31 research outputs found

    A Deflated Conjugate Gradient Solver for Extended Finite Element Models

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    In finite element analysis for solid mechanics, the solution of the linear system of equations represents the performance bottleneck in terms of both computation time and memory storage. For this task, direct solvers are a common choice due to their simplicity and robustness, however the very large amount of memory required to factorize the stiffness matrix precludes the solution of medium to large-sized problems. For this reason, substantial research effort in the field of iterative solvers has resulted in the adoption of the Conjugate Gradient (CG) method. In this procedure, explicit factorization and thus large quantities of additional memory are not necessary, due to the use of a gradient-descent optimization process. Among many available improvements of the CG, the Deflated Conjugate Gradient (DCG) solver includes information from approximate eigenvectors (known as the deflation space) to achieve a faster convergence. In this contribution, we present an application of the DCG for fracture mechanics with the eXtended Finite Element Method (XFEM). Among other features, such as holes and inclusions, cracks can be effectively modeled with this method, due to the addition of degrees of freedom and functions that enable the representation of discontinuous displacements and singular stresses within the solution space. In addition to the perspective of accelerated numerical analysis, the motivation to employ an iterative solver lies in the fact that no explicit assembly of the entire stiffness matrix is required, which has positive implications in crack propagation and large scale analyses. With this approach, the main challenge lies in the construction of the deflation space in the presence of additional displacement patterns provided by the enrichment functions. Different methods to achieve this feature are studied and tested. With respect to the CG, the decrease in the number of necessary iterations provided by the optimal method should be comparable to the one delivered in a setup without enrichment. Finally, one can observe that, especially for large simulations, such acceleration justifies the higher implementation effort required

    Moment fitted cut spectral elements for explicit analysis of guided wave propagation

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    In this work, a method for the simulation of guided wave propagation in solids defined by implicit surfaces is presented. The method employs structured grids of spectral elements in combination to a fictitious domain approach to represent complex geometrical features through singed distance functions. A novel approach, based on moment fitting, is introduced to restore the diagonal mass matrix property in elements intersected by interfaces, thus enabling the use of explicit time integrators. Since this approach can lead to significantly decreased critical time steps for intersected elements, a "leap-frog" algorithm is employed to locally comply with this condition, thus introducing only a small computational overhead. The resulting method is tested through a series of numerical examples of increasing complexity, where it is shown that it offers increased accuracy compared to other similar approaches. Due to these improvements, components of interest for SHM-related tasks can be effectively discretized, while maintaining a performance comparable or only slightly worse than the standard spectral element method.Comment: 26 pages, 16 figure

    Moment fitted cut spectral elements for explicit analysis of guided wave propagation

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    In this work, a method for the simulation of guided wave propagation in solids defined by implicit surfaces is presented. The method employs structured grids of spectral elements in combination with a fictitious domain approach to represent complex geometrical features through signed distance functions. A novel approach, based on moment fitting, is introduced to restore the diagonal mass matrix property in elements intersected by interfaces, thus enabling the use of explicit time integrators. Since this approach can lead to significantly decreased critical time steps for intersected elements, a "leap-frog" algorithm is employed to locally comply with this condition, thus introducing only a small computational overhead. The resulting method is tested through a series of numerical examples of increasing complexity, where it is shown that it offers increased accuracy compared to other similar approaches. Due to these improvements, components of interest for structural health monitoring-related tasks can be effectively discretized, while maintaining a performance comparable or only slightly worse than the standard spectral element method. (c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).ISSN:0045-7825ISSN:1879-213

    A Moment-Fitted Extended Spectral Cell Method for Structural Health Monitoring Applications

