Repositorio Institucional Universidad EAFIT ::Examinando por Materia "Numerical methods"

Examinando por Materia "Numerical methods"

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Analysis of the stability and dispersion for a Riemannian acoustic wave equation
(ELSEVIER SCIENCE INC, 2019-01-15) Quiceno, H. R.; Arias, C.; Quiceno, H. R.; Arias, C.; Universidad EAFIT. Departamento de Ciencias; Matemáticas y Aplicaciones
The construction of images of the Earth's interior using methods as reverse time migration (RTM) or full wave inversion (FWI) strongly depends on the numerical solution of the wave equation. A mathematical expression of the numerical stability and dispersion for a particular wave equation used must be known in order to avoid unbounded numbers of amplitudes. In case of the acoustic wave equation, the Courant–Friedrich–Lewy (CFL) condition is a necessary but is not a sufficient condition for convergence. Thus, we need to search other types of expression for stability condition. In seismic wave problems, the generalized Riemannian wave equation is used to model their propagation in domains with curved meshes which is suitable for zones with rugged topography. However, only a heuristic version of stability condition was reported in the literature for this equation. We derived an expression for stability condition and numerical dispersion analysis for the Riemannian acoustic wave equation in a two-dimensional medium and analyzed its implications in terms of computational cost. © 2018 Elsevier Inc.
Application of the continuous wavelet transform in the extraction of directional data on RTM imaging condition wavefields
(Ecopetrol, 2018-01-01) Paniagua-Castrillón J.-G.; Quintero-Montoya O.-L.; Universidad EAFIT. Escuela de Ciencias; Modelado Matemático
Low-frequency artifacts in reverse time migration result from unwanted cross-correlation of the source and receiver wavefields at nonreflecting points along ray-paths. These artifacts can hide important details in migrated models and increase poor interpretation risk. Some methods have been proposed to avoid or reduce the number of these artifacts, preserving reflections, and improving model quality, implementing other strategies such as modification of the wave equation, proposing other imaging conditions, and using image filtering techniques. One of these methods uses wavefield decomposition, correlating components of the wavefields that propagate in opposite directions. We propose a method for extracting directional information from the RTM imaging condition wavefields to obtain characteristics allowing for better, more refined imaging. The method works by separating directional information about the wavefields based on the continuous wavelet transform (CWT), and the analysis of the main changes on the frequency content revealed within the scalogram obtained by a Gaussian wavelet family. Through numerical applications, we demonstrate that this method can effectively remove undesired artifacts in migrated images. In addition, we use the Laguerre-Gauss filtering to improve the results obtained with the proposed method. © 2018 Ecopetrol S.A. All Rights Reserved.
Base shear determination using response-spectrum modal analysis of multi-degree-of-freedom systems with soil–structure interaction
(Springer Netherlands, 2019-01-01) Arias H.; Jaramillo J.D.; Mecánica Aplicada
Building codes and design guidelines, e.g. FEMA (NEHRP recommended seismic provisions for new buildings and other structures, FEMA P-1050, Washington, 2015) and ASCE (Minimum design loads for buildings and other structures ASCE/SEI 7-10/2010, Reston, 2010), describe the problem of multi-degree-of-freedom systems with soil-structure interaction (SSI). These systems are modeled like those having a fundamental degree of freedom on a foundation with lateral and rotational interactions and the other vibration modes isolated and supported on a fixed foundation. This model oversimplifies the problem, neglecting the effects of having all modes coupled in the foundation with SSI. A simple, easily programmable, SSI model in which all vibration modes are coupled an attached to an infinitely rigid shallow foundation subjected to soil excitation is introduced here. Initially, the total response of the coupled system is calculated. Then, using traditional procedures to combine modal responses, a simplified alternative methodology to find the total response of this coupled system is proposed. The new methodology is verified against a robust numerical technique, i.e. boundary elements method, using a wide variety of cases that combine several types of soils, building heights and two structural typologies: bending frames and shear walls. Finally, it is clear from the parametric study that current methodologies, based only on the interaction of the fundamental mode of vibration of the structure, in some cases has a significant influence on the total base shear of buildings, particularly in tall buildings founded in soft soils. © 2019, Springer Nature B.V.
