Papers by Elena Atroshchenko
Damage Detection and Localization for Indirect Bridge Monitoring Exploiting Adversarial Autoencoder and Wavelet Transform
Lecture notes in civil engineering, Jun 19, 2022
Design of metamaterial-based heat manipulators by isogeometric shape optimization
International Journal of Heat and Mass Transfer
Solutions fondamentales et méthodes aux éléments frontière en mécanique de la rupture pour les matériaux de type Cosserat
In this paper, both singular and hypersingular fundamental solutions of plane Cosserat elasticity... more In this paper, both singular and hypersingular fundamental solutions of plane Cosserat elasticity are derived and given in a ready-to-use form. The hypersingular fundamental solutions allow to formulate the analogue of Somigliana stress identity, which can be used to obtain the stress and couple stress fields inside the domain from the boundary values of the displacements, microrotation and stress and couple stress tractions. Using these newly derived fundamental solutions, the boundary integral equations of both types are formulated and solved by the boundary element method. Simultaneous use of both types of the equations (approach known as the dual BEM) allows to treat problems where parts of the boundary are overlapping, such as crack problems, and to do this for general geometry and loading conditions. The high accuracy of the boundary element method for both types of equations is demonstrated for a number of benchmark problems, including a Griffith crack problem and a plate wit...
Boundary Element Modeling of Crack Propagation in Micropolar Materials
In this work we show some applications of isogeometric collocation to problems of two-and threedi... more In this work we show some applications of isogeometric collocation to problems of two-and threedimensional acoustic scattering and radiation, modeled by the Helmholtz equation in an unbounded domain. The two major difficulties of numerical methods in acoustics are associated with a) a highly oscillatory nature of the solutions as the wave number 'k' increases, and b) the necessity to truncate the infinite domain with an artificial surface, where the Sommerfeld radiation condition is approximated.
Los fenómenos físicos, presentes en las ciencias y en las diferentes áreas de la ingeniería, a me... more Los fenómenos físicos, presentes en las ciencias y en las diferentes áreas de la ingeniería, a menudo son modelados por Ecuaciones Diferenciales Parciales (EDP). Los problemas de valor de frontera resultantes en muchos casos carecen de soluciones analíticas. Para resolver tales problemas, uno puede hacer suposiciones que simplifiquen el problema, o usar métodos numéricos para aproximar la solución. Dentro de los métodos numéricos actualmente existentes, el más popular es el Método de Elementos Finitos (FEM), que es la base de diferentes programas comerciales, como ADINA o ANSYS, entre muchos otros. La desventaja de este método es la gran cantidad de recursos computacionales y los tiempos de iteración requeridos para obtener una solución precisa del problema. Dada esta desventaja, Hughes desarrolló el Análisis IsoGeométrico (IGA). Este método permite integrar el modelo CAD con el Análisis de Elementos Finitos (FEA), por lo tanto, reduce los tiempos y los recursos necesarios para obtener una solución precisa. Pero a su vez, el IGA no tiene flexibilidad para obtener soluciones de ciertos problemas, ya que usa las mismas funciones bases para parametrizar tanto la geometría como el campo de solución. Debido a esto último, surge el Análisis IsoGeométrico Generalizado (GIFT) como una generalización del IGA, este método utiliza diferentes funciones bases para parametrizar la geometría del objeto y el campo de solución, permitiendo la selección de funciones que se adapten mejor al problema estudiado. En trabajos anteriores, el GIFT ha sido aplicado a problemas de la Ecuación de Laplace y de Elasticidad Lineal. El objetivo principal de este trabajo es estudiar el rendimiento del GIFT para problemas de flexión y de vibraciones de placas delgadas. El estudio consiste en implementar el GIFT para 3 placas diferentes y comparar los resultados numéricos con lo predicho por la Teoría de Placas de Kirchhoff-Love (KLPT). Se consideran una placa de geometría circular simple, una placa de geometría circular de dos parches y una placa cuadrada con un agujero de forma compleja, modelada por 8 parches. Las placas están parametrizadas por NURBS, mientras que las soluciones se aproximan por un parche usando NURBS o B-Splines. Los resultados se muestran en términos de curvas de convergencia, modos de vibración y frecuencias naturales. Los resultados numéricos se comparan con las soluciones analíticas para problemas con geometría simple y con la solución FEM para el problema de una placa más compleja. El análisis realizado indica que, para la misma parametrización de geometría (uniforme), (a) la solución se puede aproximar mediante un parche NURBS o B-Splines, manteniendo inalterada la geometría original, (b) los resultados obtenidos con las aproximaciones de campo NURBS y B-Splines son idénticas, (c) la tasa de convergencia depende del grado de aproximación de la solución. Para parametrizaciones geométricas no uniformes, el método no produce una tasa de convergencia óptima o resultados suficientemente precisos, al igual que el IGA tradicional.
