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. Computational Mechanics. 62(4):853-870. https://doi.org/10.1007/s00466-017-1533-xS853870624ANSYS$$^{\textregistered }$$® Academic Research Mechanical, Release 16.2Alart P, Curnier A (1991) A mixed formulation for frictional contact problems prone to Newton like solution methods. Comput Methods Appl Mech Eng 92(3):353–375. https://doi.org/10.1016/0045-7825(91)90022-XAnnavarapu C, Hautefeuille M, Dolbow JE (2012) Stable imposition of stiff constraints in explicit dynamics for embedded finite element methods. Int J Numer Methods Eng 92(June):206–228. https://doi.org/10.1002/nme.4343Annavarapu C, Hautefeuille M, Dolbow JE (2014) A Nitsche stabilized finite element method for frictional sliding on embedded interfaces. Part I: single interface. Comput Methods Appl Mech Eng 268:417–436. https://doi.org/10.1016/j.cma.2013.09.002Annavarapu C, Settgast RR, Johnson SM, Fu P, Herbold EB (2015) A weighted nitsche stabilized method for small-sliding contact on frictional surfaces. Comput Methods Appl Mech Eng 283:763–781. https://doi.org/10.1016/j.cma.2014.09.030Baiges J, Codina R, Henke F, Shahmiri S, Wall WA (2012) A symmetric method for weakly imposing Dirichlet boundary conditions in embedded finite element meshes. Int J Numer Methods Eng 90(5):636–658. https://doi.org/10.1002/nme.3339Béchet É, Moës N, Wohlmuth B (2009) A stable Lagrange multiplier space for stiff interface conditions within the extended finite element method. Int J Numer Methods Eng 78(8):931–954. https://doi.org/10.1002/nme.2515Béchet E, Moës N, Wohlmuth B (2009) A stable Lagrange multiplier space for stiff interface conditions within the extended finite element method. Int J Numer Methods Eng 78:931–954. https://doi.org/10.1002/nme.2515Belgacem F, Hild P, Laborde P (1998) The mortar finite element method for contact problems. 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. Comput Methods Appl Mech Eng 194(39–41):4135–4195. https://doi.org/10.1016/j.cma.2004.10.008Laursen T (2003) Computational contact and impact mechanics: fundamentals of modelling interfacial phenomena in nonlinear finite element analysis. Springer, BerlinLiu F, Borja RI (2008) A contact algorithm for frictional crack propagation with the extended finite element method. Int J Numer Methods Eng 76(June):1489–1512. https://doi.org/10.1002/nme.2376Liu F, Borja RI (2010) Stabilized low-order finite elements for frictional contact with the extended finite element method. Comput Methods Appl Mech Eng 199(37–40):2456–2471. https://doi.org/10.1016/j.cma.2010.03.030Marco O, Sevilla R, Zhang Y, Ródenas JJ, Tur M (2015) Exact 3D boundary representation in finite element analysis based on Cartesian grids independent of the geometry. Int J Numer Methods Eng 103(6):445–468. https://doi.org/10.1002/nme.4914Nadal E, Ródenas JJ, Albelda J, Tur M, Tarancón JE, Fuenmayor FJ (2013) Efficient finite element methodology based on cartesian grids: application to structural shape optimization. Abstr Appl Anal 2013:1–19. https://doi.org/10.1155/2013/953786Neto D, Oliveira M, Menezes L, Alves J (2016) A contact smoothing method for arbitrary surface meshes using nagata patches. Comput Methods Appl Mech Eng 299:283–315. https://doi.org/10.1016/j.cma.2015.11.011Nistor I, Guiton MLE, Massin P, Moës N, Géniaut S (2009) An X-FEM approach for large sliding contact