Characterizing points on discontinuity boundary of Filippov systems
(ACTA Press, 2008-01-01) Arango, I.; Taborda, J.A.; Arango, I.; Taborda, J.A.; Universidad EAFIT. Departamento de Ingeniería Mecánica; Mecatrónica y Diseño de Máquinas
In this paper, we presented a basic methodology to understand the behavior of discontinuous piecewise smooth autonomous systems (denominated Filippov systems) in the planar neighborhood of the discontinuity boundary (DB). This methodology is useful in detection of nonsmooth bifurcations in Filippov systems. We propose a classification of the points and events on DB. This classification is more complete in comparison with the reported papers previously. The lines and the points are characterized with didactic symbols and the exclusive conditions for their existence based in geometric criterions. Boolean-valued functions are used to formulate the conditions. An illustrative example with a friction oscillator is presented.
Chromatic aberration compensation in numerical reconstruction of digital holograms by Fresnel-Bluestein propagation
(OSA - The Optical Society, 2017-12-15) Hincapie D.; Velasquez D.; Garcia-Sucerquia J.; Universidad EAFIT. Departamento de Ciencias Básicas; Óptica Aplicada
In this Letter, we present a method for chromatic compensation in numerical reconstruction of digitally recorded holograms based on Fresnel-Bluestein propagation. The proposed technique is applied to correct the chromatic aberration that arises in the reconstruction of RGB holograms of both millimeter-and micrometer-sized objects. The results show the feasibility of this strategy to remove the wavelength dependence of the size of the numerically propagated wavefields. (C) 2017 Optical Society of America
A comparative computational study of blood flow pattern in exemplary textile vascular grafts
(Taylor and Francis Ltd., 2018-01-01) Valencia, R.A.; García, M.J.; Bustamante, J.; Mecánica Aplicada
Textile vascular grafts are biomedical devices and play an important role serving as a solution for the partial replacement of damaged arterial vessels. It is believed that the success of a textile vascular graft, in the healing process after implantation, is due to the porous micro-structure of the wall. Although the transport of fluids through textiles is of great technical interest in biomedical applications, little is known about predicting the micro-flow pattern and cellular transport through the wall. The aim of this work is to investigate how the type of fabric, permeability and porosity affect both the local fluid dynamics at several scales and the fluid-particle interaction between platelets in textile grafts, related with the graft occlusion. This study involves both experimental and computational tests. Experimental tests are performed to characterize the permeability and porosity according to the ISO 7198 standard. The numerical process is based on a multi-scale approach where the fluid flow is solved with the Finite Element Method and the discrete particles are solved with the Molecular Dynamic Method. The results have shown that the type of fabric in textile vascular grafts and the degree of porosity and permeability affect both the local fluid dynamics and the level of penetration of platelets through the wall, thus indicating their importance as design parameters. © 2017 Informa UK Limited, trading as Taylor & Francis Group.
A comparative computational study of blood flow pattern in exemplary textile vascular grafts
(Taylor and Francis Ltd., 2018-01-01) R. VALENCIA; M. GARCÍA; J. BUSTAMANTE; R. VALENCIA; M. GARCÍA; J. BUSTAMANTE; Universidad EAFIT. Departamento de Humanidades; Centro de Estudios Urbanos y Ambientales (URBAM)
Textile vascular grafts are biomedical devices and play an important role serving as a solution for the partial replacement of damaged arterial vessels. It is believed that the success of a textile vascular graft, in the healing process after implantation, is due to the porous micro-structure of the wall. Although the transport of fluids through textiles is of great technical interest in biomedical applications, little is known about predicting the micro-flow pattern and cellular transport through the wall. The aim of this work is to investigate how the type of fabric, permeability and porosity affect both the local fluid dynamics at several scales and the fluid-particle interaction between platelets in textile grafts, related with the graft occlusion. This study involves both experimental and computational tests. Experimental tests are performed to characterize the permeability and porosity according to the ISO 7198 standard. The numerical process is based on a multi-scale approach where the fluid flow is solved with the Finite Element Method and the discrete particles are solved with the Molecular Dynamic Method. The results have shown that the type of fabric in textile vascular grafts and the degree of porosity and permeability affect both the local fluid dynamics and the level of penetration of platelets through the wall, thus indicating their importance as design parameters. © 2017 Informa UK Limited, trading as Taylor & Francis Group.
