the shape modification will be driven by FEM analysis results, with the aim to reduce stress hot-spots.

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 mesh morphing computational method for geometry optimization of assembled mechanical systems with flexible components

In this paper an interactive computational methodology was developed assuming that shape and size optimization of flexible components can significantly improve energy absorption or storage ability in assembled systems with flexible components (AS-FC). A radial basis functions mesh morphing formulation in non-linear numerical finite element analysis, including contact problems and flow interaction, was adopted as optimal design method to optimize shape and size design parameters in AS-FC. Flexible components were assembled in finite element environment according to functional ISO-ASME tolerances specification; non-linear structural analysis with flow interaction analysis was performed. The results of the study showed that the proposed method allows to optimize the shape and size of the flexible components in AS-FC maximizing the system's ability to absorb or store energy. The potentiality of the method and its forecasting capability were discussed for the case study of an automotive crash shock in which the specific energy absorption was increased by over 40%. The case studied refers to a simple flexible component geometry, but the method could be extended to systems with more complex geometries.

Fast interactive CFD evaluation of hemodynamics assisted by RBF mesh morphing and reduced order models: the case of aTAA modelling

The medical digital twin is emerging as a viable opportunity to provide patient-specific information useful for treatment, prevention and surgical planning. A bottleneck toward its effective use when computational fluid dynamics (CFD) techniques and tools are adopted for the high fidelity prediction of blood flow, is the significant computing cost required. Reduced order models (ROM) looks to be a promising solution for facing the aforementioned limit. In fact, once ROM data processing is accomplished, the consumption stage can be performed outside the computer-aided engineering software adopted for simulation and, in addition, it could be also implemented on interactive software visualization interfaces that are commonly employed in the medical context. In this paper we demonstrate the soundness of such a concept by numerically investigating the effect of the bulge shape for the ascending thoracic aorta aneurysm case. Radial basis functions (RBF) based mesh morphing enables the implementation of a parametric shape, which is used to build up the ROM framework and data. The final result is an inspection tool capable to visualize, interactively and almost in real-time, the effect of shape parameters on the entire flow field. The approach is first verified considering a morphing action representing the progression from an average healthy patient to an average aneurismatic one (Capellini et al. in Proceedings VII Meeting Italian Chapter of the European Society of Biomechanics (ESB-ITA 2017), 2017; Capellini et al. in J. Biomech. Eng. 140(11):111007-1–111007-10, 2018). Then, a set of shape parameters, suitable to consistently represent a widespread number of possible bulge configurations, are defined and accordingly generated. The concept is showcased taking into account the steady flow field at systolic peak conditions, using ANSYS®Fluent®and its ROM environment for CFD and ROM calculations respectively, and the RBF MorphTM software for shape parametrization.

Automatic shape optimisation of structural parts driven by BGM and RBF mesh morphing

The great flexibility of emerging production processes based on additive manufacturing is stimulating the development of automatic shape optimisation methods. Complex optimised shapes that were previously discarded because of prohibitive construction costs are now affordable. These new designs are obtained through the application of the biological growth method (BGM), which mimics the mechanism of growth that occurs with animal bones and tree trunks. Biological structural parts self-adapt their shape by promoting surface growth at more stressed locations. This behaviour can be adapted to the design optimisation of structural parts, which can be thickened or lightened by updating the shape of the finite element model used for stress analysis. The method used to modify the finite element mesh is a critical consideration, and this paper presents a mesh morphing approach based on radial basis functions (RBFs) that is suitable for complex industrial applications. The computational mesh of the solid part is controlled by using BGM-driven algorithms to reshape its surfaces, which are sculpted by moving them inward or outward in a direction parallel to the local surface normal of the geometry. The deformation is propagated into the volume by interpolating the mesh field using RBFs. The bi-harmonic global-supported RBFs maintain a high quality mesh even for large deformations. The proposed approach is demonstrated using an industrial implementation based on the ANSYS Mechanical finite element solver and the mesh morphing extension RBF Morph. The first example studied is a cantilever beam with an initial rectangular cross section, and a 33% reduction in mass is achieved. A second example consists of a complex-shaped turbine blade, for which significant reductions in peak stress are obtained at three hotspots located on the blade fillet.