along discontinuities. Int J Numer Methods Eng 78:1407–1435. https://doi.org/10.1002/nme.2532Oliver J, Hartmann S, Cante JC, Weyler R, Hernández JA (2009) A contact domain method for large deformation frictional contact problems. Part 1: theoretical basis. Comput Methods Appl Mech Eng 198:2591–2606. https://doi.org/10.1016/j.cma.2009.03.006Piegl L, Tiller W (1995) The NURBS Book. Springer, BerlinPietrzak G, Curnier A (1999) Large deformation frictional contact mechanics: continuum formulation and augmented Lagrangian treatment. Comput Methods Appl Mech Eng 177(3–4):351–381. https://doi.org/10.1016/S0045-7825(98)00388-0Poulios K, Renard Y (2015) An unconstrained integral approximation of large sliding frictional contact between deformable solids. Comput Struct 153:75–90. https://doi.org/10.1016/j.compstruc.2015.02.027Puso MA, Laursen TA (2004) A mortar segment-to-segment frictional contact method for large deformations. Comput Methods Appl Mech Eng 193(45–47):4891–4913. https://doi.org/10.1016/j.cma.2004.06.001Renard Y (2013) Generalized Newton’s methods for the approximation and resolution of frictional contact problems in elasticity. Comput Methods Appl Mech Eng 256:38–55. https://doi.org/10.1016/j.cma.2012.12.008Ribeaucourt R, Baietto-Dubourg MC, Gravouil A (2007) A new fatigue frictional contact crack propagation model with the coupled X-FEM/LATIN method. Comput Methods Appl Mech Eng 196:3230–3247. https://doi.org/10.1016/j.cma.2007.03.004Ródenas JJ, Tur M, Fuenmayor FJ, Vercher A (2007) Improvement of the superconvergent patch recovery technique by the use of constraint equations: The SPR-C technique. Int J Numer Methods Eng 70:705–727. https://doi.org/10.1002/nme.1903Rogers DF (2001) An introduction to NURBS: with historical perspective. Elsevier, AmsterdamTemizer I, Wriggers P, Hughes TJR (2012) Three-dimensional mortar-based frictional contact treatment in isogeometric analysis with NURBS. Comput Methods Appl Mech Eng 209–212:115–128. https://doi.org/10.1016/j.cma.2011.10.014Tur M, Albelda J, Marco O, Ródenas JJ (2015) Stabilized method of imposing Dirichlet boundary conditions using a recovered stress field. Comput Methods Appl Mech Eng 296:352–375. https://doi.org/10.1016/j.cma.2015.08.001Tur M, Albelda J, Navarro-Jimenez JM, Rodenas JJ (2015) A modified perturbed Lagrangian formulation for contact problems. Comput Mech. https://doi.org/10.1007/s00466-015-1133-6Tur M, Fuenmayor FJ, Wriggers P (2009) A mortar-based frictional contact formulation for large deformations using Lagrange multipliers. Comput Methods Appl Mech Eng 198(37–40):2860–2873. https://doi.org/10.1016/j.cma.2009.04.007Tur M, Giner E, Fuenmayor F, Wriggers P (2012) 2d contact smooth formulation based on the mortar method. Comput Methods Appl Mech Eng 247–248:1–14. https://doi.org/10.1016/j.cma.2012.08.002Wriggers P (2006) Computational contact mechanics. Springer, BerlinWriggers P (2008) Nonlinear finite element methods. Springer, Berlin. https://doi.org/10.1007/978-3-540-71001-1Yang B, Laursen TA, Meng X (2005) Two dimensional mortar contact methods for large deformation frictional sliding. Int J Numer Methods Eng 62(9):1183–1225. https://doi.org/10.1002/nme.1222Zienkiewicz OC, Zhu JZ (1992) The superconvergent patch recovery and a posteriori error estimates. Part 1: the recovery technique. Int J Numer Methods. https://doi.org/10.1002/nme.162033070

