Thermal control of a spacecraft: Backward-implicit scheme programming and coating materials analysis

[EN] The passive thermal control of a satellite consists of establishing the necessary thermal parameters involved in the process of heat transfer by radiation and conduction in order to delimit the range of temperatures to which the different components will be exposed. If the obtained range implies temperatures that the elements of the satellite are unable to cope with, therefore, an external control is demanded. This work deals with the programming of the equilibrium thermal problem taken into consideration a backward-implicit scheme. The algebraic mathematical approach for steady-state and transient analysis are implemented in Matlab scripts. In addition, the work analyzes the influence of different coating materials on the passive thermal control of a benchmark spacecraft reported in the literature. The problem under scope considers the characteristics of a low Earth Orbit: the solar, albedo and planetary radiation, the radiation coming from other isotherm surfaces of the same satellite, the heat conduction and, finally, the radiation of these isotherm surfaces to the outer space. The procedure implemented is based on a feasible matrix formulation and results avoid the numerical instabilities prevalent in the forward-explicit approach, moreover, it enables further parametric and sensitivity analysis. Regarding the coating materials influence on the thermal response, the most relevant results evidence that thermal surfaces can guarantee the desirable range of temperature in a spacecraft. We confirm that certain material properties like the absorptance, emittance and its relation (absorption coefficient) are essential in the thermal response of the system. Nevertheless, these thermal properties do not influence in the same way. It is shown that the effect of the emittance is lower than the absorptance.The authors acknowledge the Agencia Estatal de Investigaci6n for the financial support received through the project DPI2017-89197-C2-2-R and the Generalitat Valenciana for the Programme PROMETEO 2016/007. The authors declare that they have no conflict of interest.Alcayde, V.; Vercher Martínez, A.; Fuenmayor Fernández, F. (2021). Thermal control of a spacecraft: Backward-implicit scheme programming and coating materials analysis. Advances in Space Research. 68(4):1975-1988. https://doi.org/10.1016/j.asr.2021.03.041S1975198868

Accurate recovery-based error upper bounds for the extended finite element framework

[EN] This paper introduces a recovery-type error estimator yielding upper bounds of the error in energy norm for linear elastic fracture mechanics problems solved using the extended finite element method (XFEM) The paper can be considered as an extension and enhancement of a previous work in which the upper bounds of the error were developed in a FEM framework The upper bound property requires the recovered solution to be equilibrated and continuous The proposed technique consists of using a recovery technique, especially adapted to the XFEM framework that yields equilibrium at a local level (patch by patch) Then a postprocess based on the partition of unity concept is used to obtain continuity The result is a very accurate but only nearly-statically admissible recovered stress field, with small equilibrium defaults introduced by the postprocess Sharp upper bounds are obtained using a new methodology accounting for the equilibrium defaults, as demonstrated by the numerical testsThis work has been carried out within the framework of the research projects DPI2007-66773-C02-01, DPI2007-66995-C03-02 and DPI2007-62395 of the Ministerio de Educacion y Ciencia (Spain). The financial support of the Generalitat Valenciana and the Universidad Politecnica de Valencia is also acknowledged.Ródenas, J.; Gonzalez-Estrada, O.; Díez, P.; Fuenmayor Fernández, F. (2010). Accurate recovery-based error upper bounds for the extended finite element framework. Computer Methods in Applied Mechanics and Engineering. 199(37-40):2607-2621. https://doi.org/10.1016/j.cma.2010.04.010S2607262119937-4

