Direct medical image-based Finite Element modelling for patient-specific simulation of future implants

[EN] In patient specific biomedical simulation, the numerical model is usually created after cumbersome, time consuming procedures which often require highly specialized human work and a great amount of man-hours to be carried out. In order to make numerical simulation available for medical practice, it is of primary importance to reduce the cost associated to these procedures by making them automatic. In this paper a method for the automatic creation of Finite Element (FE) models from medical images is presented. This method is based on the use of a hierarchical structure of nested Cartesian grids in which the medical image is immersed. An efficient h-adaptive procedure conforms the FE model to the image characteristics by refining the mesh on the basis of the distribution of elastic properties associated to the pixel values. As a result, a problem with a reasonable number of degrees of freedom is obtained, skipping the geometry creation stage. All the image information is taken into account during the calculation of the element stiffness matrix, therefore it is straightforward to include the material heterogeneity in the simulation. The proposed method is an adapted version of the Cartesian grid Finite Element Method (cgFEM) for the FE analysis of objects defined by images. cgFEM is an immersed boundary method that uses h-adaptive Cartesian meshes non-conforming to the boundary of the object to be analysed. The proposed methodology, used together with the original geometry-based cgFEM, allows prosthesis geometries to be easily introduced in the model providing a useful tool for evaluating the effect of future implants in a preoperative framework. The potential of this kind of technology is presented by mean of an initial implementation in 2D and 3D for linear elasticity problems.With the support of the European Union Framework Programme (FP7) under grant agreement No. 289361 'Integrating Numerical Simulation and Geometric Design Technology (INSIST)', the Ministerio de Economia y Competitividad of Spain (DPI2010-20542) and the Generalitat Valenciana (PROMETEO/2016/007).Giovannelli, L.; Ródenas, J.; Navarro-Jiménez, J.; Tur Valiente, M. (2017). Direct medical image-based Finite Element modelling for patient-specific simulation of future implants. Finite Elements in Analysis and Design. 136:37-57. https://doi.org/10.1016/j.finel.2017.07.010S375713

Robust h-adaptive meshing strategy considering exact arbitrary CAD geometries in a Cartesian grid framework

[EN] Geometry plays a key role in contact and shape optimization problems in which the accurate representation of the exact geometry and the use of adaptive analysis techniques are crucial to obtaining accurate computationally-efficient Finite Element (FE) simulations. We propose a novel algorithm to generate 3D h-adaptive meshes for an Immersed Boundary Method (IBM) based on Cartesian grids and the so-called NEFEM (NURBS-Enhanced FE Method) integration techniques. To increase the accuracy of the results at the minimum computational cost we seek to keep the efficient Cartesian structure of the mesh during the whole analysis process while considering the exact boundary representation of domains given by NURBS or T-Splines. Within the framework of Cartesian grids, the two significant contributions of this paper are: (a) the methodology used for the mesh-geometry intersection, which represents a considerable challenge due to their independence; and (b) the robust procedure used to generate the integration subdomains that exactly represent the CAD model. The numerical examples given show the proper convergence of the method, its capacity to mesh complex 3D geometries and that Cartesian grid-based IBM can be considered a robust and reliable tool in terms of accuracy and computational cost.The authors wish to thank the Spanish Ministerio de Economia y Competitividad for the financial support received through Project DPI2013-46317-R and the FPI program (BES-2011-044080), also the Generalitat Valenciana for the assistance received through Project PROMETEO/2016/007.Marco, O.; Ródenas, J.; Navarro-Jiménez, J.; Tur Valiente, M. (2017). Robust h-adaptive meshing strategy considering exact arbitrary CAD geometries in a Cartesian grid framework. Computers & Structures. 193:87-109. doi:10.1016/j.compstruc.2017.08.004S8710919

Superconvergent patch recovery with constraints for three-dimensional contact problems within the Cartesian grid Finite Element Method