Adaptive enriched geometry independent field approximation for 2D time-harmonic acoustics
Computers & Structures, 2022
Isogeometric collocation for acoustic problems with higher-order boundary conditions
Wave Motion, 2022
Multi-scale fracture, model reduction, CAD and image as a model
Case A1 Similar elements, both geo and solution using NURBS, Σ u " Σ g (except end knots for p u ... more Case A1 Similar elements, both geo and solution using NURBS, Σ u " Σ g (except end knots for p u ‰ p g) Case A2 Same as A1 except Σ u ‰ Σ g Case B1 Similar elements, geo using NURBS, and solution using B-Splines, Σ u " Σ g (except weights, and end knots for p u ‰ p g) Case B2 Same as B1 except Σ u ‰ Σ g Case C1 Nonuniform elements (with parameter δ), both geo and solution using NURBS, Σ u " Σ g , δ u " δ g (except end knots for p u ‰ p g) Case C2 Same as C1 except δ u ‰ δ g Case C3 Same as C1 except Σ u ‰ Σ g , and δ u ‰ δ g Some numerical results Convergence results
Microblog Texts Classification Using Word Networks
In isogeometric analysis (IGA), the same spline representation is employed for both the geometry ... more In isogeometric analysis (IGA), the same spline representation is employed for both the geometry of the domain and approximation of the unknown fields over this domain.This identity of the geometry and field approximation spaces was put forward in the now classic 2005 paper [20] as a key advantage on the way to the integration of Computer Aided Design (CAD) and subsequent analysis in Computer Aided Engineering (CAE). [20] claims indeed that any change to the geometry of the domain is automatically inherited by the approximation of the field variables, without requiring the regeneration of the mesh at each change of the domain geometry. Yet, in Finite Element versions of IGA, a parameterization of the interior of the domain must still be constructed, since CAD only provides information about the boundary. The identity of the boundary and field representation decreases the flexibility of the modeling process, because an approximation able to represent the domain geometry accurately ne...
We present recent advances in geometry independent field approximations. The GIFT approach is a g... more We present recent advances in geometry independent field approximations. The GIFT approach is a generalisation of isogeometric analysis where the approximation used to describe the field variables no-longer has to be identical to the approximation used to describe the geometry of the domain. As such, the geometry can be described using usual CAD representations, e.g. NURBS, which are the most common in the CAD area, whilst local refinement and meshes approximations can be used to describe the field variables, enabling local adaptivity. We show in which cases the approach passes the patch test and present applications to various mechanics, fracture and multi-physics problems. Stéphane Bordas et al.
Journal of Computational and Applied Mathematics, 2021
Up to now, the isogeometric boundary element method (IGBEM) has been widely applied in different ... more Up to now, the isogeometric boundary element method (IGBEM) has been widely applied in different fields, and the solved problems are basically independent of time. But an excellent numerical method is more than that, so it is necessary to explore a new IGBEM which can solve time-domain problems. Based on this, the isogeometric dual reciprocity boundary element method (IG-DRBEM) is proposed to solve transient heat transfer problems with heat sources. The introduction of the dual reciprocal method enables the IGBEM to solve the transient heat transfer problem conveniently. At the same time, it does not need to divide elements within the domain, which maintains the advantage of the IGBEM. First, the boundary domain integral equation is established by the weighted residual method and the field variables are discretized by NURBS basis functions. Then, the domain integral in the integral equation is transformed into the boundary by the classical dual reciprocity method. Finally, the standard first-order ordinary differential equations are formed. In order to examine the accuracy of the proposed method, several typical numerical examples are discussed carefully. The presented method can provide a new idea for solving time-dependent problems by IGBEM.
