Dynamic response of periodic infinite structure to arbitrary moving load based on the Finite Element Method

[EN] A common problem in railway engineering is the dynamic of repetitive structures subject to moving loads. Bridges, rails or catenaries are the most representative periodic structures, over which the train acts as a moving exciter. Usually, these structures are long enough to consider that their dynamic response is in permanent regime. To assume the steady-state regime some features have to be considered: infinite length structure, perfect periodicity and constant velocity of the moving load. This paper adopts these assumptions and provides the steady-state solution of a generic periodic structure subject to an arbitrary and also periodic moving load. The structure is divided into repetitive blocks modelled by the Finite Element Method. By applying the periodicity condition it is possible to consider the entire structure dynamics with only one block. The problem is stated in the frequency domain and moved back to time domain by means of Discrete Fourier Transform.The authors would like to acknowledge the financial support received from the Spanish Ministry of Economy, Industry and Competitiveness (TRA2017-84736-R).Gil-Romero, J.; Gregori, S.; Tur, M.; Fuenmayor, F. (2022). Dynamic response of periodic infinite structure to arbitrary moving load based on the Finite Element Method. En Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference. Editorial Universitat Politècnica de València. 326-333. https://doi.org/10.4995/YIC2021.2021.12606OCS32633

A recovery-type error estimator for the extended finite element method based on singular+smooth stress field splitting

[EN] A new stress recovery procedure that provides accurate estimations of the discretization error for linear elastic fracture mechanic problems analyzed with the extended finite element method (XFEM) is presented. The procedure is an adaptation of the superconvergent patch recovery (SPR) technique for the XFEM framework. It is based oil three fundamental aspects: (a) the use of a singular+smooth stress field decomposition technique involving the use of different recovery methods (or each field: standard SPR for the smooth field and reconstruction of the recovered singular field using the stress intensity factor K for the singular field: (b) direct calculation of smoothed stresses at integation points using conjoint polynomial enhancement and (c) assembly of patches with elements intersected by the crack using different stress interpolation polynomials at each side of the crack. The method was validated by testing it oil problems with an exact solution in mode I, mode II, and mixed mode and oil it problem without analytical solution. The results obtained showed the accuracy of the proposed error estimator.This paper was developed within the framework of the research projects DP12007-66773-C02-01 and DPI2007-66995-C03-02 of the Ministerio de Educacion y Ciencia (Spain). Funding was also received from the Generalitat Valenciana and the Universidad Politecnica de Valencia.Ródenas, J.; González-Estrada, O.; Taráncón, J.; Fuenmayor, F. (2008). A recovery-type error estimator for the extended finite element method based on singular+smooth stress field splitting. International Journal for Numerical Methods in Engineering. 76(4):545-571. https://doi.org/10.1002/nme.2313S54557176

Enhanced error estimator based on a nearly equilibrated moving least squares recovery technique for FEM and XFEM

International audienceIn this paper a new technique aimed to obtain accurate estimates of the error in energy norm using a moving least squares (MLS) recovery-based procedure is presented. We explore the capabilities of a recovery technique based on an enhanced MLS fitting, which directly provides continuous interpolated fields, to obtain estimates of the error in energy norm as an alternative to the superconvergent patch recovery (SPR). Boundary equilibrium is enforced using a nearest point approach that modifies the MLS functional. Lagrange multipliers are used to impose a nearly exact satisfaction of the internal equilibrium equation. The numerical results show the high accuracy of the proposed error estimator

Fretting fatigue life prediction using the extended finite element method

In this work, fretting fatigue tests available in the literature are modeled using the extended finite element method (XFEM). The aim is to numerically evaluate the stress intensity factors (SIFs) for cracks of different lengths emanating at the end of the contact zone and to estimate the propagation life corresponding to each of the tests. This propagation life is combined with the initiation life calculated analytically using a multiaxial fatigue criterion (Fatemi-Socie), following a initiation-propagation approach for life estimation. The predicted lives are then compared with the reported experimental lives. It is shown that the consideration of the crack-contact interaction through the numerical models tends to improve the life estimation when compared with a fully analytical approach for the calculation of both initiation and propagation lives.Ministerio de Ciencia y Tecnología DPI2007-66995-C0301Ministerio de Ciencia y Tecnología DPI2007-66995-C03-02

