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 industrially-sized 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

multiphysics numerical investigation on the aeroelastic stability of a le mans prototype car

Abstract In the analysis and design of racing competition cars, numerical tools allow to investigate a wide range of solutions in short time and with high confidence in results. The great available computational power permits to combine simulation software so that different physics involved can be tackled at the same time. An important class of multi-physics simulations for motor sport addresses the fluid-structure interactions happening between the aerodynamic components of the car and the surrounding flow: this interaction can induce structural deformations and vibrations which, in turn, can influence the surrounding fluxes. In this paper, the flutter analysis of the front wing splitter mounted on the 2001 Le Mans Prototype car by Dallara (LMP1) is presented. The study was set up adopting high fidelity CAE models: a 400k shell elements FEM represents the full front wing assembly including the mounting frame, a 240M cells CFD represents the full car immersed in a box shaped wind tunnel. FEM extracted structural modal shapes are mapped onto the CFD mesh adopting Radial Basis Functions (RBF) mesh morphing so that the surfaces of the CFD model can be deformed according to retained modes. Such deformation is then propagated so that the volume mesh is adapted accordingly. The elastic CFD model with modes embedded was then loaded by applying a transient signal individually to each retained mode with a smoothed step function. A Reduced Order Model (ROM) for the aerodynamics of the coupled system was then extracted combining the results of the individual transient run. The critical speed experimentally observed to be in the operating range of the car was captured by the model quite well. The same workflow was then adopted to investigate a different design in which a stiffener has been introduced to increase the first mode natural frequency from 40Hz to 49.4Hz. Flutter speed was increased and moved outside the vehicle range. The car equipped with the improved part proved to perform on the track without previously detected instabilities

Data-driven quasi-interpolant spline surfaces for point cloud approximation

In this paper we investigate a local surface approximation, the Weighted Quasi Interpolant Spline Approximation (wQISA), specifically designed for large and noisy point clouds. We briefly describe the properties of the wQISA representation and introduce a novel data-driven implementation, which combines prediction capability and complexity efficiency. We provide an extended comparative analysis with other continuous approximations on real data, including different types of surfaces and levels of noise, such as 3D models, terrain data and digital environmental data

Fluid structure interaction analysis: vortex shedding induced vibrations

Abstract Fluid Structure Interaction (FSI) numerical modelling requires an efficient workflow to properly capture the physics involved. Computational Structural Mechanics (CSM) and Computation Fluid Dynamics (CFD) have to be coupled and at the moment there is a lack of monolithic solvers capable to tackle industrial applications that involves high fidelity models which mesh can be comprised of hundred millions of cells. This paper shows an efficient approach based on standard commercial tools. The FEM solver ANSYS® Mechanical™ is used to extract a given number of eigenmodes. Then the modal shapes are imported in the CFD solver Fluent® using the Add On RBF Morph™. Updating the modal coordinates it is possible to adapt the shape of the model by taking into account the elasticity of the CFD model. Transient analysis is faced using a time marching solution by updating the shape of the mesh at each time step (weak coupling, evaluated as single DOF systems and integrating modal forces over the CFD grid). Numerical performances and solution accuracy of this approach are analyzed on a practical application (NACA0009 Hydrofoil) for which experimental data are available. A comparison between proposed method and experiment is provided. Transient coupled solver is used for the computation of eigenvalues in water by post processing the free vibration response in calm fluid

Hermiteova interpolacija radijalnim baznim funkcijama u metodi kontrolnih volumena

Primjena metode kontrolnih volumena na proizvoljnoj poliedarskoj mreži poželjna je kod rješavanja inženjerskih problema zbog svoje konzervativnosti i upotrebljivosti kod vrlo složenih geometrija. S druge strane, nedostatak korištenja poliedarske mreže očituje se u ograničenom broju upotrebljivih shema interpolacije i aproksimacije gradijenta, koje su potrebne za računanje konvekcijskog i difuzijskog toka. Taj je problem posebno naglašen kada se radi o metodama visokog reda točnosti. Općenito, razvoj metode kontrolnih volumena visokog reda točnosti za proračune nestlačivih viskoznih tokova zaostaje za razvojem metoda za stlačive neviskozne tokove. Hermiteova interpolacija radijalnim baznim funkcijama primjerena je u metodi kontrolnih volumena na proizvoljnoj poliedarskoj mreži, jer ne nameće topologiju točaka u kojima se zadaju interpolacijski uvjeti. Nadalje, generalizacija Hermiteove interpolacije omogućuje računanje interpolanta, kako u slučajevima s Neumannovim rubnim uvjetom, tako i iz prosjeka u ćelijama u formulaciji visokog reda točnosti. U ovom se radu generalizirana interpolacija koristi za rekonstrukciju u konvektivnom i difuzivnom članu. U fokusu su metode za eliptične i degenerirane eliptične-parabolične probleme, jer se metoda koristi za računanje nestlačivog viskoznog toka. Nadalje, istražuje se particija jedinice koja je primjerena promatranoj klasi problema, a koja je efikasnija od particija jedinice WENO tipa čije korištenje tipično prilikom proračuna hiperboličkih tokova u kojima se pretpostavlja da će se diskontinuiteti pojavljivati u domeni kao dio rješenja. Ovaj je rad doprinos razvoju metode kontrolnih volumena visokog reda točnosti za računanje nestlačivih viskoznih tokova fluida na proizvoljnim poliedarskim mrežama