Crack propagation analysis of ITER Vacuum Vessel port stub with Radial Basis Functions mesh morphing

The ITER Vacuum Vessel (VV) is one of the most important components of the tokamak machine. The severe operating conditions impose a design to withstand strong dynamic loads. A special focus is put on defects embedded in the component that, due to the not total accessibility of the VV to non-destructive examination (NDE), but also to identify their minimum safe dimension, must be assessed through Fracture Mechanics (FM) analyses. Nuclear codes give useful guidelines for design verification using simplified models that, for practical sake, do not give a detailed description of the physical phenomena. Nowadays, Finite Element Method (FEM) is a common tool for the assessment of structural components, and detailed methods for Crack Propagation analyses have been developed. A novel procedure for the crack shape evolution during cyclic loadings will be presented in this article, relying on Finite Elements Analysis (FEA) in conjunction with Radial Basis Function morphing technique, allowing a fast arrangement of the existing mesh to a new configuration. The results of the proposed method are compared with those available in literature references and in nuclear codes.

High fidelity numerical fracture mechanics assisted by RBF mesh morphing

The study and design of cyclically loaded structures cannot neglect the evaluation of their fatigue behavior. Today numerical prediction tools allow adopting, in various industrial fields, refined and consolidated procedures for the assessment of cracked parts through analyses based on fracture mechanics. An high level of detail can be obtained through the use of well consolidated FEM methods, allowing an accurate and reliable calculation of the flaw Stress Intensity Factor (SIF) and its resulting prediction in terms of crack propagation. A challenging step for this computational workflow remains, however, the generation and update of the computational grid during crack evolution. It is in this context that radial basis functions (RBF) mesh morphing is emerging as a viable solution to replace the complex and time-consuming remeshing operation. The flaw front is updated, according to its propagation, by automatically deforming the numerical grid obtaining an evolutionary workflow suitable to be used for industriallysized numerical meshes (many millions of nodes). A review of applications, obtained by exploiting FEA (Ansys Mechanical) and mesh morphing (RBF Morph) state of-the-art tools, is presented in this work. At first the proposed workflow is applied on a circular notched bar with a defect controlled by a two-parameters evolution. The same approach is then refined and demonstrated for a Multi Degree of Freedom (MDoF) case on the same geometry and on the vacuum vessel port stub from the fusion nuclear reactor Iter.

RBF-based mesh morphing approach to perform icing simulations in the aviation sector

Purpose Numerical simulation of icing has become a standard. Once the iced shape is known, however, the analyst needs to update the computational fluid dynamics (CFD) grid. This paper aims to propose a method to update the numerical mesh with ice profiles. Design/methodology/approach The present paper concerns a novel and fast radial basis functions (RBF) mesh morphing technique to efficiently and accurately perform ice accretion simulations on industrial models in the aviation sector. This method can be linked to CFD analyses to dynamically reproduce the ice growth. Findings To verify the consistency of the proposed approach, one of the most challenging ice profile selected in the LEWICE manual was replicated and simulated through CFD. To showcase the effectiveness of this technique, predefined ice profiles were automatically applied on two-dimensional (2D) and three-dimensional (3D) cases using both commercial and open-source CFD solvers. Practical implications If ice accreted shapes are available, the meshless characteristic of the proposed approach enables its coupling with the CFD solvers currently supported by the RBF4AERO platform including OpenFOAM, SU2 and ANSYS Fluent. The advantages provided by the use of RBF are the high performance and reliability, due to the fast application of mesh smoothing and the accuracy in controlling surface mesh nodes. Originality/value As far as authors’ knowledge is concerned, this is the first time in scientific literature that RBF are proposed to handle icing simulations. Due to the meshless characteristic of the RBF mesh morphing, the proposed approach is cross solver and can be used for both 2D and 3D geometries.

Optimal airfoil’s shapes by high fidelity CFD

Purpose There is an increasing interest in airfoils that modify their shape to adapt at the flow conditions. As an example of application, the authors search the optimal 4-digit NACA airfoil that maximizes the lift-over-drag ratio for a constant lift coefficient of 0.6, from Re = 104 to 3 × 106. Design/methodology/approach The authors consider a γ−Reθt transition model and a κ – ω SST turbulence model with a covariance matrix adaptation evolutionary optimization algorithm. The shape is adapted by radial basis functions mesh morphing using four parameters (angle of attack, thickness, camber and maximum camber position). The objective of the optimization is to find the airfoil that enables a maximum lift-over-drag ratio for a target lift coefficient of 0.6. Findings The computation of the optimal airfoils confirmed the expected increase with Re of the lift-over-drag ratio. However, although the observation of efficient biological fliers suggests that the thickness increases monotonically with Re, the authors find that it is constant but for a 1.5 per cent step increase at Re = 3 × 105. Practical implications The authors propose and validate an efficient high-fidelity method for the shape optimization of airfoils that can be adopted to define robust and reliable industrial design procedures. Originality/value The authors show that the difference in the numerical error between two-dimensional and three-dimensional simulations is negligible, and that the numerical uncertainty of the two-dimensional simulations is sufficiently small to confidently predict the aerodynamic forces across the investigated range of Re.