Acoustic modelling of exhaust devices with nonconforming finite element meshes and transfer matrices

[EN] Transfer matrices are commonly considered in the numerical modelling of the acoustic behaviour associated with exhaust devices in the breathing system of internal combustion engines, such as catalytic converters, particulate filters, perforated mufflers and charge air coolers. In a multidimensional finite element approach, a transfer matrix provides a relationship between the acoustic fields of the nodes located at both sides of a particular region. This approach can be useful, for example, when one-dimensional propagation takes place within the region substituted by the transfer matrix. As shown in recent investigations, the sound attenuation of catalytic converters can be properly predicted if the monolith is replaced by a plane wave four-pole matrix. The finite element discretization is retained for the inlet/outlet and tapered ducts, where multidimensional acoustic fields can exist. In this case, only plane waves are present within the capillary ducts, and three-dimensional propagation is possible in the rest of the catalyst subcomponents. Also, in the acoustic modelling of perforated mufflers using the finite element method, the central passage can be replaced by a transfer matrix relating the pressure difference between both sides of the perforated surface with the acoustic velocity through the perforations. The approaches in the literature that accommodate transfer matrices and finite element models consider conforming meshes at connecting interfaces, therefore leading to a straightforward evaluation of the coupling integrals. With a view to gaining flexibility during the mesh generation process, it is worth developing a more general procedure. This has to be valid for the connection of acoustic subdomains by transfer matrices when the discretizations are nonconforming at the connecting interfaces. In this work, an integration algorithm similar to those considered in the mortar finite element method, is implemented for nonmatching grids in combination with acoustic transfer matrices. A number of numerical test problems related to some relevant exhaust devices are then presented to assess the accuracy and convergence performance of the proposed procedure.Authors gratefully acknowledge the financial support of Ministerio de Ciencia e Innovacion and the European Regional Development Fund by means of the Projects DPI2007-62635 and DPI2010-15412.Denia, F.; Martínez-Casas, J.; Baeza, L.; Fuenmayor, F. (2012). Acoustic modelling of exhaust devices with nonconforming finite element meshes and transfer matrices. Applied Acoustics. 73(8):713-722. https://doi.org/10.1016/j.apacoust.2012.02.003S71372273

A finite element approach for the acoustic modelling of perforated dissipative mufflers with non-homogeneous properties

[EN] In this work, a finite element approach is presented for modeling sound propagation in perforated dissipative mufflers with non-homogeneous properties. The spatial variations of the acoustic properties can arise, for example, from uneven filling processes during manufacture and degradation associated with the flow of soot particles within the absorbent material. First, the finite element method is applied to the wave equation for a propagation medium with variable properties (outer chamber with absorbent material) and a homogeneous medium (central passage). For the case of a dissipative muffler, the characterization of the absorbent material is carried out by means of its equivalent complex density and speed of sound. To account for the spatial variations of these properties, a coordinate-dependent function is proposed for the filling density of the absorbent material. The coupling between the outer chamber and the central passage is achieved by using the acoustic impedance of the perforated central pipe, that relates the acoustic pressure jump and the normal velocity through the perforations. The acoustic impedance of the perforated central duct includes the influence of the absorbent material and therefore a spatial variation of the impedance is also taken into account. A detailed study is then presented to assess the influence of the heterogeneous properties and the perforated duct porosity on the acoustic attenuation performance of the muffler.The authors gratefully acknowledge the financial support of Ministerio de Ciencia e Innovacion and the European Regional Development Fund by means of the projects DPI2007-62635 and DPI2010-15412.Antebas, A.; Denia Guzmán, FD.; Pedrosa Sanchez, AM.; Fuenmayor Fernández, FJ. (2013). A finite element approach for the acoustic modelling of perforated dissipative mufflers with non-homogeneous properties. Mathematical and Computer Modelling. 57(7):1970-1978. https://doi.org/10.1016/j.mcm.2012.01.021S1970197857

A 3D absolute nodal coordinate finite element model to compute the initial configuration of a railway catenary

