Examinando por Autor "Mejia, D."

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    Appraisal of open software for finite element simulation of 2D metal sheet laser cut
    (Springer-Verlag France, 2017-08-01) Mejia, D.; Moreno, A.; Ruiz-Salguero, O.; Barandiaran, I.; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAE
    FEA simulation of thermal metal cutting is central to interactive design and manufacturing. It is therefore relevant to assess the applicability of FEA open software to simulate 2D heat transfer in metal sheet laser cuts. Application of open source code (e.g. FreeFem++, FEniCS, MOOSE) makes possible additional scenarios (e.g. parallel, CUDA, etc.), with lower costs. However, a precise assessment is required on the scenarios in which open software can be a sound alternative to a commercial one. This article contributes in this regard, by presenting a comparison of the aforementioned freeware FEM software for the simulation of heat transfer in thin (i.e. 2D) sheets, subject to a gliding laser point source. We use the commercial ABAQUS software as the reference to compare such open software. A convective linear thin sheet heat transfer model, with and without material removal is used. This article does not intend a full design of computer experiments. Our partial assessment shows that the thin sheet approximation turns to be adequate in terms of the relative error for linear alumina sheets. Under mesh resolutions better than m , the open and reference software temperature differ in at most 1 of the temperature prediction. Ongoing work includes adaptive re-meshing, nonlinearities, sheet stress analysis and Mach (also called 'relativistic') effects.
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    Hessian eigenfunctions for triangular mesh parameterization
    (SciTePress, 2016-02-27) Mejia, D.; Ruiz OE; Cadavid, C.; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAE
    Hessian Locally Linear Embedding (HLLE) is an algorithm that computes the nullspace of a Hessian functional H for Dimensionality Reduction (DR) of a sampled manifold M. This article presents a variation of classic HLLE for parameterization of 3D triangular meshes. Contrary to classic HLLE which estimates local Hessian nullspaces, the proposed approach follows intuitive ideas from Differential Geometry where the local Hessian is estimated by quadratic interpolation and a partition of unity is used to join all neighborhoods. In addition, local average triangle normals are used to estimate the tangent plane TxM at x ? M instead of PCA, resulting in local parameterizations which reflect better the geometry of the surface and perform better when the mesh presents sharp features. A high frequency dataset (Brain) is used to test our algorithm resulting in a higher rate of success (96.63%) compared to classic HLLE (76.4%). © Copyright 2016 by SCITEPRESS - Science and Technology Publications, Lda. All rights reserved.
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    Ítem
    Hessian eigenfunctions for triangular mesh parameterization
    (SciTePress, 2016-02-27) Mejia, D.; Ruiz OE; Cadavid, C.; Mejia, D.; Ruiz OE; Cadavid, C.; Universidad EAFIT. Departamento de Ciencias; Matemáticas y Aplicaciones
    Hessian Locally Linear Embedding (HLLE) is an algorithm that computes the nullspace of a Hessian functional H for Dimensionality Reduction (DR) of a sampled manifold M. This article presents a variation of classic HLLE for parameterization of 3D triangular meshes. Contrary to classic HLLE which estimates local Hessian nullspaces, the proposed approach follows intuitive ideas from Differential Geometry where the local Hessian is estimated by quadratic interpolation and a partition of unity is used to join all neighborhoods. In addition, local average triangle normals are used to estimate the tangent plane TxM at x ? M instead of PCA, resulting in local parameterizations which reflect better the geometry of the surface and perform better when the mesh presents sharp features. A high frequency dataset (Brain) is used to test our algorithm resulting in a higher rate of success (96.63%) compared to classic HLLE (76.4%). © Copyright 2016 by SCITEPRESS - Science and Technology Publications, Lda. All rights reserved.
