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Amstutz S.,Université Ibn Tofail | Giusti S.M.,Laboratorio Nacional Of Computacao Cientifica Lncc Mct | Novotny A.A.,Laboratorio Nacional Of Computacao Cientifica Lncc Mct | De Souza Neto E.A.,University of Swansea
International Journal for Numerical Methods in Engineering | Year: 2010

This paper proposes an algorithm for the synthesis/optimization of microstructures based on an exact formula for the topological derivative of the macroscopic elasticity tensor and a level set domain representation. The macroscopic elasticity tensor is estimated by a standard multi-scale constitutive theory where the strain and stress tensors are volume averages of their microscopic counterparts over a representative volume element. The algorithm is of simple computational implementation. In particular, it does not require artificial algorithmic parameters or strategies. This is in sharp contrast with existing microstructural optimization procedures and follows as a natural consequence of the use of the topological derivative concept. This concept provides the correct mathematical framework to treat topology changes such as those characterizing microstuctural optimization problems. The effectiveness of the proposed methodology is illustrated in a set of finite element-based numerical examples. © 2010 John Wiley & Sons, Ltd.


Peric D.,University of Swansea | De Souza Neto E.A.,University of Swansea | Feijoo R.A.,Laboratorio Nacional Of Computacao Cientifica Lncc Mct | Partovi M.,University of Swansea | Molina A.J.C.,University of Swansea
International Journal for Numerical Methods in Engineering | Year: 2011

This work describes a homogenization-based multi-scale procedure required for the computation of the material response of non-linear microstructures undergoing small strains. Such procedures are important for computer modelling of heterogeneous materials when the length-scale of heterogeneities is small compared to the dimensions of the body. The described multi-scale procedure relies on a unified variational basis which, apart from the continuum-based variational formulation at both micro- and macroscales of the problem, also includes the variational formulation governing micro-to-macro transitions. This unified variational basis leads naturally to a generic finite element-based framework for homogenization-based multi-scale analysis of heterogenous solids. In addition, the unified variational formulation provides clear axiomatic basis and hierarchy related to the choice of boundary conditions at the microscale. Classical kinematical constraints are considered over the representative volume element: (i) Taylor, (ii) linear boundary displacements, (iii) periodic boundary displacement fluctuations and (iv) minimal constraint, also known as uniform boundary tractions. In this context the Hill-Mandel averaging requirement, which links microscopic and macroscopic stress power, plays a fundamental role in defining the microscopic forces compatible with the assumed kinematics. Numerical examples of both microscale and two-scale finite element simulations of elasto-plastic material with microcavities are presented to illustrate the main features and scope of the described computational strategy. © 2010 John Wiley & Sons, Ltd.


Amstutz S.,University of Strasbourg | Novotny A.A.,Laboratorio Nacional Of Computacao Cientifica Lncc Mct | De Souza Neto E.A.,University of Swansea
Computer Methods in Applied Mechanics and Engineering | Year: 2012

An algorithm for topology optimization of elastic structures under plane stress subject to the Drucker-Prager stress constraint is presented. The algorithm is based on the use of the topological derivative of the associated objective functional in conjunction with a level-set representation of the structure domain. In this context, a penalty functional is proposed to enforce the point-wise stress constraint and a closed formula for its topological derivative is derived. The resulting algorithm is of remarkably simple computational implementation. It does not require post-processing procedures of any kind and features only a minimal number of user-defined algorithmic parameters. This is in sharp contrast with current procedures for topological structural optimization with local stress constraints. The effectiveness and efficiency of the algorithm presented here are demonstrated by means of numerical examples. The examples show, in particular, that it can easily handle structural optimization problems with underlying materials featuring strong asymmetry in their tensile and compressive yield strengths. © 2012 Elsevier B.V.


de Souza C.E.,Laboratorio Nacional Of Computacao Cientifica Lncc Mct | Xie L.,Nanyang Technological University | Coutinho D.F.,Grande Rio University
Automatica | Year: 2010

This paper is concerned with the problems of robust H∞ and H2 filtering for 2-dimensional (2-D) discrete-time linear systems described by a Fornasini-Marchesini second model with matrices that depend affinely on convex-bounded uncertain parameters. By a suitable transformation, the system is represented by an equivalent difference-algebraic representation. A parameter-dependent Lyapunov function approach is then proposed for the design of 2-D stationary discrete-time linear filters that ensure either a prescribed H∞ performance or H2 performance for all admissible uncertain parameters. The filter designs are given in terms of linear matrix inequalities. Numerical examples illustrate the effectiveness of the proposed filter design methods. © 2010 Elsevier Ltd. All rights reserved.


Novotny A.A.,Laboratorio Nacional Of Computacao Cientifica Lncc Mct
Mathematical Methods in the Applied Sciences | Year: 2010

A simple analytical expression for crack nucleation sensitivity analysis is proposed relying on the concept of topological derivative and applied within a two-dimensional linear elastic fracture mechanics theory (LEFM). In particular, the topological asymptotic expansion of the total potential energy together with a Griffith-type energy of an elastic cracked body is calculated. As a main result, we derive a crack nucleation criterion based on the topological derivative and a criterion for determining the direction of crack growth based on the topological gradient. The proposed methodology leads to an axiomatic approach of crack nucleation sensitivity analysis. Copyright © 2010 John Wiley & Sons, Ltd.