In this paper we propose a method of finding the initial equilibrium configuration of cable structures discretized by finite elements applied to the shape-finding of the railway overhead system. Absolute nodal coordinate formulation finite elements, which allow for axial and bending deformation, are used for the contact and messenger wires. The other parts of the overhead system are discretized with non-linear bars or equivalent springs. The proposed method considers the constraints introduced during the assembly of the catenary, such as the position of droppers, cable tension, and height of the contact wire. The formulation is general and can be applied to different catenary configurations or transitions both in 2D and 3D with straight or curved track paths. A comparison of the results obtained for reference catenaries in the bibliography is also included.The authors wish to thank Generatitat Valenciana for the financial support received in the framework of the Programme PROME-TEO 2012/023.Tur Valiente, M.; García, E.; Baeza González, LM.; Fuenmayor Fernández, FJ. (2014). A 3D absolute nodal coordinate finite element model to compute the initial configuration of a railway catenary. Engineering Structures. 71:234-243. https://doi.org/10.1016/j.engstruct.2014.04.015S2342437

Locally equilibrated stress recovery for goal oriented error estimation in the extended finite element method

[EN] Goal oriented error estimation and adaptive procedures are essential for the accurate and efficient evaluation of finite element numerical simulations that involve complex domains. By locally improving the approximation quality, for example, by using the extended finite element method (XFEM), we can solve expensive problems which could result intractable otherwise. Here, we present an error estimation technique for enriched finite element approximations that is based on an equilibrated recovery technique, which considers the stress intensity factor as the quantity of interest. The locally equilibrated superconvergent patch recovery is used to obtain enhanced stress fields for the primal and dual problems defined to evaluate the error estimate.This work was supported by the EPSRC grant EP/G042705/1 "Increased Reliability for Industrially Relevant Automatic Crack Growth Simulation with the eXtended Finite Element Method". Stephane Bordas also thanks partial funding for his time provided by the European Research Council Starting Independent Research Grant (ERC Stg Grant Agreement No. 279578) "RealTCut Towards real time multiscale simulation of cutting in non-linear materials with applications to surgical simulation and computer guided surgery". This work has been carried out within the framework of the research project DPI2010-20542 of the Ministerio de Ciencia e Innovacion (Spain). The financial support of the FPU program (AP2008-01086), the funding from Universitat Politecnica de Valencia and Generalitat Valenciana (PROMETEO/2012/023) are also acknowledged.González Estrada, OA.; Ródenas, J.; Bordas, S.; Nadal, E.; Kerfriden, P.; Fuenmayor Fernández, FJ. (2015). Locally equilibrated stress recovery for goal oriented error estimation in the extended finite element method. Computers and Structures. 152:1-10. https://doi.org/10.1016/j.compstruc.2015.01.015S11015

A recovery-explicit error estimator in energy norm for linear elasticity

[EN] Significant research effort has been devoted to produce one-sided error estimates for Finite Element Analyses, in particular to provide upper bounds of the actual error. Typically, this has been achieved using residual-type estimates. One of the most popular and simpler (in terms of implementation) techniques used in commercial codes is the recovery-based error estimator. This technique produces accurate estimations of the exact error but is not designed to naturally produce upper bounds of the error in energy norm. Some attempts to remedy this situation provide bounds depending on unknown constants. Here, a new step towards obtaining error bounds from the recovery-based estimates is proposed. The idea is (1) to use a locally equilibrated recovery technique to obtain an accurate estimation of the exact error, (2) to add an explicit-type error bound of the lack of equilibrium of the recovered stresses in order to guarantee a bound of the actual error and (3) to efficiently and accurately evaluate the constants appearing in the bounding expressions, thus providing asymptotic bounds. The numerical tests with h-adaptive refinement process show that the bounding property holds even for coarse meshes, providing upper bounds in practical applications.The authors also thank the support of the Framework Programme 7 Initial Training Network Funding under grant number 289361 "Integrating Numerical Simulation and Geometric Design Technology".Nadal Soriano, E.; Díez, P.; Ródenas, J.; Tur Valiente, M.; Fuenmayor Fernández, FJ. (2015). A recovery-explicit error estimator in energy norm for linear elasticity. Computer Methods in Applied Mechanics and Engineering. 287:172-190. https://doi.org/10.1016/j.cma.2015.01.013S17219028