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-

Imposing Dirichlet boundary conditions in hierarchical Cartesian meshes by means of stabilized Lagrange multipliers

This is the pre-peer reviewed version of the following article: Tur, M., Albelda, J., Nadal, E. and Ródenas, J. J. (2014), Imposing Dirichlet boundary conditions in hierarchical Cartesian meshes by means of stabilized Lagrange multipliers. Int. J. Numer. Meth. Engng, 98: 399–417, which has been published in final form at http://dx.doi.org/10.1002/nme.4629 . This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.[EN] The use of Cartesian meshes independent of the geometry has some advantages over the traditional meshes used in the finite element method. The main advantage is that their use together with an appropriate hierarchical data structure reduces the computational cost of the finite element analysis. This improvement is based on the substitution of the traditional mesh generation process by an optimized procedure for intersecting the Cartesian mesh with the boundary of the domain and the use efficient solvers based on the hierarchical data structure. One major difficulty associated to the use of Cartesian grids is the fact that the mesh nodes do not, in general, lie over the boundary of the domain, increasing the difficulty to impose Dirichlet boundary conditions. In this paper, Dirichlet boundary conditions are imposed by means of the Lagrange multipliers technique. A new functional has been added to the initial formulation of the problem that has the effect of stabilizing the problem. The technique here presented allows for a simple definition of the Lagrange multipliers field that even allow us to directly condense the degrees of freedom of the Lagrange multipliers at element level.The authors acknowledge the financial support received from the research project DPI2010-20542 of the Ministerio de Economia y Competitividad. Also, we appreciated the financial support of the FPU program (AP2008-01086) of the Universitat Politecnica de Valencia and the Generalitat Valenciana (PROMETEO/2012/023). The authors are also grateful for the support of the Framework Program 7 Initial Training Network Funding under grant number 289361 'Integrating Numerical Simulation and Geometric Design Technology (INSIST)'.Tur Valiente, M.; Albelda Vitoria, J.; Nadal Soriano, E.; Ródenas García, JJ. (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. https://doi.org/10.1002/nme.462939941798

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. International Journal for Numerical Methods in Engineering, 85(13), 1609-1632. doi:10.1002/nme.3032Dauge, M., Düster, A., & Rank, E. (2015). Theoretical and Numerical Investigation of the Finite Cell Method. Journal of Scientific Computing, 65(3), 1039-1064. doi:10.1007/s10915-015-9997-3Elfverson, D., Larson, M. G., & Larsson, K. (2018). CutIGA with basis function removal. Advanced Modeling and Simulation in Engineering Sciences, 5(1). doi:10.1186/s40323-018-0099-2Verhoosel, C. V., van Zwieten, G. J., van Rietbergen, B., & de Borst, R. (2015). Image-based goal-oriented adaptive isogeometric analysis with application to the micro-mechanical modeling of trabecular bone. Computer Methods in Applied Mechanics and Engineering, 284, 138-164. doi:10.1016/j.cma.2014.07.009Burman, E. (2010). Ghost penalty. Comptes Rendus Mathematique, 