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    The spectral cell method has been shown as an efficient tool for performing dynamic analyses over complex domains. Its good performance can be attributed to the combination of the spectral element method with mesh-independent geometrical descriptions and the adoption of customized mass lumping procedures for elements intersected by a boundary, which enable it to exploit highly efficient, explicit solvers. In this contribution, we introduce the use of partition-of-unity enrichment functions, so that additional domain features, such as cracks or material interfaces, can be seamlessly added to the modeling process. By virtue of the optimal lumping paradigm, explicit time integration algorithms can be readily applied to the non-enriched portion of a domain, which allows one to maintain fast computing simulations. However, the handling of enriched elements remains an open issue, particularly with respect to stability and accuracy concerns. In addressing this, we propose a novel mass lumping method for enriched spectral elements in the form of a customized moment-fitting procedure and study its accuracy and stability. While the moment-fitting equations are deployed in an effort to minimize the lumping error, stability issues are alleviated by deploying a leap-frog algorithm for the solution of the equations of motion. This approach is numerically benchmarked in the 2D and 3D modeling of damaged aluminium components and validated in comparison with experimental scanning laser Doppler vibrometer data of a composite panel under piezo-electric excitation.ISSN:2076-341

    Crack detection in Mindlin-Reissner plates under dynamic loads based on fusion of data and models

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    In this paper, system identification is coupled with optimization-based damage detection to provide accurate localization of cracks in thin plates, under dynamic loading. Detection relies on exploitation of strain measurements from a network of sensors deployed onto the plate structure. The data-driven approach is based on the detection of discrepancies between healthy and damaged modal strain curvatures, while the model-based method exploits an enriched finite element method coupled to an optimization algorithm to minimize discrepancies between the measured and modelled response of the structure. It is demonstrated, through a series of numerical experiments, that the fusion of data-driven and model-based approaches can be beneficial both in terms of accuracy and localization, as well as in terms of computational requirements.ISSN:0045-7949ISSN:1879-224

    Chemometric analysis of Hymenoptera toxins and defensins: A model for predicting the biological activity of novel peptides from venoms and hemolymph

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    When searching for prospective novel peptides, it is difficult to determine the biological activity of a peptide based only on its sequence. The trial and error approach is generally laborious, expensive and time consuming due to the large number of different experimental setups required to cover a reasonable number of biological assays. To simulate a virtual model for Hymenoptera insects, 166 peptides were selected from the venoms and hemolymphs of wasps, bees and ants and applied to a mathematical model of multivariate analysis, with nine different chemometric components: GRAVY, aliphaticity index, number of disulfide bonds, total residues, net charge, pI value, Boman index, percentage of alpha helix, and flexibility prediction. Principal component analysis (PCA) with non-linear iterative projections by alternating least-squares (NIPALS) algorithm was performed, without including any information about the biological activity of the peptides. This analysis permitted the grouping of peptides in a way that strongly correlated to the biological function of the peptides. Six different groupings were observed, which seemed to correspond to the following groups: chemotactic peptides, mastoparans, tachykinins, kinins, antibiotic peptides, and a group of long peptides with one or two disulfide bonds and with biological activities that are not yet clearly defined. The partial overlap between the mastoparans group and the chemotactic peptides, tachykinins, kinins and antibiotic peptides in the PCA score plot may be used to explain the frequent reports in the literature about the multifunctionality of some of these peptides. The mathematical model used in the present investigation can be used to predict the biological activities of novel peptides in this system, and it may also be easily applied to other biological systems. © 2011 Elsevier Inc

    Profiling the peptidome of the venom from the social wasp Agelaia pallipes pallipes

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    The wasp Agelaia pallipes pallipes is one of the most aggressive species from the neotropical region, causing many stinging accidents every year, characterized by severe envenoming reactions. The identification of peptides is important for understanding the envenoming process; however, the tiny amount of venom produced by these insects makes this task a challenge, using classical analytical approaches. Thus, the venom was previously fractionated, and the sequences were obtained through the use of electrospray ionization with a tridimensional ion-trap and time-of-flight mass analysis under CID conditions. This approach permitted the sequence assignment of nine peptides. The presence of type -d and -w ions generated from the fragmentation of the side chains was used to resolve I/L ambiguity. The distinction between K and Q residues was achieved through esterification of the alpha- and epsilon-amino groups in the peptides, followed by mass spectrometry analysis. Six of these peptides were short, linear and polycationic, while the three other peptides presented a single disulfide bridge. The use of reduction and alkylation protocols, followed by ESI-IT-TOF/MS analysis under CID conditions, permitted easy sequencing of the three peptides presenting this post-translational modification. These peptides presented activity related to mast cell degranulation, hemolysis, or even the chemotaxis of leukocytes. (C) 2011 Elsevier B.V. All rights reserved.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq
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