21,373 research outputs found

    IGA-based Multi-Index Stochastic Collocation for random PDEs on arbitrary domains

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    This paper proposes an extension of the Multi-Index Stochastic Collocation (MISC) method for forward uncertainty quantification (UQ) problems in computational domains of shape other than a square or cube, by exploiting isogeometric analysis (IGA) techniques. Introducing IGA solvers to the MISC algorithm is very natural since they are tensor-based PDE solvers, which are precisely what is required by the MISC machinery. Moreover, the combination-technique formulation of MISC allows the straight-forward reuse of existing implementations of IGA solvers. We present numerical results to showcase the effectiveness of the proposed approach.Comment: version 3, version after revisio

    A distortion measure to validate and generate curved high-order meshes on CAD surfaces with independence of parameterization

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    This is the accepted version of the following article: [Gargallo-Peiró, A., Roca, X., Peraire, J., and Sarrate, J. (2016) A distortion measure to validate and generate curved high-order meshes on CAD surfaces with independence of parameterization. Int. J. Numer. Meth. Engng, 106: 1100–1130. doi: 10.1002/nme.5162], which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/nme.5162/abstractA framework to validate and generate curved nodal high-order meshes on Computer-Aided Design (CAD) surfaces is presented. The proposed framework is of major interest to generate meshes suitable for thin-shell and 3D finite element analysis with unstructured high-order methods. First, we define a distortion (quality) measure for high-order meshes on parameterized surfaces that we prove to be independent of the surface parameterization. Second, we derive a smoothing and untangling procedure based on the minimization of a regularization of the proposed distortion measure. The minimization is performed in terms of the parametric coordinates of the nodes to enforce that the nodes slide on the surfaces. Moreover, the proposed algorithm repairs invalid curved meshes (untangling), deals with arbitrary polynomial degrees (high-order), and handles with low-quality CAD parameterizations (independence of parameterization). Third, we use the optimization procedure to generate curved nodal high-order surface meshes by means of an a posteriori approach. Given a linear mesh, we increase the polynomial degree of the elements, curve them to match the geometry, and optimize the location of the nodes to ensure mesh validity. Finally, we present several examples to demonstrate the features of the optimization procedure, and to illustrate the surface mesh generation process.Peer ReviewedPostprint (author's final draft

    Toolpaths Programming in an Intelligent Step-NC Manufacturing Context

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    The current language for CNC programming is G-code which dates from the beginning of the eighties with the norm ISO 6983. With the new technologies, G-code becomes obsolete. It presents drawbacks that create a rupture in the numerical chain at the manufacturing step. A new standard, STEP-NC, aims to overtake these lacks. A STEP-NC file includes all the information for manufacturing, as geometry description of the entities, workplan, machining strategies, tools, etc. For rough pocket milling, the ISO norms propose different kind of classical strategies as bidirectional, parallel or spiral contour, etc. This paper describes a new way of toolpath programming by the repetition of a pattern all along a guide curve. It presents several advantages as building fastness and easiness. The integration of pattern strategies in STEP-NC standard is an other step for the development of these strategies but also for the enrichment of STEP-NC possibilities. A complete STEP-NC numerical chain was built, integrating these pattern strategies. The implementation of this approach of building pattern strategies was made by the development of tools for the complete manufacturing cycle, from the CAD file to the machined part. Several application cases were experimented on machine tool to validate this approach and the efficiency of the developped tools
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