Examinando por Materia "Numerical solution"
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Ítem 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 AplicacionesThe 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.Ítem Analytic approximation to the scattering of antiplane shear waves by free surfaces of arbitrary shape via superposition of incident, reflected and diffracted rays(OXFORD UNIV PRESS, 2013-03-01) Jaramillo, Juan; Gomez, Juan; Externo - Escuela - Ciencias; Vergara, Juan; Mecánica AplicadaThe scattering induced by surface topographies of arbitrary shapes, submitted to horizontally polarized shear waves (SH) is studied analytically. In particular, we propose an analysis technique based on a representation of the scattered field like the superposition of incident, reflected and diffracted rays. The diffraction contribution is the result of the interaction of the incident and reflectedwaves, with the geometric singularities present in the surface topography. This splitting of the solution into different terms, makes the difference between our method and alternative numerical/analytical approaches, where the complete field is described by a single term. The contribution from the incident and reflected fields is considered using standard techniques, while the diffracted field is obtained using the idea of a ray as was introduced by the geometrical theory of diffraction. Our final solution however, is an approximation in the sense that, surface-diffracted rays are neglected while we retain the contribution from corner-diffracted rays and its further diffraction. These surface rays are only present when the problem has smooth boundaries combined with shadow zones, which is far from being the typical scenario in far-field earthquake engineering. The proposed technique was tested in the study of a combined hill-canyon topography and the results were compared with those of a boundary element algorithm. After considering only secondary sources of diffraction, a difference of 0.09 per cent (with respect to the incident field amplitude) was observed. The proposed analysis technique can be used in the interpretation of numerical and experimental results and in the preliminary prediction of the response in complex topographies. © The Authors 2012. Published by Oxford University Press on behalf of The Royal Astronomical Society.Ítem Modelling 3D metal cutting problems with the particle finite element method(Springer Verlag, 2020-01-01) Carbonell, J.M.; Rodríguez, J.M.; Oñate, E.; Carbonell, J.M.; Rodríguez, J.M.; Oñate, E.; Universidad EAFIT. Departamento de Ingeniería Mecánica; Mecatrónica y Diseño de MáquinasThis work presents the development of the Particle Finite Element Method (PFEM) for the modelling of 3D solid mechanics problems under cutting conditions. The study and analysis of numerical models reproducing the cut of a material is a matter of interest in several areas; namely, the improvement of the material properties, the optimization of the process and tool geometries and the prediction of unexpected failures. The analysis of bi-dimensional (2D) models is the most common approach for different reasons. Just focusing on the simulation point of view, it is the simplest procedure, the cheapest in terms of computational cost and sometimes the only feasible numerical solution. However, many industrial machining processes, such as cutting, blanking, milling and drilling have not a possible simplification to 2D models. Actually even a simple turning processes for non-orthogonal cuts can not be simplified to 2D. This work present an upgrade of the PFEM techniques in order to deal with the 3D machining problems. We present recent improvements in the finite element formulation, the meshing re-connections and the contact detection. By applying these developments the PFEM has the capability for modelling a wide range of practical machining processes. In this paper the capacity of the formulation and the accuracy of the results are analyzed and validated with some representative examples. © 2020, Springer-Verlag GmbH Germany, part of Springer Nature.