Control of Porosity in Freeze Casting
(J O M Institute, 2020-01-01) Gil-Duran S.; Arola D.; Ossa E.A.; Gil-Duran S.; Arola D.; Ossa E.A.; Universidad EAFIT. Departamento de Ingeniería de Producción; Materiales de Ingeniería
Many biologic structural materials have porous microstructures with a distribution and orientation of pores that are challenging to achieve using traditional methods of processing. In this investigation, numerical and experimental methods of evaluation were used to understand effects from the primary processing parameters on the temperature gradients during solidification in freeze casting of ceramics. The location and orientation of the temperature gradients were found to be highly dependent on the geometrical and thermal properties of the mold material used in processing. Furthermore, it was found that careful control of these processing variables can be used to design bioinspired porous materials with graded orientations and distributions of pores. © 2020, The Minerals, Metals & Materials Society.
Dislocation density based flow stress model applied to the PFEM simulation of orthogonal cutting processes of Ti-6Al-4V
(MDPI AG, 2020-01-01) Rodríguez, J.M.; Larsson, S.; Carbonell, J.M.; Jonsén, P.; Rodríguez, J.M.; Larsson, S.; Carbonell, J.M.; Jonsén, P.; Universidad EAFIT. Departamento de Ingeniería Mecánica; Mecatrónica y Diseño de Máquinas
Machining of metals is an essential operation in the manufacturing industry. Chip formation in metal cutting is associated with large plastic strains, large deformations, high strain rates and high temperatures, mainly located in the primary and in the secondary shear zones. During the last decades, there has been significant progress in numerical methods and constitutive modeling for machining operations. In this work, the Particle Finite Element Method (PFEM) together with a dislocation density (DD) constitutive model are introduced to simulate the machining of Ti-6Al-4V. The work includes a study of two constitutive models for the titanium material, the physically based plasticity DD model and the phenomenology based Johnson-Cook model. Both constitutive models were implemented into an in-house PFEM software and setup to simulate deformation behaviour of titanium Ti6Al4V during an orthogonal cutting process. Validation show that numerical and experimental results are in agreement for different cutting speeds and feeds. The dislocation density model, although it needs more thorough calibration, shows an excellent match with the results. This paper shows that the combination of PFEM together with a dislocation density constitutive model is an excellent candidate for future numerical simulations of mechanical cutting. © 2020 by the authors.
Evaluación de una red neuronal para la solución de ecuaciones diferenciales
(Universidad EAFIT, 2023) Machado-Loaiza, José Manuel; Guarín-Zapata, Nicolás
Fast analytic simulation for multi-laser heating of sheet metal in GPU
(MDPI AG, 2018-11-01) Mejia-Parra D.; Montoya-Zapata D.; Arbelaiz A.; Moreno A.; Posada J.; Ruiz-Salguero O.; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAE
Interactive multi-beam laser machining simulation is crucial in the context of tool path planning and optimization of laser machining parameters. Current simulation approaches for heat transfer analysis (1) rely on numerical Finite Element methods (or any of its variants), non-suitable for interactive applications; and (2) require the multiple laser beams to be completely synchronized in trajectories, parameters and time frames. To overcome this limitation, this manuscript presents an algorithm for interactive simulation of the transient temperature field on the sheet metal. Contrary to standard numerical methods, our algorithm is based on an analytic solution in the frequency domain, allowing arbitrary time/space discretizations without loss of precision and non-monotonic retrieval of the temperature history. In addition, the method allows complete asynchronous laser beams with independent trajectories, parameters and time frames. Our implementation in a GPU device allows simulations at interactive rates even for a large amount of simultaneous laser beams. The presented method is already integrated into an interactive simulation environment for sheet cutting. Ongoing work addresses thermal stress coupling and laser ablation. © 2018 by the authors.