"This is the peer reviewed version of the following article: Navarro-Jiménez, José M., Héctor Navarro-García, Manuel Tur, and Juan J. Ródenas. 2019. Superconvergent Patch Recovery with Constraints for Three-dimensional Contact Problems within the Cartesian Grid Finite Element Method. International Journal for Numerical Methods in Engineering 121 (6). Wiley: 1297 1313. doi:10.1002/nme.6266, which has been published in final form at https://doi.org/10.1002/nme.6266. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving."[EN] The superconvergent patch recovery technique with constraints (SPR-C) consists in improving the accuracy of the recovered stresses obtained with the original SPR technique by considering known information about the exact solution, like the internal equilibrium equation, the compatibility equation or the Neumann boundary conditions, during the recovery process. In this paper the SPR-C is extended to consider the equilibrium around the contact area when solving contact problems with the Cartesian grid Finite Element Method. In the proposed method, the Finite Element stress fields of both bodies in contact are considered during the recovery process and the equilibrium is enforced by means of the continuity of tractions along the contact surface.The authors would like to thank Generalitat Valenciana (PROMETEO/2016/007), the Spanish Ministerio de Economía, Industria y Competitividad (DPI2017-89816-R), the Spanish Ministerio de Ciencia, Innovación y Universidades (FPU17/03993), and Universitat Politècnica de València (FPI2015) for the financial support to this work.Navarro-Jiménez, J.; Navarro-García, H.; Tur Valiente, M.; Ródenas, JJ. (2020). Superconvergent patch recovery with constraints for three-dimensional contact problems within the Cartesian grid Finite Element Method. International Journal for Numerical Methods in Engineering. 121(6):1297-1313. https://doi.org/10.1002/nme.6266S129713131216Wriggers, P. (2006). Computational Contact Mechanics. doi:10.1007/978-3-540-32609-0Marco, O., Sevilla, R., Zhang, Y., Ródenas, J. J., & Tur, M. (2015). Exact 3D boundary representation in finite element analysis based on Cartesian grids independent of the geometry. International Journal for Numerical Methods in Engineering, 103(6), 445-468. doi:10.1002/nme.4914Navarro-Jiménez, J. M., Tur, M., Albelda, J., & Ródenas, J. J. (2018). Large deformation frictional contact analysis with immersed boundary method. Computational Mechanics, 62(4), 853-870. doi:10.1007/s00466-017-1533-xMarco, O., Ródenas, J. J., Navarro-Jiménez, J. M., & Tur, M. (2017). Robust h-adaptive meshing strategy considering exact arbitrary CAD geometries in a Cartesian grid framework. Computers & Structures, 193, 87-109. doi:10.1016/j.compstruc.2017.08.004Ródenas, J. J., Tur, M., Fuenmayor, F. J., & Vercher, A. (2007). Improvement of the superconvergent patch recovery technique by the use of constraint equations: the SPR-C technique. International Journal for Numerical Methods in Engineering, 70(6), 705-727. doi:10.1002/nme.1903Zienkiewicz, O. C., & Zhu, J. Z. (1992). The superconvergent patch recovery (SPR) and adaptive finite element refinement. Computer Methods in Applied Mechanics and Engineering, 101(1-3), 207-224. doi:10.1016/0045-7825(92)90023-dRódenas, J. J., González-Estrada, O. A., Díez, P., & Fuenmayor, F. J. (2010). Accurate recovery-based upper error bounds for the extended finite element framework. Computer Methods in Applied Mechanics and Engineering, 199(37-40), 2607-2621. doi:10.1016/j.cma.2010.04.010Blacker, T., & Belytschko, T. (1994). Superconvergent patch recovery with equilibrium and conjoint interpolant enhancements. International Journal for Numerical Methods in Engineering, 37(3), 517-536. doi:10.1002/nme.1620370309Díez, P., José Ródenas, J., & Zienkiewicz, O. C. (2007). Equilibrated patch recovery error estimates: simple and accurate upper bounds of the error. International Journal for Numerical Methods in Engineering, 69(10), 2075-2098. doi:10.1002/nme.1837Nadal, E., Díez, P., Ródenas, J. J., Tur, M., & Fuenmayor, F. J. (2015). A recovery-explicit error estimator in energy norm for linear elasticity. Computer Methods in Applied Mechanics and Engineering, 287, 172-190. doi:10.1016/j.cma.2015.01.013Badia, S., Verdugo, F., & Martín, A. F. (2018). The aggregated unfitted finite element method for elliptic problems. Computer Methods in Applied Mechanics and Engineering, 336, 533-553. doi:10.1016/j.cma.2018.03.022Zienkiewicz, O. C., Zhu, J. Z., & Wu, J. (1993). Superconvergent patch recovery techniques - some further tests. Communications in Numerical Methods in Engineering, 9(3), 251-258. doi:10.1002/cnm.1640090309FUENMAYOR, F. J., & OLIVER, J. L. (1996). CRITERIA TO ACHIEVE NEARLY OPTIMAL MESHES IN THEh-ADAPTIVE FINITE ELEMENT METHOD. International Journal for Numerical Methods in Engineering, 39(23), 4039-4061. doi:10.1002/(sici)1097-0207(19961215)39:233.0.co;2-cBabuška, I., Strouboulis, T., & Upadhyay, C. . (1994). A model study of the quality of a posteriori error estimators for linear elliptic problems. Error estimation in the interior of patchwise uniform grids of triangles. Computer Methods in Applied Mechanics and Engineering, 114(3-4), 307-378. doi:10.1016/0045-7825(94)90177-