348(21-22), 1217-1220. doi:10.1016/j.crma.2010.10.006BadiaS VerdugoF MartínAF. The aggregated unfitted finite element method for elliptic problems;2017.Jomo, J. N., de Prenter, F., Elhaddad, M., D’Angella, D., Verhoosel, C. V., Kollmannsberger, S., … Rank, E. (2019). Robust and parallel scalable iterative solutions for large-scale finite cell analyses. Finite Elements in Analysis and Design, 163, 14-30. doi:10.1016/j.finel.2019.01.009Béchet, É., Moës, N., & Wohlmuth, B. (2008). A stable Lagrange multiplier space for stiff interface conditions within the extended finite element method. International Journal for Numerical Methods in Engineering, 78(8), 931-954. doi:10.1002/nme.2515Hautefeuille, M., Annavarapu, C., & Dolbow, J. E. (2011). Robust imposition of Dirichlet boundary conditions on embedded surfaces. International Journal for Numerical Methods in Engineering, 90(1), 40-64. doi:10.1002/nme.3306Hansbo, P., Lovadina, C., Perugia, I., & Sangalli, G. (2005). A Lagrange multiplier method for the finite element solution of elliptic interface problems using non-matching meshes. Numerische Mathematik, 100(1), 91-115. doi:10.1007/s00211-005-0587-4Burman, E., & Hansbo, P. (2012). Fictitious domain finite element methods using cut elements: II. A stabilized Nitsche method. Applied Numerical Mathematics, 62(4), 328-341. doi:10.1016/j.apnum.2011.01.008Gerstenberger, A., & Wall, W. A. (2008). An eXtended Finite Element Method/Lagrange multiplier based approach for fluid–structure interaction. Computer Methods in Applied Mechanics and Engineering, 197(19-20), 1699-1714. doi:10.1016/j.cma.2007.07.002AxelssonO. Iterative solution methods;1994.Stenberg, R. (1995). On some techniques for approximating boundary conditions in the finite element method. Journal of Computational and Applied Mathematics, 63(1-3), 139-148. doi:10.1016/0377-0427(95)00057-7Zienkiewicz, O. C., & Zhu, J. Z. (1987). A simple error estimator and adaptive procedure for practical engineerng analysis. International Journal for Numerical Methods in Engineering, 24(2), 337-357. doi:10.1002/nme.1620240206Zienkiewicz, O. C., & Zhu, J. Z. (1992). The superconvergent patch recovery anda posteriori error estimates. Part 1: The recovery technique. International Journal for Numerical Methods in Engineering, 33(7), 1331-1364. doi:10.1002/nme.1620330702Blacker, 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.1837Xiao, Q. Z., & Karihaloo, B. L. (s. f.). Statically Admissible Stress Recovery using the Moving Least Squares Technique. Progress in Computational Structures Technology, 111-138. doi:10.4203/csets.11.5Ródenas, 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.1903Zhang, Z. (2001). Advances in Computational Mathematics, 15(1/4), 363-374. doi:10.1023/a:1014221409940González-Estrada, O. A., Nadal, E., Ródenas, J. J., Kerfriden, P., Bordas, S. P. A., & Fuenmayor, F. J. (2013). Mesh adaptivity driven by goal-oriented locally equilibrated superconvergent patch recovery. Computational Mechanics, 53(5), 957-976. doi:10.1007/s00466-013-0942-8Nadal, 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.2015.01.013ZienkiewiczOC TaylorRL. The finite element method fifth edition volume 1: the basis.MA:Butterworth‐Heinemann;2000.Brenner, S. C., & Scott, L. R. (1994). The Mathematical Theory of Finite Element Methods. Texts in Applied Mathematics. doi:10.1007/978-1-4757-4338-