Computers & Mathematics with Applications, 2020
In this article, the condition number of the stiffness matrix κ(K) is compared for three high ord... more In this article, the condition number of the stiffness matrix κ(K) is compared for three high order finite element methods (FEMs), i.e., the p-version of the FEM, the spectral element method (SEM), and the NURBS-based isogeometric analysis (IGA). Note that only problems in linear elasticity are considered in the analysis. It is wellknown that the condition number is one factor strongly influencing the number of significant digits for direct solvers or the required iteration count for iterative solution schemes. Therefore, it is important to investigate the effect of the choice of the shape functions and the element distortion on κ(K). Based on numerous one-and two-, and three-dimensional examples, these influences are comprehensively studied, and the numerical results are compared with condition number estimates extracted from the literature. Overall, a good agreement is observed for p-FEM, SEM and two-dimensional IGA, while discrepancies are noted for three-dimensional isogeometric elements. These are important findings as theoretical results may be only available for very restricted scenarios, where one-element geometries, constant Jacobi matrices of the element maps, etc. are considered.
Composite Structures, 2020
In this work, we propose to leverage the advantages of both the Artificial Neural Network (ANN) b... more In this work, we propose to leverage the advantages of both the Artificial Neural Network (ANN) based Second Order Reliability Method (SORM) and Importance sampling to yield an Adaptive Importance Sampling based ANN, with specific application towards failure probability and sensitivity estimates of Variable Stiffness Composite Laminate (VSCL) plates, in the presence of multiple independent geometric and material uncertainties. The performance function for the case studies is defined based on the fundamental frequency of the VSCL plate. The accuracy in both the reliability estimates and sensitivity studies using the proposed method were found to be in close agreement with that obtained using the ANN based brute-force MCS method, with a significant computational savings of 95%. Moreover, the importance of taking into account the randomness in ply thickness for failure probability estimates is also highlighted quantitatively under the sensitivity studies section.
Computers & Structures, 2019
The Linear Smoothing (LS) scheme [1] ameliorates linear and quadratic approximations over convex ... more The Linear Smoothing (LS) scheme [1] ameliorates linear and quadratic approximations over convex polytopes by employing a three-point integration scheme. In this work, we propose a linearly consistent one point integration scheme which possesses the properties of the LS scheme with three integration points but requires one third of the integration computational time. The essence of the proposed technique is to approximate the strain by the smoothed nodal derivatives that are determined by the discrete form of the divergence theorem. This is done by the Taylor's expansion of the weak form which facilitates the evaluation of the smoothed nodal derivatives acting as stabilization terms. The smoothed nodal derivatives are evaluated only at the centroid of each integration cell. These integration cells are the simplex subcells (triangle/tetrahedron in two and three dimensions) obtained by subdividing the polytope. The salient feature of the proposed technique is that it requires only n integrations for an n− sided polytope as opposed to 3n in [1] and 13n integration points in the conventional approach. The convergence properties, the accuracy, and the efficacy of the LS with one point integration scheme are discussed by solving few benchmark problems in elastostatics.
Engineering Analysis with Boundary Elements, 2018
In this paper, a new approach is developed for structural shape optimization, which consists in c... more In this paper, a new approach is developed for structural shape optimization, which consists in coupling the particle swarm optimization (PSO) algorithm and the isogeometric boundary element method (IGA-BEM). The IGA-BEM is based on the combination of the isogeometric analysis (IGA) and the boundary element method (BEM), where Non-Uniform Rational B-Splines (NURBS) are employed as shape functions for geometry parameterization and approximation of the field variables. The method inherits the main advantage of the IGA-based shape optimization, i.e., the control points are used as design variables, thus the design model, analysis model and optimization model are uniformly described with the NURBS, providing easy communication between the three models and resulting in a smooth optimized boundary. However, the main feature of the proposed method is the use of PSO, which provides an attractive gradient-free alternative to complicated sensitivity analysis. The efficiency and accuracy of the proposed approach are demonstrated through four 2D shape optimization examples.
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 2015
In this paper we prove the existence of weak solutions for the inclusion problem in anti-plane Co... more In this paper we prove the existence of weak solutions for the inclusion problem in anti-plane Cosserat elasticity in Sobolev space setting, and for the corresponding systems of boundary integral equations.
An isogeometric boundary element method for fracture modeling
Uploads
Papers by Elena Atroshchenko