Large deformation frictional contact analysis with immersed boundary method

[EN] This paper proposes a method of solving 3D large deformation frictional contact problems with the Cartesian Grid Finite Element Method. A stabilized augmented Lagrangian contact formulation is developed using a smooth stress field as stabilizing term, calculated by Zienckiewicz and Zhu Superconvergent Patch Recovery. The parametric definition of the CAD surfaces (usually NURBS) is considered in the definition of the contact kinematics in order to obtain an enhanced measure of the contact gap. The numerical examples show the performance of the method.The authors wish to thank the Spanish Ministerio de Economia y Competitividad the Generalitat Valenciana and the Universitat Politecnica de Valencia for their financial support received through the projects DPI2013-46317-R, Prometeo 2016/007 and the FPI2015 program.Navarro-Jiménez, J.; Tur Valiente, M.; Albelda Vitoria, J.; Ródenas, JJ. (2018). Large deformation frictional contact analysis with immersed boundary method. 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Math Comput Model 28(4–8):263–271. https://doi.org/10.1016/S0895-7177(98)00121-6De Lorenzis L, Wriggers P, Zavarise G (2012) A mortar formulation for 3D large deformation contact using NURBS-based isogeometric analysis and the augmented Lagrangian method. Comput Mech 49(1):1–20. https://doi.org/10.1007/s00466-011-0623-4Dittmann M, Franke M, Temizer I, Hesch C (2014) Isogeometric Analysis and thermomechanical Mortar contact problems. Comput Methods Appl Mech Eng 274:192–212. https://doi.org/10.1016/j.cma.2014.02.012Dolbow J, Moës N, Belytschko T (2001) An extended finite element method for modeling crack growth with frictional contact. Comput Methods Appl Mech Eng 190:6825–6846. https://doi.org/10.1016/S0045-7825(01)00260-2Dolbow JE, Devan a (2004) Enrichment of enhanced assumed strain approximations for representing strong discontinuities: addressing volumetric incompressibility and the discontinuous patch test. Int J Numer Methods Eng 59(1):47–67. https://doi.org/10.1002/nme.862Fischer KA, Wriggers P (2006) Mortar based frictional contact formulation for higher order interpolations using the moving friction cone. Comput Methods Appl Mech Eng 195(37–40):5020–5036. https://doi.org/10.1016/j.cma.2005.09.025Giovannelli L, Ródenas J, Navarro-Jiménez J, Tur M (2017) Direct medical image-based Finite Element modelling for patient-specific simulation of future implants. Finite Elem Anal Des. https://doi.org/10.1016/j.finel.2017.07.010Gitterle M, Popp A, Gee MW, Wall WA (2010) Finite deformation frictional mortar contact using a semi-smooth Newton method with consistent linearization. Int J Numer Methods Eng. https://doi.org/10.1002/nme.2907Hammer ME (2013) Frictional mortar contact for finite deformation problems with synthetic contact kinematics. Comput Mech 51(6):975–998. https://doi.org/10.1007/s00466-012-0780-0Hansbo P, Rashid A, Salomonsson K (2015) Least-squares stabilized augmented Lagrangian multiplier method for elastic contact. Finite Elem Anal Des 116:32–37. https://doi.org/10.1016/j.finel.2016.03.005Haslinger J, Renard Y (2009) A new fictitious domain approach inspired by the extended finite element method. SIAM J Numer Anal 47(2):1474–1499. https://doi.org/10.1137/070704435Hautefeuille M, Annavarapu C, Dolbow JE (2012) Robust imposition of Dirichlet boundary conditions on embedded surfaces. Int J Numer Methods Eng 90:40–64. https://doi.org/10.1002/nme.3306Heintz P, Hansbo P (2006) Stabilized Lagrange multiplier methods for bilateral elastic contact with friction. Comput Methods Appl Mech Eng 195(33–36):4323–4333. https://doi.org/10.1016/j.cma.2005.09.008Hughes T, Cottrell J, Bazilevs Y (2005) Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. 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Metodología jerárquica h adaptativa basada en subdivisión de elementos