Fast Spectral Formulations of Thin Plate Laser Heating with GPU Implementation
(Institute of Electrical and Electronics Engineers Inc., 2020-01-01) Mejia-Parra D.; Arbelaiz A.; Moreno A.; Posada J.; Ruiz-Salguero O.; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAE
In the context of numerical methods, the problem of frequency-domain (spectral) simulations is crucial for the solution of Partial Differential Equations. Fast Fourier Transform (FFT) algorithms significantly reduce the computational cost of such simulations and enable parallelization using Graphics Processing Units (GPUs). In the particular subdomain of laser heating/cutting of rectangular metal plates, fast simulation is required for tool path planning, parameter optimization and additive manufacturing. The currently used methods include frequency-domain analytic solutions for single-beam and multi-beam laser heating. However, the problem of formulating these spectral problems in terms of Fourier methods and implementing them in efficient manner remains. To overcome these limitations, this article presents two different schemes that translate the problem of laser beam heating of metal plates into equivalent FFT problems. The results show significant improvements in terms of executions times, being 100× faster than current state-of-the-art algorithms. Future work needed involves the inclusion of stress analysis, complex plate geometries and non-constant material properties for the plate. © 2020 IEEE.
Finite difference calculations of permeability in large domains in a wide porosity range
(Springer Verlag, 2015-08-01) Osorno, M.; Uribe, D.; Ruiz, O.E.; Steeb, H.; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAE
Determining effective hydraulic, thermal, mechanical and electrical properties of porous materials by means of classical physical experiments is often time-consuming and expensive. Thus, accurate numerical calculations of material properties are of increasing interest in geophysical, manufacturing, bio-mechanical and environmental applications, among other fields. Characteristic material properties (e.g. intrinsic permeability, thermal conductivity and elastic moduli) depend on morphological details on the porescale such as shape and size of pores and pore throats or cracks. To obtain reliable predictions of these properties it is necessary to perform numerical analyses of sufficiently large unit cells. Such representative volume elements require optimized numerical simulation techniques. Current state-of-the-art simulation tools to calculate effective permeabilities of porous materials are based on various methods, e.g. lattice Boltzmann, finite volumes or explicit jump Stokes methods. All approaches still have limitations in the maximum size of the simulation domain. In response to these deficits of the well-established methods we propose an efficient and reliable numerical method which allows to calculate intrinsic permeabilities directly from voxel-based data obtained from 3D imaging techniques like X-ray microtomography. We present a modelling framework based on a parallel finite differences solver, allowing the calculation of large domains with relative low computing requirements (i.e. desktop computers). The presented method is validated in a diverse selection of materials, obtaining accurate results for a large range of porosities, wider than the ranges previously reported. Ongoing work includes the estimation of other effective properties of porous media. © 2015, Springer-Verlag Berlin Heidelberg.