Coutinho D.,Federal University of Santa Catarina | De Souza C.E.,Laboratorio Nacional Of Computacao Cientifica Lncc Mct
IEEE Transactions on Circuits and Systems I: Regular Papers | Year: 2012

This work addresses the design of state feedback controllers for locally stabilizing open-loop unstable quadratic systems with guaranteed stability domain and performance. First, a method is derived to design a stabilizing nonlinear static state feedback controller, which is quadratic in the system state, while providing an enlarged stability region for the closed-loop system. The stabilization method is then extended in three directions. The first one is to ensure a quadratic regulator-type performance, the second is the local stabilization, in sense of integral input-to-state stability, of quadratic systems disturbed by energy-bounded exogenous signals, whereas the third extension provides a solution to the ℋ ∞ control problem. The developed control methods are tailored via finite sets of state-dependent linear matrix inequalities. Several numerical examples are presented to illustrate the potentials of the proposed controller designs. © 2012 IEEE.


Amstutz S.,Université Ibn Tofail | Novotny A.A.,Laboratorio Nacional Of Computacao Cientifica Lncc Mct
ESAIM - Control, Optimisation and Calculus of Variations | Year: 2011

The topological asymptotic analysis provides the sensitivity of a given shape functional with respect to an infinitesimal domain perturbation, like the insertion of holes, inclusions, cracks. In this work we present the calculation of the topological derivative for a class of shape functionals associated to the Kirchhoff plate bending problem, when a circular inclusion is introduced at an arbitrary point of the domain. According to the literature, the topological derivative has been fully developed for a wide range of second-order differential operators. Since we are dealing here with a forth-order operator, we perform a complete mathematical analysis of the problem. © EDP Sciences, SMAI, 2010.


Amstutz S.,Université Ibn Tofail | Novotny A.A.,Laboratorio Nacional Of Computacao Cientifica Lncc Mct
Structural and Multidisciplinary Optimization | Year: 2010

The topological asymptotic analysis provides the sensitivity of a given shape functional with respect to an infinitesimal domain perturbation. Therefore, this sensitivity can be naturally used as a descent direction in a structural topology design problem. However, according to the literature concerning the topological derivative, only the classical approach based on flexibility minimization for a given amount of material, without control on the stress level supported by the structural device, has been considered. In this paper, therefore, we introduce a class of penalty functionals that mimic a pointwise constraint on the Von Mises stress field. The associated topological derivative is obtained for plane stress linear elasticity. Only the formal asymptotic expansion procedure is presented, but full justifications can be deduced from existing works. Then, a topology optimization algorithm based on these concepts is proposed, that allows for treating local stress criteria. Finally, this feature is shown through some numerical examples. © Springer-Verlag 2009.


Guedes I.A.,Laboratorio Nacional Of Computacao Cientifica Lncc Mct | de Magalhaes C.S.,Federal Rural University of Rio de Janeiro | Dardenne L.E.,Laboratorio Nacional Of Computacao Cientifica Lncc Mct
Biophysical Reviews | Year: 2014

Docking methodology aims to predict the experimental binding modes and affinities of small molecules within the binding site of particular receptor targets and is currently used as a standard computational tool in drug design for lead compound optimisation and in virtual screening studies to find novel biologically active molecules. The basic tools of a docking methodology include a search algorithm and an energy scoring function for generating and evaluating ligand poses. In this review, we present the search algorithms and scoring functions most commonly used in current molecular docking methods that focus on protein-ligand applications. We summarise the main topics and recent computational and methodological advances in protein-ligand docking. Protein flexibility, multiple ligand binding modes and the free-energy landscape profile for binding affinity prediction are important and interconnected challenges to be overcome by further methodological developments in the docking field. © 2013 International Union for Pure and Applied Biophysics (IUPAB) and Springer-Verlag Berlin Heidelberg.


Novotny A.A.,Laboratorio Nacional Of Computacao Cientifica Lncc Mct
Mechanics Research Communications | Year: 2013

The topological derivative represents the first term of the asymptotic expansion of a given shape functional with respect to the small parameter which measures the size of singular domain perturbations. The topological derivative has been successfully applied in the treatment of problems such as topology optimization, inverse analysis and image processing. In this paper, the calculation of the topological derivative for a general class of shape functionals is presented. In particular, we evaluate the topological derivative of a modified energy shape functional associated to the steady-state heat conduction problem, considering the nucleation of a small circular inclusion as the topological perturbation. Several methods were proposed to calculate the topological derivative. In this paper, the so-called topological-shape sensitivity method is extended to deal with a modified adjoint method, leading to an alternative approach to calculate the topological derivative based on shape sensitivity analysis together with a modified Lagrangian method. Since we are dealing with a general class of shape functionals, which are not necessarily associated to the energy, we will show that this new approach simplifies the most delicate step of the topological derivative calculation, namely, the asymptotic analysis of the adjoint state. © 2013 Elsevier Ltd.

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