[EN] This paper presents a hierarchical h adaptive methodology for Finite Element Analysis based on the hierarchical relations between parent and child elements that come out if these elements are geometrically similar. Under this similarity condition the terms involved in the evaluation of element stiffness matrices of parent and child elements are related by a constant which is a function of the element sizes ratio (scaling factor). These relations have been the basis for the development of a hierarchical h adaptivity methodology based on element subdivision and the use of multipoint-constraints to ensure C0 continuity. The use of a hierarchical data structure significantly reduces the amount of calculations required for the mesh refinement, the evaluation of the global stiffness matrix, element stresses and element error estimation. The data structure also produces a natural reordering of the global stiffness matrix that improves the behaviour of the Cholesky factorization.[ES] En este artículo se presenta una metodología h adaptativa para el Análisis por Elementos Finitos basada en las relaciones jerárquicas entre elementos padre e hijo que surgen si estos elementos son geométricamente similares. Bajo esta condición de similitud, los términos resultantes de la evaluación de las matrices de rigidez de elementos padre e hijo están relacionados por una constante que es una función de la relación de tamaños de elemento (factor de escala). Estas relaciones han sido la base para el desarrollo de una metodología jerárquica h adaptativa basada en la subdivisión de elementos y el uso de restricciones multipunto para asegurar la continuidad C0 . El uso de una estructura de datos jerárquica reduce significativamente la cantidad de cálculos requeridos para el refinamiento de la malla, la evaluación de la matriz de rigidez global, las tensiones de los elementos y la estimación del error del elemento. La estructura de datos también produce un reordenamiento natural de la matriz de rigidez global que mejora el comportamiento de la factorización de Cholesky.The authors wish to thank the Spanish Ministerio de Economía y Competitividad for the fiancial support received through the project DPI2013-46317-R and the Generalitat Valenciana through the project PROMETEO/2016/007. The support of the Universidad Politécnica de Valencia is also acknowledged. The authors also want to thank Ana Ródenas’s help in the translation of this paper.Ródenas, J.; Albelda Vitoria, J.; Tur Valiente, M.; Fuenmayor Fernández, F. (2017). A hierarchical h adaptivity methodology based on element subdivision. Revista UIS Ingenierías. 16(2):263-280. https://doi.org/10.18273/revuin.v16n2-2017024S26328016

3D analysis of the influence of specimen dimensions on fretting stresses

[EN] In this paper, the contact conditions and stresses that arise in a fretting test have been analyzed by means of a three-dimensional finite element model of the contact between a sphere and a flat surface. An h-adaptive process, based on element subdivision, has been used in order to obtain a low discretization error at a reasonable computational cost. The influence of finite dimensions of the specimen in the stress fields has been evaluated. The results have been compared with the classical Cattaneo-Mindlin solution.The authors wish to thank the financial support received from CICYT by means of the project PB97-0696-C02-02.Tur Valiente, M.; Fuenmayor Fernández, F.; J.J. Ródenas; Giner Maravilla, E. (2003). 3D analysis of the influence of specimen dimensions on fretting stresses. Finite Elements in Analysis and Design. 39(10):933-949. https://doi.org/10.1016/S0168-874X(02)00139-7S933949391