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. Int J Numer Methods Eng 50(7):1587–1606Arora JS (1993) An exposition of the material derivative approach for structural shape sensitivity analysis. Comput Methods Appl Mech Eng 105(1):41–62Arora JS, Lee TH, Cardoso JB (1992) Structural shape sensitivity analysis: relationship between material derivative and control volume approaches. AIAA J 30(6):1638–1648Belegundu D, Zhang S, Manicka Y, Salagame R (1991) The natural approach for shape optimization with mesh distortion control. Technical report. Penn State University, State CollegeBennett JA, Botkin ME (1985) Structural shape optimization with geometric problem description and adaptive mesh refinement. AIAA J 23(3):459–464Bischof C, Carle A, Khademi P, Mauer A (1996) The adifor 2.0 system for the automatic differentiation of fortran 77 programs. IEEE Comput Sci Eng 3(3):18–32Braibant V, Fleury C (1984) Shape optimal design using b-splines. Comput Methods Appl Mech Eng 44(3):247–267Bugeda G, Oliver J (1993) A general methodology for structural shape optimization problems using automatic adaptive remeshing. Int J Numer Methods Eng 36(18):3161–3185Cho S, Ha SH (2009) Isogeometric shape design optimization: exact geometry and enhanced sensitivity. Struct Multidiscip Optim 38(1):53–70Choi K, Kim N (2005) Structural sensitivity analysis and optimization, mechanical engineering series, vol 1. Springer, Berlin, HeidelbergChoi KK, Chang KH (1994) A study of design velocity field computation for shape optimal design. Finite Elem Anal Des 15(4):317–341Choi KK, Duan W (2000) Design sensitivity analysis and shape optimization of structural components with hyperelastic material. Comput Methods Appl Mech Eng 187(1–2):219–243Choi KK, Twu SL (1989) Equivalence of continuum and discrete methods of shape design sensitivity analysis. AIAA J 27(10):1419–1424Choi MJ, Cho S (2014) Isogeometric shape design sensitivity analysis of stress intensity factors for curved crack problems. Comput Methods Appl Mech Eng 279:469–496Chowdhury MS, Song C, Gao W (2014) Shape sensitivity analysis of stress intensity factors by the scaled boundary finite element method. Eng Fract Mech 116:13–30Doctor LJ, Torborg JG (1981) Display techniques for octree-encoded objects. IEEE Comput Graph Appl 1(3):29–38El-Sayed MEM, Zumwalt KW (1991) Efficient design sensitivity derivatives for multi-load case structures as an integrated part of finite element analysis. Comput Struct 40(6):1461–1467Escobar JM, Montenegro R, Rodríguez E, Cascón JM (2014) The meccano method for isogeometric solid modeling and applications. Eng Comput 30(3):331–343Farhat C, Lacour C, Rixen D (1998) Incorporation of linear multipoint constraints in substructure based iterative solvers. Part 1: a numerically scalable algorithm. Int J Numer Methods Eng 43(6):997–1016Fuenmayor FJ, Domínguez J, Giner E, Oliver JL (1997) Calculation of the stress intensity factor and estimation of its error by a shape sensitivity analysis. Fatigue Fract Eng Mater Struct 20(5):813–828Fuenmayor FJ, Oliver JL, Ródenas JJ (1997) Extension of the Zienkiewicz-Zhu error estimator to shape sensitivity analysis. Int J Numer Methods Eng 40(8):1413–1433Gil AJ, Arranz-Carreño A, Bonet J, Hassan O (2010) The immersed structural potential method for haemodynamic applications. J Comput Phys 229(22):8613–8641Giner E, Fuenmayor FJ, Besa AJ, Tur M (2002) An implementation of the stiffness derivative method as a discrete analytical sensitivity analysis and its application to mixed mode in LEFM. Eng Fract Mech 69(18):2051–2071Griewank A, Juedes D, Utke J (1996) ADOL-C, a package for the automatic differentiation of algorithms written in C/C++. ACM Trans Math Softw (TOMS) 22(2):131–167Ha SH, Choi K, Cho S (2010) Numerical method for shape optimization using T-spline based isogeometric method. Struct Multidiscip Optim 42(3):417–428Haftka RT (1993) Semi-analytical static nonlinear structural sensitivity analysis. AIAA J 31(7):1307–1312Haftka RT, Adelman H (1989) Recent developments in structural sensitivity analysis. Struct Optim 1(3):137–151Haftka RT, Barthelemy B (1989) Discretization methods and structural optimization—procedures and applications. In: Proceedings of a GAMM-Seminar October 5–7, 1988, Siegen, FRG, Springer, Berlin, Heidelberg, chap On the Accuracy of shape sensitivity derivatives, pp 