Crack Propagation Analysis of Near-Surface Defects with Radial Basis Functions Mesh Morphing

Fracture mechanics analysis is nowadays adopted in several industrial fields to assess the capability of components to withstand fatigue loads. Finite Element Method (FEM) is a well-established tool for the evaluation of flaw Stress Intensity Factors (SIF) and for the survey of its propagation. Nevertheless the study of the growth of near-surface circular and elliptical cracks is still an arduous task to be faced with FEM. In fact, the interaction of the flaw with free surfaces leads the crack front to assume complex shapes, whose simulation cannot be easily accomplished. A possible answer to deal with such a problem is to use the mesh morphing technique, a nodal relocation methodology, that allows to cover different problems. In fact, with mesh morphing, it is possible to fit the baseline flaw front with the desired shape (generic shape) and to automatically simulate its evolution at a certain number of cycles. In the proposed work this approach is demonstrated exploiting ANSYS Mechanical as FEM tool and RBF Morph ACT Extension as mesh-morpher. The results of the proposed workflow are compared with those available in literature.

Radial basis functions mesh morphing for the analysis of cracks propagation

Damage tolerant design requires the implementation of effective tools for fracture mechanics analysis suitable for complex shaped components. FEM methods are very well consolidated in this field and reliable procedures for the strength assessment of cracked parts are daily used in many industrial fields. Nevertheless the generation of the computational grid of the cracked part and its update after a certain evolution are still a challenging part of the computational workflow. Mesh morphing, that consists in the repositioning of nodal locations without changing the topology of the mesh, can be a meaningful answer to this problem as it allows the mesh updating without the need of rebuilding it from scratch. Fast Radial Basis Functions (RBF) can be used as an effective tool for enabling mesh morphing on very large meshes that are typically used in advanced industrial applications (many millions of nodes). The applicability of this concept is demonstrated in this paper exploiting state of the art tools for FEA (ANSYS Mechanical) and for advanced mesh morphing (RBF Morph ACT Extension). Proposed method is benchmarked using as a reference a circular notched bar with a surface defect. Reliability of fracture parameter extraction on the morphed mesh is first verified using as a reference literature data and ANSYS Mechanical tools based on re-meshing: different crack shapes are achieved using the new geometry as a morphing target. Crack propagation workflow is then demonstrated showing the computed shape evolution for different size and shape of the initial crack.

Glider fuselage-wing junction optimization using CFD and RBF mesh morphing

Purpose The present paper aims to address the description of a numerical optimization procedure, based on mesh morphing, and its application for the improvement of the aerodynamic performance of an industrial glider which suffers of a large separation occurring in the wing–fuselage junction region at high incidence angles. Design/methodology/approach Shape variations were applied to the baseline configuration through a mesh morphing technique founded on the mathematical framework of radial basis functions (RBF). The aerodynamic solutions were obtained coupling an RANS code with the mesh morphing tool RBF Morph™. Two shape modifiers were set up to generate a parametric numerical model. An optimization procedure, based on a design of experiment sampling, was set up implementing the fully automated workflow within a high performance computing (HPC) environment. The optimal candidates maximizing the aerodynamic efficiency were identified by means of a cubic RBF response surface approach. Findings The separation was significantly reduced, modifying the local geometry of fuselage and fairing and maintaining the wing aerofoil unchanged. A relevant aerodynamic efficiency improvement was finally gained. Practical implications The developed procedure proved to be a very powerful and efficient tool in facing aerodynamic design problems. However, it might be computationally very expensive if a large number of design variables are adopted and, in those cases, the method can be suitably used only within the HPC environment. Originality/value Such an optimization study is part of an explorative set of analyses that focused on better addressing the numerical strategies to be used in the development of the EU FP7 Project RBF4AERO.