An approach to geometric optimisation of railway catenaries

[EN] The quality of current collection becomes a limiting factor when the aim is to increase the speed of the present railway systems. In this work an attempt is made to improve current collection quality optimising catenary geometry by means of a genetic algorithm (GA). As contact wire height and dropper spacing are thought to be highly influential parameters, they are chosen as the optimisation variables. The results obtained show that a GA can be used to optimise catenary geometry to improve current collection quality measured in terms of the standard deviation of the contact force. Furthermore, it is highlighted that apart from the usual pre-sag, other geometric parameters should also be taken into account when designing railway catenaries.The authors would like to acknowledge the financial support received from the FPU program offered by the Ministerio de Educación, Cultura y Deporte (MECD), under grant number [FPU13/04191], and also the funding provided by the Generalitat Valenciana [PROMETEO/2016/007].Gregori Verdú, S.; Tur Valiente, M.; Nadal, E.; Fuenmayor Fernández, F. (2017). An approach to geometric optimisation of railway catenaries. Vehicle System Dynamics. 1-25. https://doi.org/10.1080/00423114.2017.1407434S125Nåvik, P., Rønnquist, A., & Stichel, S. (2015). The use of dynamic response to evaluate and improve the optimization of existing soft railway catenary systems for higher speeds. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 230(4), 1388-1396. doi:10.1177/0954409715605140Harèll, P., Drugge, L., & Reijm, M. (2005). Study of Critical Sections in Catenary Systems During Multiple Pantograph Operation. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 219(4), 203-211. doi:10.1243/095440905x8934Bruni, S., Ambrosio, J., Carnicero, A., Cho, Y. H., Finner, L., Ikeda, M., … Zhang, W. (2014). The results of the pantograph–catenary interaction benchmark. Vehicle System Dynamics, 53(3), 412-435. doi:10.1080/00423114.2014.953183Shabana, A. A. (1998). Nonlinear Dynamics, 16(3), 293-306. doi:10.1023/a:1008072517368Zhou, N., & Zhang, W. (2011). Investigation on dynamic performance and parameter optimization design of pantograph and catenary system. Finite Elements in Analysis and Design, 47(3), 288-295. doi:10.1016/j.finel.2010.10.008Kim, J.-W., & Yu, S.-N. (2013). Design variable optimization for pantograph system of high-speed train using robust design technique. International Journal of Precision Engineering and Manufacturing, 14(2), 267-273. doi:10.1007/s12541-013-0037-7Ambrósio, J., Pombo, J., & Pereira, M. (2013). Optimization of high-speed railway pantographs for improving pantograph-catenary contact. Theoretical and Applied Mechanics Letters, 3(1), 013006. doi:10.1063/2.1301306Lee, J.