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

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

[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

PACDIN statement of methods

This is an Accepted Manuscript of an article published by Taylor & Francis in Vehicle System Dynamics on 2014 available online: https://doi.org/10.1080/00423114.2014.963126[EN] PAntograph-Catenary Dynamic Interaction (PACDIN) is a code developed by the vehicle technology research centre (CITV) of the Universitat Politecnica de Valencia in collaboration with the railway company Talgo S.L. The model of the catenary is a finite element model using absolute nodal coordinates. It is based on a general formulation that can be applied for analysing a wide range of catenary configurations, including stitch wire, transitions or non-straight path tracks. The formulation is fully non-linear and includes large deformations, dropper slackening and contact interaction. The model is linearised when deformations are small, as in the case of the benchmark dynamic analysis. The results of the PACDIN code show a good agreement with the average results of other benchmark codes.The authors wish to thank Generatitat Valenciana for the financial support received in the framework of the PROMETEO 2012/023 Programme.Tur Valiente, M.; Baeza González, LM.; Fuenmayor Fernández, F.; Garcia, E. (2014). PACDIN statement of methods. Vehicle System Dynamics. 53(3):402-411. https://doi.org/10.1080/00423114.2014.963126S402411533Shabana, A. A. (1998). Nonlinear Dynamics, 16(3), 293-306. doi:10.1023/a:1008072517368BERZERI, M., & SHABANA, A. A. (2000). DEVELOPMENT OF SIMPLE MODELS FOR THE ELASTIC FORCES IN THE ABSOLUTE NODAL CO-ORDINATE FORMULATION. Journal of Sound and Vibration, 235(4), 539-565. doi:10.1006/jsvi.1999.2935Gerstmayr, 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/s11071-006-1856-1Tur, 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.2014.04.015Collina, A., & Bruni, S. (2002). Numerical Simulation of Pantograph-Overhead Equipment Interaction. Vehicle System Dynamics, 38(4), 261-291. doi:10.1076/vesd.38.4.261.828

Direction of crack propagation in a complete contact fretting-fatigue problem

In this work, the orientation and propagation of a crack in a fretting fatigue problem is analyzed numerically and correlated experimentally. The analysis is performed using a 2D model of a complete-contact fretting problem, consisting of two square indenters pressed onto a specimen subjected to cyclic fatigue. For the simulation, we use the extended finite element method (X-FEM), allowing for crack face contact during the corresponding parts of the fatigue cycle. The problem is highly non-linear and non-proportional and an orientation criterion is introduced to predict the crack direction in each step of the crack growth simulation. It is shown that the proposed criterion predicts crack orientation directions that are in good agreement with those found experimentally, in contrast to the directions found by application of conventional orientation criteria used in LEFM, such as the MTS criterion.The authors gratefully acknowledge the financial support given by the SGPI of the Spanish Ministry of Economics and Competitiveness (Projects DPI2007-66995-C03-02 and DPI2010-20990). The support of the Generalitat Valenciana, Programme PROMETEO 2012/023, is also acknowledged. The authors thank the collaboration of Mr. Pere Dasi Rodriguez.Giner Maravilla, E.; Sabsabi, M.; Ródenas García, JJ.; Fuenmayor Fernández, FJ. (2014). Direction of crack propagation in a complete contact fretting-fatigue problem. International Journal of Fatigue. 58:172-180. https://doi.org/10.1016/j.ijfatigue.2013.03.001S1721805

Influence of the mineral staggering on the elastic properties of the mineralized collagen fibril in lamellar bone

In this work, a three-dimensional finite element model of the staggered distribution of the mineral within the mineralized collagen fibril has been developed to characterize the lamellar bone elastic behavior at the sub-micro length scale. Minerals have been assumed to be embedded in a collagen matrix, and different degrees of mineralization have been considered allowing the growth of platelet-shaped minerals both in the axial and the transverse directions of the fibril, through the variation of the lateral space between platelets. We provide numerical values and trends for all the elastic constants of the mineralized collagen fibril as a function of the volume fraction of mineral. In our results, we verify the high influence of the mineral overlapping on the mechanical response of the fibril and we highlight that the lateral distance between crystals is relevant to the mechanical behavior of the fibril and not only the mineral overlapping in the axial direction.The authors acknowledge the Ministerio de Economia y Competitividad the financial support given through the project DPI2013-46641-R and to the Programme Prometeo 2012/023.Vercher Martínez, A.; Giner Maravilla, E.; Arango Villegas, C.; Fuenmayor Fernández, FJ. (2015). Influence of the mineral staggering on the elastic properties of the mineralized collagen fibril in lamellar bone. Journal of the Mechanical Behavior of Biomedical Materials. 42:243-256. https://doi.org/10.1016/j.jmbbm.2014.11.022S2432564