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A User’s Guide

Most engineering and scientific phenomena, such as the surface of a landscape or the continuously changing temperature at a location are inherently infinite in space or time or both. We cannot measure all the data. Generally it is possible to record surface elevation values or the temperature only at some specific locations and times.

Interpolation and Approximation

Aerodynamic shape optimization using a novel optimizer based on machine learning techniques

Mechanical Vibrations Theory And Applications

Radial basis functions (RBFs) are a mathematical tool mature enough for consistently handling engineering applications. As their theoretical foundation is very well established and the mathematical framework they are based on can be adapted in several ways, such a numerical means has proven to be effective in many technical fields. As a matter of fact, a candidate engineering application can be faced taking the advantage of the peculiar features of RBF such as the availability of many radial functions with global and compact support as well as the interpolation and regression they allow in a multidimensional space. Such a flexibility makes RBF really attractive for users but, actually, their great potential is just partially exploited. This is due to the difficulty in doing a first step towards the effective usage of RBF not only because they are not commonly part of the cultural background of an engineer, but also, and above all, for the numerical complexity of the RBF problems that scale-up very quickly with the number of the considered RBF centres. Fast RBF algorithms are available to alleviate this latter boundary and, additionally, high-performance computing (HPC) systems and solutions can give a further aid of course. Nevertheless, a consolidate tradition in using RBF for engineering applications is still missing and the beginners may be confused by open literature that, in many cases, is presented with language and symbolisms that are comfortable for mathematicians, but that sound rather cryptic and discouraging to engineers. The aim of this book is to put the interested readers in a better position with respect to RBF providing them with a clear vision of their potential, computational tools ready for practical use and precise guidelines to let them implement their own customised workflows in order to handle engineering applications employing RBF. To this end, the book is divided into two main parts. The first one covers the foundation of RBF, the tools available for their quick implementation and the guidelines for facing new challenges, whilst the second part is a collection of practical applications of RBF in several engineering sectors. Such applications deal with lots of technical and scientific topics including, among others, response surface interpolation in n-dimensional spaces, mapping of magnetic and pressure loads,

Fast Radial Basis Functions for Engineering Applications

A numerical static aeroelastic analysis procedure, applying a modal approach in coupling the fluid dynamic and structural solutions, is presented. The method is based on a preliminary structural modal analysis from which a number of natural modes is selected to be used in the creation of a fluid dynamic domain morphing criterion. The mesh is made parametric on modal coordinates and updated using a mesh morphing tool based on radial basis functions (RBF) within the progress of the fluid dynamic computation. An intrinsically elastic numerical model is then created, and no further iteration with the structural solver is required. The modal forces are extracted by integrating the pressure on the wall boundaries and used to define the weights of the morphing action of each modal shape. This is a simplifying alternative to the traditional fluid dynamic-structural analysis coupling approach that makes it possible to bypass several complexities related to the implementation of 2-way fluid-structure intera...

Static Aeroelastic Analysis of an Aircraft Wind-Tunnel Model by Means of Modal RBF Mesh Updating

Adjoint solvers are acquiring nowadays a growing importance in shape optimization especially when dealing with fluid dynamic applications; their use for structural optimization is however still limited. In this work an optimization workflow based on the synergic use of a structural continuum-discrete adjoint variable solver and the commercial morpher RBF Morph™ is presented. Shape sensitivity information with respect to the objective function is exported as deformation maps on the interested geometry and transferred to the morpher that, after a proper filtering and setup, allows to update automatically the numerical grid. By employing a gradient based logic it is finally possible to achieve an evolutionary optimization. The proposed method effectiveness is shown with two examples: a cantilever beam and a structural bracket.

Shape optimization using structural adjoint 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.

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

A balanced load mapping method based on radial basis functions and fuzzy sets

This paper aims to present a fast and effective approach to tackle complex fluid structure interaction problems that are relevant for the aeronautical design.,High fidelity computer-aided engineering models (computational fluid dynamics [CFD] and computational structural mechanics) are coupled by embedding modal shapes into the CFD solver using RBF mesh morphing.,The theoretical framework is first explained and its use is then demonstrated with a review of applications including both steady and unsteady cases. Different flow and structural solvers are considered to showcase the portability of the concept.,The method is flexible and can be used for the simulation of complex scenarios, including components vibrations induced by external devices, as in the case of flapping wings.,The computation mesh of the CFD model becomes parametric with respect to the modal shape and, so, capable to self-adapt to the loads exerted by the surrounding fluid both for steady and transient numerical studies.

Corrado Groth

Papers

Static Aeroelastic Analysis of an Aircraft Wind-Tunnel Model by Means of Modal RBF Mesh Updating

Shape optimization using structural adjoint and RBF mesh morphing

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

A balanced load mapping method based on radial basis functions and fuzzy sets

Fast high fidelity CFD/CSM fluid structure interaction using RBF mesh morphing and modal superposition method