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    Ítem
    Spectral-based mesh segmentation
    (Springer-Verlag France, 2017-08-01) Mejia, D.; Ruiz-Salguero, O.; Cadavid, C.A.; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAE
    In design and manufacturing, mesh segmentation is required for FACE construction in boundary representation (B-Rep), which in turn is central for feature-based design, machining, parametric CAD and reverse engineering, among others. Although mesh segmentation is dictated by geometry and topology, this article focuses on the topological aspect (graph spectrum), as we consider that this tool has not been fully exploited. We pre-process the mesh to obtain a edge-length homogeneous triangle set and its Graph Laplacian is calculated. We then produce a monotonically increasing permutation of the Fiedler vector (2nd eigenvector of Graph Laplacian) for encoding the connectivity among part feature sub-meshes. Within the mutated vector, discontinuities larger than a threshold (interactively set by a human) determine the partition of the original mesh. We present tests of our method on large complex meshes, which show results which mostly adjust to B-Rep FACE partition. The achieved segmentations properly locate most manufacturing features, although it requires human interaction to avoid over segmentation. Future work includes an iterative application of this algorithm to progressively sever features of the mesh left from previous sub-mesh removals.
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    Ítem
    Spectral-based mesh segmentation
    (Springer-Verlag France, 2017-08-01) Mejia, D.; Ruiz-Salguero, O.; Cadavid, C.A.; Mejia, D.; Ruiz-Salguero, O.; Cadavid, C.A.; Universidad EAFIT. Departamento de Ciencias; Matemáticas y Aplicaciones
    In design and manufacturing, mesh segmentation is required for FACE construction in boundary representation (B-Rep), which in turn is central for feature-based design, machining, parametric CAD and reverse engineering, among others. Although mesh segmentation is dictated by geometry and topology, this article focuses on the topological aspect (graph spectrum), as we consider that this tool has not been fully exploited. We pre-process the mesh to obtain a edge-length homogeneous triangle set and its Graph Laplacian is calculated. We then produce a monotonically increasing permutation of the Fiedler vector (2nd eigenvector of Graph Laplacian) for encoding the connectivity among part feature sub-meshes. Within the mutated vector, discontinuities larger than a threshold (interactively set by a human) determine the partition of the original mesh. We present tests of our method on large complex meshes, which show results which mostly adjust to B-Rep FACE partition. The achieved segmentations properly locate most manufacturing features, although it requires human interaction to avoid over segmentation. Future work includes an iterative application of this algorithm to progressively sever features of the mesh left from previous sub-mesh removals.
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    Ítem
    Triangular mesh parameterization with trimmed surfaces
    (Springer-Verlag France, 2015-04-28) Ruiz, O.E.; Mejia, D.; Cadavid, C.A.; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAE
    Given a 2-manifold triangular mesh M subset of R-3, with border, a parameterization of M is a FACE or trimmed surface F = {S, L-0, ... , L-m. F is a connected subset or region of a parametric surface S, bounded by a set of LOOPs L-0, ... , L-m such that each L-i subset of S is a closed 1-manifold having no intersection with the other L-j LOOPs. The parametric surface S is a statistical fit of the mesh M. L-0 is the outermost LOOP bounding F and L-i is the LOOP of the i-th hole in F (if any). The problem of parameterizing triangular meshes is relevant for reverse engineering, tool path planning, feature detection, redesign, etc. State-of-art mesh procedures parameterize a rectangular mesh M. To improve such procedures, we report here the implementation of an algorithm which parameterizes meshes M presenting holes and concavities. We synthesize a parametric surface S subset of R-3 which approximates a superset of the mesh M. Then, we compute a set of LOOPs trimming S, and therefore completing the FACE F = {S, L-0, ... , L-m. Our algorithm gives satisfactory results for M having low Gaussian curvature (i.e., M being quasi-developable or developable). This assumption is a reasonable one, since M is the product of manifold segmentation pre-processing. Our algorithm computes: (1) a manifold learning mapping phi : M -> U subset of R-2, (2) an inverse mapping S : W subset of R-2 -> R-3, with W being a rectangular grid containing and surpassing U. To compute phi we test IsoMap, Laplacian Eigenmaps and Hessian local linear embedding (best results with HLLE). For the back mapping (NURBS) S the crucial step is to find a control polyhedron P, which is an extrapolation of M. We calculate P by extrapolating radial basis functions that interpolate points inside phi(M). We successfully test our implementation with several datasets presenting concavities, holes, and are extremely non-developable. Ongoing work is being devoted to manifold segmentation which facilitates mesh parameterization.