136–144Haslinger J, Jedelsky D (1996) Genetic algorithms and fictitious domain based approaches in shape optimization. Struc Optim 12:257–264Hughes TJR, Cottrell JA, Bazilevs Y (2005) Isogeometric analysis: CAD, finite elements, NURBS, exact geometry, and mesh refinement. Comput Methods Appl Mech Eng 194:4135–4195Iman MH (1982) Three-dimensional shape optimization. Int J Numer Methods Eng 18(5):661–673Jackins CL, Tanimoto SL (1980) Oct-tree and their use in representing three-dimensional objects. Comput Graph Image Process 14(3):249–270Kanninen MF, Popelar CH (1985) Advanced fracture mechanics. Oxford Engineering Science Series. Oxford University Press, Oxfordvan Keulen F, Haftka R, Kim N (2005) Review of options for structural design sensitivity analysis. Part I: linear systems. Comput Methods Appl Mech Eng 194(30–33):3213–3243Kibsgaard S (1992) Sensitivity analysis-the basis for optimization. Int J Numer Methods Eng 34(3):901–932Kiendl J, Schmidt R, Wüchner R, Bletzinger KU (2014) Isogeometric shape optimization of shells using semi-analytical sensitivity analysis and sensitivity weighting. Comput Methods Appl Mech Eng 274:148–167Kirsch U (2002) Design-oriented analysis: a unified approach. Springer Netherlands, DordrechtKunisch K, Peichl G (1996) Numerical gradients for shape optimization based on embedding domain techniques. Comput Optim 18:95–114Lee BY (1996) Consideration of body forces in axisymmetric design sensitivity analysis using the bem. Comput Struct 61(4):587–596Lee BY (1997) Direct differentiation formulation for boundary element shape sensitivity analysis of axisymmetric elastic solids. Int J Solids Struct 34(1):99–112Li FZ, Shih CF, Needleman A (1985) A comparison of methods for calculating energy release rates. Eng Fract Mech 21(2):405–421Li K, Qian X (2011) Isogeometric analysis and shape optimization via boundary integral. Comput Aided Des 43(11):1427–1437Lian H, Bordas SPA, Sevilla R, Simpson RN (2012) Recent developments in the integration of computer aided design and analysis. Comput Technol Rev 6:1–36Lian H, Kerfriden P, Bordas SPA (2016) Implementation of regularized isogeometric boundary element methods for gradient-based shape optimization in two-dimensional linear elasticity. Int J Numer Methods Eng 106(12):972–1017Liu L, Zhang Y, Hughes TJR, Scott MA, Sederberg TW (2014) Volumetric T-spline construction using boolean operations. Eng Comput 30(4):425–439Liu WK, Tang S (2007) Mathematical foundations of the immersed finite element method. Comput Mech 39(3):211–222Liu WK, Liu Y, Darell D, Zhang L, Wang XS, Fukui Y, Patankar N, Zhang Y, Bajaj C, Lee J, Hong J, Chen X, Hsu H (2006) Immersed finite element method and its applications to biological systems. Comput Methods Appl Mech Eng 195(13):1722–1749Marco O, Sevilla R, Zhang Y, Ródenas JJ, Tur M (2015) Exact 3D boundary representation in finite element analysis based on Cartesian grids independent of the geometry. Int J Numer Methods Eng 103:445–468Marco O, Ródenas JJ, Navarro-Jiménez JM, Tur M (2017) Robust h-adaptive meshing strategy considering exact arbitrary CAD geometries in a Cartesian grid framework. Comput Struct 193:87–109Meagher D (1980) Octree encoding: a new technique for the representation, manipulation and display of arbitrary 3-D objects by computer. Tech. Rep. IPL-TR-80-11 I, Rensselaer Polytechnic InstituteMoita JS, Infanta J, Mota CM (2000) Sensitivity analysis and optimal design of geometrically non-linear laminated plates and shells. Comput Struct 76(1–3):407–420Nadal E (2014) Cartesian grid FEM (cgFEM): high performance h-adaptive FE analysis with efficient error control. Application to structural shape optimization. Ph.D. Thesis. Universitat Politècnica de ValènciaNadal E, Ródenas JJ, Albelda J, Tur M, Tarancón JE, Fuenmayor FJ (2013) Efficient finite element methodology based on cartesian grids: application to structural shape optimization. Abstract and Applied Analysis 2013Navarrina F, López-Fontán S, Colominas I, Bendito E, Casteleiro M (2000) High order shape design sensitivities: a unified approach. Comput Methods Appl Mech Eng 188(4):681–696Neittaanmäki P, Salmenjoki K (1989) Comparison of various techniques for shape design sensitivity analysis. In: Computer aided optimum design of structures: recent advances. Springer, Berlin, Heidelberg, pp 367–377Nguyen VP, Anitescu C, Bordas SPA, Rabczuk