-H., Kim, Y.-G., Paik, J.-S., & Park, T.-W. (2012). Performance evaluation and design optimization using differential evolutionary algorithm of the pantograph for the high-speed train. Journal of Mechanical Science and Technology, 26(10), 3253-3260. doi:10.1007/s12206-012-0833-5Massat, J.-P., Laurent, C., Bianchi, J.-P., & Balmès, E. (2014). Pantograph catenary dynamic optimisation based on advanced multibody and finite element co-simulation tools. Vehicle System Dynamics, 52(sup1), 338-354. doi:10.1080/00423114.2014.898780Cho, Y. H., Lee, K., Park, Y., Kang, B., & Kim, K. (2010). Influence of contact wire pre-sag on the dynamics of pantograph–railway catenary. International Journal of Mechanical Sciences, 52(11), 1471-1490. doi:10.1016/j.ijmecsci.2010.04.002Zhang, W., Mei, G., & Zeng, J. (2002). A Study of Pantograph/Catenary System Dynamics with Influence of Presag and Irregularity of Contact Wire. Vehicle System Dynamics, 37(sup1), 593-604. doi:10.1080/00423114.2002.11666265Koziel, S., & Yang, X.-S. (Eds.). (2011). Computational Optimization, Methods and Algorithms. Studies in Computational Intelligence. doi:10.1007/978-3-642-20859-1Hare, W., Nutini, J., & Tesfamariam, S. (2013). A survey of non-gradient optimization methods in structural engineering. Advances in Engineering Software, 59, 19-28. doi:10.1016/j.advengsoft.2013.03.001Tur, M., Baeza, L., Fuenmayor, F. J., & García, E. (2014). PACDIN statement of methods. Vehicle System Dynamics, 53(3), 402-411. doi:10.1080/00423114.2014.963126Tur, M., García, E., Baeza, L., & Fuenmayor, F. J. (2014). A 3D absolute nodal coordinate finite element model to compute the initial configuration of a railway catenary. Engineering Structures, 71, 234-243. doi:10.1016/j.engstruct.2014.04.015Gregori, S., Tur, M., Nadal, E., Aguado, J. V., Fuenmayor, F. J., & Chinesta, F. (2017). Fast simulation of the pantograph–catenary dynamic interaction. Finite Elements in Analysis and Design, 129, 1-13. doi:10.1016/j.finel.2017.01.007Gerstmayr, J., & Shabana, A. A. (2006). Analysis of Thin Beams and Cables Using the Absolute Nodal Co-ordinate Formulation. Nonlinear Dynamics, 45(1-2), 109-130. doi:10.1007/s11071-006-1856-1Collina, A., & Bruni, S. (2002). Numerical Simulation of Pantograph-Overhead Equipment Interaction. Vehicle System Dynamics, 38(4), 261-291. doi:10.1076/vesd.38.4.261.8286Ambrósio, J., Pombo, J., Antunes, P., & Pereira, M. (2014). PantoCat statement of method. Vehicle System Dynamics, 53(3), 314-328. doi:10.1080/00423114.2014.969283Nåvik, P., Rønnquist, A., & Stichel, S. (2017). Variation in predicting pantograph–catenary interaction contact forces, numerical simulations and field measurements. Vehicle System Dynamics, 55(9), 1265-1282. doi:10.1080/00423114.2017.130852