An evaluation of partial differential equations based digital inpainting algorithms

Partial Differential equations (PDEs) have been used to model various phenomena/tasks in different scientific and engineering endeavours. This thesis is devoted to modelling image inpainting by numerical implementations of certain PDEs. The main objectives of image inpainting include reconstructing damaged parts and filling-in regions in which data/colour information are missing. Different automatic and semi-automatic approaches to image inpainting have been developed including PDE-based, texture synthesis-based, exemplar-based, and hybrid approaches. Various challenges remain unresolved in reconstructing large size missing regions and/or missing areas with highly textured surroundings. Our main aim is to address such challenges by developing new advanced schemes with particular focus on using PDEs of different orders to preserve continuity of textural and geometric information in the surrounding of missing regions. We first investigated the problem of partial colour restoration in an image region whose greyscale channel is intact. A PDE-based solution is known that is modelled as minimising total variation of gradients in the different colour channels. We extend the applicability of this model to partial inpainting in other 3-channels colour spaces (such as RGB where information is missing in any of the two colours), simply by exploiting the known linear/affine relationships between different colouring models in the derivation of a modified PDE solution obtained by using the Euler-Lagrange minimisation of the corresponding gradient Total Variation (TV). We also developed two TV models on the relations between greyscale and colour channels using the Laplacian operator and the directional derivatives of gradients. The corresponding Euler-Lagrange minimisation yields two new PDEs of different orders for partial colourisation. We implemented these solutions in both spatial and frequency domains. We measure the success of these models by evaluating known image quality measures in inpainted regions for sufficiently large datasets and scenarios. The results reveal that our schemes compare well with existing algorithms, but inpainting large regions remains a challenge. Secondly, we investigate the Total Inpainting (TI) problem where all colour channels are missing in an image region. Reviewing and implementing existing PDE-based total inpainting methods reveal that high order PDEs, applied to each colour channel separately, perform well but are influenced by the size of the region and the quantity of texture surrounding it. Here we developed a TI scheme that benefits from our partial inpainting approach and apply two PDE methods to recover the missing regions in the image. First, we extract the (Y, Cb, Cr) of the image outside the missing region, apply the above PDE methods for reconstructing the missing regions in the luminance channel (Y), and then use the colourisation method to recover the missing (Cb, Cr) colours in the region. We shall demonstrate that compared to existing TI algorithms, our proposed method (using 2 PDE methods) performs well when tested on large datasets of natural and face images. Furthermore, this helps understanding of the impact of the texture in the surrounding areas on inpainting and opens new research directions. Thirdly, we investigate existing Exemplar-Based Inpainting (EBI) methods that do not use PDEs but simultaneously propagate the texture and structure into the missing region by finding similar patches within the rest of image and copying them into the boundary of the missing region. The order of patch propagation is determined by a priority function, and the similarity is determined by matching criteria. We shall exploit recently emerging Topological Data Analysis (TDA) tools to create innovative EBI schemes, referred to as TEBI. TDA studies shapes of data/objects to quantify image texture in terms of connectivity and closeness properties of certain data landmarks. Such quantifications help determine the appropriate size of patch propagation and will be used to modify the patch propagation priority function using the geometrical properties of curvature of isophotes, and to improve the matching criteria of patches by calculating the correlation coefficients from the spatial, gradient and Laplacian domains. The performance of this TEBI method will be tested by applying it to natural dataset images, resulting in improved inpainting when compared with other EBI methods. Fourthly, the recent hybrid-based inpainting techniques are reviewed and a number of highly performing innovative hybrid techniques that combine the use of high order PDE methods with the TEBI method for the simultaneous rebuilding of the missing texture and structure regions in an image are proposed. Such a hybrid scheme first decomposes the image into texture and structure components, and then the missing regions in these components are recovered by TEBI and PDE based methods respectively. The performance of our hybrid schemes will be compared with two existing hybrid algorithms. Fifthly, we turn our attention to inpainting large missing regions, and develop an innovative inpainting scheme that uses the concept of seam carving to reduce this problem to that of inpainting a smaller size missing region that can be dealt with efficiently using the inpainting schemes developed above. Seam carving resizes images based on content-awareness of the image for both reduction and expansion without affecting those image regions that have rich information. The missing region of the seam-carved version will be recovered by the TEBI method, original image size is restored by adding the removed seams and the missing parts of the added seams are then repaired using a high order PDE inpainting scheme. The benefits of this approach in dealing with large missing regions are demonstrated. The extensive performance testing of the developed inpainting methods shows that these methods significantly outperform existing inpainting methods for such a challenging task. However, the performance is still not acceptable in recovering large missing regions in high texture and structure images, and hence we shall identify remaining challenges to be investigated in the future. We shall also extend our work by investigating recently developed deep learning based image/video colourisation, with the aim of overcoming its limitations and shortcoming. Finally, we should also describe our on-going research into using TDA to detect recently growing serious “malicious” use of inpainting to create Fake images/videos