T (2015) Isogeometric analysis: an overview and computer implementation aspects. Math Comput Simul 117:89–116Ozaki I, Kimura F, Berz M (1995) Higher-order sensitivity analysis of finite element method by automatic differentiation. Comput Mech 16(4):223–234Pandey PC, Bakshi P (1999) Analytical response sensitivity computation using hybrid finite elements. Comput Struct 71(5):525–534Peskin CS (1977) Numerical analysis of blood flow in the heart. J Comput Phys 25:220–252Phelan DG, Haber RB (1989) Sensitivity analysis of linear elastic systems using domain parametrization and a mixed mutual energy principle. Comput Methods Appl Mech Eng 77(1–2):31–59Piegl L, Tiller W (1995) The NURBS book. Springer, New YorkPoldneff MJ, Rai IS, Arora JS (1993) Implementation of design sensitivity analysis for nonlinear structures. AIAA J 31(11):2137–2142Qian X (2010) Full analytical sensitivities in NURBS based isogeometric shape optimization. Comput Methods Appl Mech Eng 199(29–32):2059–2071Rice JR (1968) A path independent integral and the approximate analysis of strain concentration by notches and cracks. J Appl Mech 35(2):379–386Ródenas JJ (2001) Error de Discretización en el Cálculo de Sensibilidades mediante el Método de los Elementos Finitos. Ph.D. ThesisRódenas JJ, Fuenmayor FJ, Tarancón JE (2003) A numerical methodology to assess the quality of the design velocity field computation methods in shape sensitivity analysis. Int J Numer Methods Eng 59(13):1725–1747Rodenas JJ, Tur M, Fuenmayor FJ, Vercher A (2007) Improvement of the superconvergent patch recovery technique by the use of constraint equations: the SPR-C technique. Int J Numer Methods Eng 70(6):705–727Ródenas JJ, Bugeda G, Albelda J, Oñate E (2011) On the need for the use of error-controlled finite element analyses in structural shape optimization processes. Int J Numer Methods Eng 87(11):1105–1126Rogers DF (2001) An introduction to NURBS: with historical perspective. Elsevier, LondonSchramm U, Pilkey WW (1993) The coupling of geometric descriptions and finite elements using NURBs a study in shape optimization. Finite Elem Anal Des 15(1):11–34Sevilla R, Fernández-Méndez S, Huerta A (2011) 3D-NURBS-enhanced finite element method (NEFEM). Int J Numer Methods Eng 88(2):103–125Sevilla R, Fernández-Méndez S, Huerta A (2011) NURBS-enhanced finite element method (NEFEM): a seamless bridge between CAD and FEM. Arch Comput Methods Eng 18(4):441–484Shiriaev D, Griewank A (1996) ADOL-F: automatic differentiation of fortran codes. Comput Differ Tech Appl Tools (SIAM) 1:375–384Shivakumar KN, Raju IS (1992) An equivalent domain integral method for three-dimensional mixed-mode fracture problems. Eng Fract Mech 42(6):935–959Silva CAC, Bittencourt ML (2007) Velocity fields using NURBS with distortion control for structural shape optimization. Struct Multidiscip Optim 33(2):147–159Tur M, Albelda J, Nadal E, Ródenas JJ (2014) Imposing dirichlet boundary conditions in hierarchical cartesian meshes by means of stabilized lagrange multipliers. Int J Numer Methods Eng 98(6):399–417Tur M, Albelda J, Marco O, Ródenas JJ (2015) Stabilized method to impose dirichlet boundary conditions using a smooth stress field. Comput Methods Appl Mech Eng 296:352–375Wujek BA, Renaud JE (1998) Automatic differentiation for more efficient system analysis and optimization. Eng Optim 31(1):101–139Yang RJ, Fiedler MJ (1987) Design modelling for large-scale three-dimensional shape optimization problems. ASME Comput Eng 15:177–182Yoon BG, Belegundu AD (1988) Iterative methods for design sensitivity analysis. AIAA J 26(11):1413–1415Zhang L, Gerstenberger A, Wang X, Liu WK (2004) Immersed finite element method. Comput Methods Appl Mech Eng 293(21):2051–2067Zhang W, Beckers P (1989) Comparison of different sensitivity analysis approaches for structural shape optimization. In: Computer aided optimum design of structures: recent advances. Springer, Berlin, Heidelberg, pp 347–356Zhang Y, Wang W, Hughes TJR (2013) Conformal solid T-spline construction from boundary T-spline representations. Comput Mech 6(51):1051–1059Zienkiewicz OC, Zhu JZ (1987) A simple error estimator and adaptive procedure for practical engineering analysis. Int J Numer Methods Eng 24(2):337–357Zienkiewicz OC, Taylor RL, Zhu J (2013) The finite element method: its basis and fundamentals, 7th edn. Butterworth-Heinemann, Oxfor