Frequency-domain analytic method for efficient thermal simulation under curved trajectories laser heating
(Elsevier BV, 2019-01-01) Mejia-Parra D.; Moreno A.; Posada J.; Ruiz-Salguero O.; Barandiaran I.; Poza J.C.; Chopitea R.; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAE
In the context of Computer Simulation, the problem of heat transfer analysis of thin plate laser heating is relevant for downstream simulations of machining processes. Alternatives to address the problem include (i) numerical methods, which require unaffordable time and storage computing resources even for very small domains, (ii) analytical methods, which are less expensive but are limited to simple geometries, straight trajectories and do not account for material non-linearities or convective cooling. This manuscript presents a parallel efficient analytic method to determine, in a thin plate under convective cooling, the transient temperature field resulting from application of a laser spot following a curved trajectory. Convergence of both FEA (Finite Element Analysis) and the analytic approaches for a small planar plate is presented, estimating a maximum relative error for the analytic approach below 3.5% at the laser spot. Measured computing times evidence superior efficiency of the analytic approach w.r.t. FEA. A study case, with the analytic solution, for a large spatial and time domain (1m×1m and 12s history, respectively) is presented. This case is not tractable with FEA, where domains larger than 0.05m×0.05m and 2s require high amounts of computing time and storage. © 2019 International Association for Mathematics and Computers in Simulation (IMACS)
Kinematic identification of parallel mechanisms by a divide and conquer strategy
(INSTICC-INST SYST TECHNOLOGIES INFORMATION CONTROL & COMMUNICATION, 2010-01-01) Durango S.; Externo - Escuela - Ingeniería; Ruiz O.; Restrepo-Giraldo J.; Achiche S.; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAE
This paper presents a Divide and Conquer strategy to estimate the kinematic parameters of parallel symmetrical mechanisms. The Divide and Conquer kinematic identification is designed and performed independently for each leg of the mechanism. The estimation of the kinematic parameters is performed using the inverse calibration method. The identification poses are selected optimizing the observability of the kinematic parameters from a Jacobian identification matrix. With respect to traditional identification methods the main advantages of the proposed Divide and Conquer kinematic identification strategy are: (i) reduction of the kinematic identification computational costs, (ii) improvement of the numerical efficiency of the kinematic identification algorithm and, (iii) improvement of the kinematic identification results. The contributions of the paper are: (i) The formalization of the inverse calibration method as the Divide and Conquer strategy for the kinematic identification of parallel symmetrical mechanisms and, (ii) a new kinematic identification protocol based on the Divide and Conquer strategy. As an application of the proposed kinematic identification protocol the identification of a planar 5R symmetrical mechanism is simulated. The performance of the calibrated mechanism is evaluated by updating the kinematic model with the estimated parameters and developing simulations.
Numerical methods to value an option including risk aversion with a CRRA utility function
(Universidad EAFIT, 2021) Manzur Guevara, Diego; Marín Sánchez, Fredy Hernán; Pareja Vasseur, Julián Alberto
Prenolin: International benchmark on 1D nonlinear: Site-response analysis—validation phase exercise
(Seismological Society of America, 2018-04-01) Régnier J.; Bonilla L.-F.; Bard P.-Y.; Bertrand E.; Hollender F.; Kawase H.; Sicilia D.; Arduino P.; Amorosi A.; Asimaki D.; Boldini D.; Chen L.; Chiaradonna A.; Demartin F.; Elgamal A.; Falcone G.; Foerster E.; Foti S.; Garini E.; Gazetas G.; Gélis C.; Ghofrani A.; Giannakou A.; Gingery J.; Glinsky N.; Harmon J.; Hashash Y.; Iai S.; Kramer S.; Kontoe S.; Kristek J.; Lanzo G.; Lernia A.D.; Lopez-Caballero F.; Marot M.; McAllister G.; Mercerat E.D.; Moczo P.; Montoya-Noguera S.; Musgrove M.; Nieto-Ferro A.; Pagliaroli A.; Passeri F.; Richterova A.; Sajana S.; Santisi D’Avila M.P.; Shi J.; Silvestri F.; Taiebat M.; Tropeano G.; Vandeputte D.; Verrucci L.; Mecánica Aplicada
This article presents the main results of the validation phase of the PRENOLIN project. PRENOLIN is an international benchmark on 1D nonlinear (NL) site-response analysis. This project involved 19 teams with 23 different codes tested. It was divided into two phases; with the first phase verifying the numerical solution of these codes on idealized soil profiles using simple signals and real seismic records. The second phase described in this article referred to code validation for the analysis of real instrumented sites. This validation phase was performed on two sites (KSRH10 and Sendai) of the Japanese strong-motion networks KiK-net and Port and Airport Research Institute (PARI), respectively, with a pair of accelerometers at surface and depth. Extensive additional site characterizations were performed at both sites involving in situ and laboratory measurements of the soil properties. At each site, sets of input motions were selected to represent different peak ground acceleration (PGA) and frequency content. It was found that the code-to-code variability given by the standard deviation of the computed surface-response spectra is around 0.1 (in log10 scale) regardless of the site and input motions. This indicates a quite large influence of the numerical methods on site-effect assessment and more generally on seismic hazard. Besides, it was observed that sitespecific measurements are of primary importance for defining the input data in siteresponse analysis. The NL parameters obtained from the laboratory measurements should be compared with curves coming from the literature. Finally, the lessons learned from this exercise are synthesized, resulting also in a few recommendations for future benchmarking studies, and the use of 1D NL, total stress site-response analysis. © 2018, Seismological Society of America. All rights reserved.