On the use of stabilization techniques in the Cartesian grid finite element method framework for iterative solvers

"This is the peer reviewed version of the following article: Navarro-Jiménez, José Manuel, Enrique Nadal, Manuel Tur, José Martínez-Casas, and Juan José Ródenas. 2020. "On the Use of Stabilization Techniques in the Cartesian Grid Finite Element Method Framework for Iterative Solvers." International Journal for Numerical Methods in Engineering 121 (13). Wiley: 3004-20. doi:10.1002/nme.6344, which has been published in final form at https://doi.org/10.1002/nme.6344. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving."[EN] Fictitious domain methods, like the Cartesian grid finite element method (cgFEM), are based on the use of unfitted meshes that must be intersected. This may yield to ill-conditioned systems of equations since the stiffness associated with a node could be small, thus poorly contributing to the energy of the problem. This issue complicates the use of iterative solvers for large problems. In this work, we present a new stabilization technique that, in the case of cgFEM, preserves the Cartesian structure of the mesh. The formulation consists in penalizing the free movement of those nodes by a smooth extension of the solution from the interior of the domain, through a postprocess of the solution via a displacement recovery technique. The numerical results show an improvement of the condition number and a decrease in the number of iterations of the iterative solver while preserving the problem accuracy.The authors wish to thank the Spanish "Ministerio de Economía y Competitividad," the "Generalitat Valenciana," and the "Universitat Politècnica de València" for their financial support received through the projects DPI2017-89816-R, Prometeo 2016/007 and the FPI2015 program, respectively.Navarro-Jiménez, J.; Nadal, E.; Tur Valiente, M.; Martínez Casas, J.; Ródenas, JJ. (2020). On the use of stabilization techniques in the Cartesian grid finite element method framework for iterative solvers. International Journal for Numerical Methods in Engineering. 121(13):3004-3020. https://doi.org/10.1002/nme.6344S3004302012113Burman, E., & Hansbo, P. (2010). Fictitious domain finite element methods using cut elements: I. A stabilized Lagrange multiplier method. Computer Methods in Applied Mechanics and Engineering, 199(41-44), 2680-2686. doi:10.1016/j.cma.2010.05.011Ruiz-Gironés, E., & Sarrate, J. (2010). Generation of structured hexahedral meshes in volumes with holes. Finite Elements in Analysis and Design, 46(10), 792-804. doi:10.1016/j.finel.2010.04.005Geuzaine, C., & Remacle, J.-F. (2009). Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities. International Journal for Numerical Methods in Engineering, 79(11), 1309-1331. doi:10.1002/nme.2579Parvizian, J., Düster, A., & Rank, E. (2007). Finite cell method. Computational Mechanics, 41(1), 121-133. doi:10.1007/s00466-007-0173-yDüster, A., Parvizian, J., Yang, Z., & Rank, E. (2008). The finite cell method for three-dimensional problems of solid mechanics. Computer Methods in Applied Mechanics and Engineering, 197(45-48), 3768-3782. doi:10.1016/j.cma.2008.02.036Nadal, E., Ródenas, J. J., Albelda, J., Tur, M., Tarancón, J. E., & Fuenmayor, F. J. (2013). Efficient Finite Element Methodology Based on Cartesian Grids: Application to Structural Shape Optimization. Abstract and Applied Analysis, 2013, 1-19. doi:10.1155/2013/953786Nadal, E., Ródenas, J. J., Sánchez-Orgaz, E. M., López-Real, S., & Martí-Pellicer, J. (2014). Sobre la utilización de códigos de elementos finitos basados en mallados cartesianos en optimización estructural. Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería, 30(3), 155-165. doi:10.1016/j.rimni.2013.04.009Giovannelli, L., Ródenas, J. J., Navarro-Jiménez, J. M., & Tur, M. (2017). Direct medical image-based Finite Element modelling for patient-specific simulation of future implants. Finite Elements in Analysis and Design, 136, 37-57. doi:10.1016/j.finel.2017.07.010Schillinger, D., & Ruess, M. (2014). The Finite Cell Method: A Review in the Context of Higher-Order Structural Analysis of CAD and Image-Based Geometric Models. Archives of Computational Methods in Engineering, 22(3), 391-455. doi:10.1007/s11831-014-9115-yBurman, E., Claus, S., Hansbo, P., Larson, M. G., & Massing, A. (2014). CutFEM: Discretizing geometry and partial differential equations. International Journal for Numerical Methods in Engineering, 104(7), 472-501. doi:10.1002/nme.4823Tur, M., Albelda, J., Marco, O., & Ródenas, J. J. (2015). Stabilized method of imposing Dirichlet boundary conditions using a recovered stress field. Computer Methods in Applied Mechanics and Engineering, 296, 352-375. doi:10.1016/j.cma.2015.08.001Tur, M., Albelda, J., Nadal, E., & Ródenas, J. J. (2014). Imposing Dirichlet boundary conditions in hierarchical Cartesian meshes by means of stabilized Lagrange multipliers. International Journal for Numerical Methods in Engineering, 98(6), 399-417. doi:10.1002/nme.4629De Prenter, F., Verhoosel, C. V., van Zwieten, G. J., & van Brummelen, E. H. (2017). Condition number analysis and preconditioning of the finite cell method. Computer Methods in Applied Mechanics and Engineering, 316, 297-327. doi:10.1016/j.cma.2016.07.006Berger-Vergiat, L., Waisman, H., Hiriyur, B., Tuminaro, R., & Keyes, D. (2011). Inexact Schwarz-algebraic multigrid preconditioners for crack problems modeled by extended finite element methods. International Journal for Numerical Methods in Engineering, 90(3), 311-328. doi:10.1002/nme.3318Menk, A., & Bordas, S. P. A. (2010). A robust preconditioning technique for the extended finite element method. 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An extension of shape sensitivity analysis to an immersed boundary method based on Cartesian grids