Metodología jerárquica h-adaptativa basada en subdivisión de elementos

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 multi-point-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.Este artículo presenta una metodología h-adaptativa jerárquica para el análisis de elementos finitos basado en las relaciones jerárquicas entre los elementos padre e hijo que aparecen si estos elementos son geométricamente similares. Bajo esta condición de similitud, los términos implicados en la evaluación de las matrices de rigidez de elementos de los 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 h-adaptativa jerárquica basada en la subdivisión de elementos y el uso de restricciones multipunto para asegurar la continuidad C0. El uso de una estructura jerárquica de datos 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

Metodología jerárquica h-adaptativa basada en subdivisión de elementos

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 multi-point-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.Este artículo presenta una metodología h-adaptativa jerárquica para el análisis de elementos finitos basado en las relaciones jerárquicas entre los elementos padre e hijo que aparecen si estos elementos son geométricamente similares. Bajo esta condición de similitud, los términos implicados en la evaluación de las matrices de rigidez de elementos de los 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 h-adaptativa jerárquica basada en la subdivisión de elementos y el uso de restricciones multipunto para asegurar la continuidad C0. El uso de una estructura jerárquica de datos 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

Spatial Effects in Industrial Location Choices: Industry Characteristics and Urban Accessibility

In this paper we study how neighbourhood-related spillovers affect location choices of manufacturing firms at a local level. A spatial Dirichlet-multinomial regression model is applied to 90,000 new establishments of the Spanish Mediterranean Axis. Empirical findings show that spatial spillovers play an important role, together with traditional explanatory factors, in driving decisions of companies. Their size and scope depends on two main issues, the specific characteristics of the manufacturing industry the firm belongs to, and the accessibility of the urban environment where the firm is located

Use of a PBL-approach to develop and to assess generic competences in a Master's degree in Mechanical Engineering

[EN] This paper presents the work carried out within the framework of an educational innovation and improvement project developed during the last two years in the Master's Degree in Mechanical Engineering at the Technical University of Valencia (UPV). One of the main objectives of this project is the development and implementation of new methodologies for the evaluation of generic competences. Among these new methodologies, there is an approach through project-based learning, which allows for the incorporation of the assessment of some generic competences that was not done previously in a proper way. Therefore, several subjects have been coordinated, a new type of Master¿s Thesis has been proposed, with the collaboration of a company, and new assessment tools have been designed.The authors acknowledge the financial contribution by the Universitat Politècnica de València through the project PIME/2018/DPTO.IMM.Carballeira, J.; Tur Valiente, M.; Besa Gonzálvez, AJ.; Albelda Vitoria, J.; Tarancón Caro, JE.; Martínez Casas, J.; Denia Guzmán, FD.... (2020). Use of a PBL-approach to develop and to assess generic competences in a Master's degree in Mechanical Engineering. IATED Academy. 4913-4916. https://doi.org/10.21125/edulearn.2020.1286S4913491

Relaciones entre la gestión de recursos humanos en organizaciones de servicios y la satisfacción de los usuarios: el «efecto de desbordamiento»

En las organizaciones de servicios, la simultaneidad entre la prestación del servicio y su uso hace visible para los usuarios las prácticas de gestión de recursos humanos, ya que el usuario es capaz de evaluar in situ el comportamiento de los empleados de contacto y los obstáculos que éstos pueden encontrar en el desempeño de su trabajo. Por ello, se ha propuesto la existencia de un efecto de desbordamiento (spillover effect) de la gestión de recursos humanos en organizaciones de servicios sobre la satisfacción de los usuarios. La gestión de recursos humanos que subyace en el comportamiento de los empleados se extiende más allá de los límites de la organización, influyendo sobre las evaluaciones que realizan los clientes externos. Sin embargo, existen pocas investigaciones donde este efecto de desbordamiento se haya estudiado. El presente trabajo intenta llenar, al menos en parte, esta laguna. De hecho, se ponen a prueba empíricamente las relaciones entre la gestión de los recursos humanos (frecuencia de realización de tareas y obstáculos situacionales en la gestión) y la satisfacción de los usuarios. Para ello, se usa una muestra de 67 gerentes de organizaciones de servicios y otra de 1.070 usuarios. Los primeros valoraban la gestión de recursos humanos que se desarrolla en sus organizaciones, mientras que los segundos expresaban la satisfacción con el uso de esas mismas organizaciones de servicios. Los resultados indican que son los obstáculos derivados de la gestión de recursos humanos los que provocan un efecto de desbordamiento sobre la satisfacción de los usuarios. En cambio, la frecuencia más o menos idónea de realización de tareas apenas influye en las evaluaciones de los usuarios. Así pues, las «malas experiencias» (obstáculos) en la prestación del servicio vienen a ser especialmente críticas a la hora de entender la satisfacción de los usuarios