Statistical assessment of global and local cylinder wear
(IEEE, 2007-01-01) Ruiz, Oscar; Vanegas, Carlos; Universidad EAFIT. Departamento de Ingeniería Mecánica; Laboratorio CAD/CAM/CAE
Assessment of cylindricity has been traditionally performed on the basis of cylindrical crowns containing a set of points that are supposed to belong to a controlled cylinder. As such, all sampled points must lie within a crown. In contrast, the present paper analyzes the cylindricity for wear applications, in which a statistical trend is assessed, rather than to assure that all points fall within a given tolerance. Principal Component Analysis is used to identify the central axis of the sampled cylinder, allowing to And the actual (expected value of the) radius and axis of the cylinder. Application of k-cluster and transitive closure algorithms allow to identify particular areas of the cylinder which are specially deformed. For both, the local areas and the global cylinder, a quantile analysis allows to numerically grade the degree of deformation of the cylinder. The algorithms implemented are part of the CYLWEAR© system and used to assess local and global wear cylinders. © 2007 IEEE.
A stiffness derivative local hypercomplex-variable finite element method for computing the energy release rate
(Elsevier BV, 2019-01-01) Aguirre-Mesa A.M.; Ramirez-Tamayo D.; Garcia M.J.; Montoya A.; Millwater H.; Mecánica Aplicada
A “local” hypercomplex-variable finite element method, L-ZFEM, is proposed for the computation of the energy release rate (ERR) using the stiffness derivative equation. This approach is analogous to the stiffness derivative method proposed by Parks and Hellen but has superior numerical accuracy. In addition, this method is significantly more efficient than the previously published “global” hypercomplex-variable finite element method, ZFEM, in that the global hypercomplex system of FE equations is not assembled nor solved. Instead, the displacement field is computed using a traditional, real-valued finite element method, and the numerical derivative of the stiffness matrix at the element level is only computed for a group of local, surrounding elements to the crack tip by using a Taylor series expansion based on complex numbers or dual numbers. The ERR is then determined as a sum of the element contributions. Derivatives of the ERR with respect to an arbitrary model parameter such as a crack extension, material property, or geometric feature are also available using a combination of the global and local methods, GL-ZFEM. Both L-ZFEM and GL-ZFEM were implemented into the commercial finite element software Abaqus through user defined element subroutines. Numerical results show that the ERR obtained by L-ZFEM has the same accuracy as that estimated through the global ZFEM or the J-integral methods but exhibits superior computational efficiency. © 2019 Elsevier Ltd
A study of the effect of the transition curve in the coupling elements between the carbody and the bogie
(INDERSCIENCE ENTERPRISES LTD, 2014-01-01) Martinod, Ronald M.; Betancur, German R.; Osorio, Jose F.; Castaneda, Leonel F.; Universidad EAFIT. Departamento de Ingeniería Mecánica; Estudios en Mantenimiento (GEMI)
This work describes an analysis of the effect of the transition curves in the coupling elements between the carbody and the bogie, by means of recorded variables under commercial operation conditions of a railway vehicle. A set of field tests are developed and applied to the railway system as a basis to validate a numerical model. The dataset is obtained from a numerical model based on the multi-body systems theory using a transient method. The study focuses on the dynamic evaluation of the vehicle to determine the transversal dynamic effect generated by the circulation in the transition curve sections, especially in curves with short radius. The work includes a case study of a passenger railway, and it is used to identify aspects of the railway system that could be improved by the operators, such as inspection routines, rail track design and elements subjected to considerable loads. Copyright © 2014 Inderscience Enterprises Ltd.

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