[EN] Gradient-based shape optimization processes of mechanical components require the gradients (sensitivity) of the magnitudes of interest to be calculated with sufficient accuracy. The aim of this study was to develop algorithms for the calculation of shape sensitivities considering geometric representation by parametric surfaces (i.e. NURBS or T-splines) using 3D Cartesian h-adapted meshes independent of geometry. A formulation of shape sensitivities was developed for an environment based on Cartesian meshes independent of geometry, which implies, for instance, the need to take into account the special treatment of boundary conditions imposed in non body-fitted meshes. The immersed boundary framework required to implement new methods of velocity field generation, which have a primary role in the integration of both the theoretical concepts and the discretization tools in shape design optimization. Examples of elastic problems with three-dimensional components are given to demonstrate the efficiency of the algorithms.The authors wish to thank the Spanish Ministerio de Economia y Competitividad for the financial support received through the project DPI2013-46317-R and the FPI program (BES-2011-044080), and the Generalitat Valenciana through the Project PROMETEO/2016/007.Marco, O.; Ródenas, JJ.; Fuenmayor Fernández, F.; Tur Valiente, M. (2018). An extension of shape sensitivity analysis to an immersed boundary method based on Cartesian grids. Computational Mechanics. 62(4):701-723. https://doi.org/10.1007/s00466-017-1522-0S701723624Abel JF, Shephard MS (1979) An algorithm for multipoint constraints in finite element analysis. Int J Numer Methods Eng 14(3):464–467Akgün MA, Garcelon GH, Haftka RT (2001) Fast exact linear and nonlinear structural reanalysis and the sherman-morrison-woodbury formulas. 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Structural simulation of 2D aluminium foam images by the use ofhomogenization and machine learning techniques

[EN] The use of resistant, rigid, low-weight materials with good both acoustic and thermal properties is very interesting intoday¿s industry. Among these materials, one can find aluminium foams, whose mechanical behaviour is necessaryfor their application. In order to obtain the geometry of an aluminium foam, several techniques can be applied, and allof them are based in the fact that information is initially obtained by a Computed Axial Tomography (CAT). One ofthese techniques, known as segmentation, involves a CAD being generated from an image in order to build the FiniteElement (FE) model. Another option is to use techniques such as CutFEM or cgFEM, in which a certain amount ofpixels, which define the properties of the material, are embedded in each element. Among the existing methods forevaluating the material properties matrix, this study proposes the use of homogenization techniques, sped up by the useof machine learning techniques. This method has been applied to real problems obtaining a high speed up, conservingprecision.[ES] En la industria actual, el uso de materiales resistentes, rígidos, de bajo peso y con buenas propiedades tanto acústicas como térmicas es de gran interés. Entre estos materiales encontramos las espumas de aluminio. Para su uso, es necesario conocer su comportamiento estructural. Para la obtención de la geometría de una espuma de aluminio se pueden plantear diversas técnicas, todas ellas basadas en que la información inicial proviene de una imagen obtenida mediante una Tomografía Axial Computarizada (TAC). Una posible metodología, conocida comúnmente como segmentación, consiste en generar un CAD a partir de la imagen y de ahí el modelo de Elementos Finitos (EF). Otra opción es usar técnicas como el CellFEM o el cgFEM, donde cierta cantidad de píxeles, que definen las propiedades del material, son embebidos en cada elemento. De entre los diversos métodos que existen para evaluar la matriz de propiedades del material, en este trabajo se propone el uso de técnicas de homogeneización aceleradas mediante técnicas de machine learning. Dicha técnica se ha aplicado a problemas reales obteniendo un elevado speed up sin sacrificar la precisión.Los autores agradecen la ayuda recibida por el Ministerio de Economía y Competitividad a través del proyecto DPI2013-46317-R así como el apoyo recibido por la Generalitat Valenciana mediante el proyecto Prometeo/2016/007.Ferrándiz-Catalá, B.; Tur Valiente, M.; Nadal, E. (2018). Simulación estructural de espumas de aluminio a partir de imágenes 2D mediante la combinación de técnicas de homogeneización y machine learning. Revista UIS Ingenierías. 17(2):223-240. https://doi.org/10.18273/revuin.v17n2-2018020S22324017