Browsing by Author "Gutierrez, Sergio"

Now showing 1 - 6 of 6
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    An optimization algorithm applied to the Morrey conjecture in nonlinear elasticity
    (PERGAMON-ELSEVIER SCIENCE LTD, 2007) Gutierrez, Sergio; Villavicencio, Jorge
    For a long time it has been studied whether rank-one convexity and quasiconvexity give rise to different families of constitutive relations in planar nonlinear elasticity. Stated in 1952 the Morrey conjecture says that these families are different, but no example has come forward to prove it. Now we attack this problem by deriving a specialized optimization algorithm based on two ingredients: first, a recently found necessary condition for the quasiconvexity of fourth-degree polynomials that distinguishes between both classes in the three dimensional case, and secondly, upon a characterization of rank-one convex fourth-degree polynomials in terms of infinitely many constraints.
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    Detection of weak defects in elastic bodies through small amplitude homogenization
    (TAYLOR & FRANCIS LTD, 2011) Mura, Joaquin; Gutierrez, Sergio
    This article is devoted to the detection of inclusions using a single boundary measurement obtained from quasi-static essays in linear elasticity. The idea is to minimize the misfit between the displacement field obtained on part of the boundary and the boundary data coming from solving the elasticity equations with a guess inclusion. The optimization algorithm comes from the work of Allaire and Gutierrez [G. Allaire and S. Gutierrez, Optimal design in small amplitude homogenization, Math. Model. Numer. Anal. 41(3) (2007), pp. 543-574] and it is based on the assumption that the contrast on the values of the Lame elastic coefficients between the defect and the matrix is not very large. This approach is promising because it is well adapted to cases when the defect is caused, for example, by weak inhomogeneities during the fabrication process. From the numerical examples we conclude that the method is quite robust under noisy measurements and errors in the characterization of the defect.
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    Elasto-plastic optimal profile of the flanges of a double-T steel beam
    (ELSEVIER SCI LTD, 2008) Galvez, Leonardo; Gutierrez, Sergio
    For a given amount of steel we look for the optimal profile of the width of the symmetrical flanges of a double-T steel beam, in order to optimize a weighted compromise between elastic performance, measured by the compliance, and collapse factor. We approximately determine curves of optimal profiles when varying the relative weight given to each performance measure and use these profiles to obtain a plot showing the variation of the ductility and the collapse factor as functions of the relative weights. The steel is assumed elastic-perfectly plastic. (c) 2007 Elsevier Ltd. All rights reserved.
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    Integration of Near-Surface Complementary Geophysical Techniques for the Study of Ancient Archaeological Areas in the Atacama Desert (Pampa Iluga, Northern Chile)
    (2023) Gallegos-Poch, Fernanda; Viguier, Benoit; Menanno, Giovanni; Mandakovic, Valentina; Yanez, Gonzalo; Gutierrez, Sergio; Lizarde, Catalina; Araya, Jaime Vargas; Lopez-Contreras, Camila; Mendez-Quiros, Pablo; Maldonado, Antonio; Uribe, Mauricio
    Near-surface geophysical techniques are useful for the characterization of archaeological areas because of their ability to rapidly cover wide extensions and obtain high-resolution data to identify the location for archaeological excavations. However, in hyperarid environments usual geophysical techniques may fail to obtain the expected results due to the dry near surface. This study proposes an integration of ground penetrating radar (GPR) and electromagnetic induction (EMI) techniques, to elucidate the origin of thousands of aligned circular features located at the Iluga archaeological area emplaced on one of the driest places on Earth (Pampa del Tamarugal, Atacama Desert). The GPR was useful to recognize alluvial deposits, sandy aeolian filling in pre-existing holes and roots right underneath circular features. Magnetic susceptibility data derived from the EMI in-phase component, usually considered a complementary result, were useful to identify fireplaces in the vicinity of the alignments. These geophysical findings were verified with an archaeological excavation. It has been found that circular features resulted from an extensive deforestation process in the Pampa del Tamarugal, consisting in the extraction of both trunk and roots of algarrobos (Prosopis chilensis) or tamarugos (Prosopis tamarugo), likely for recent charcoal production. The proposed methodology delivers promising results for archaeological and shallow geological studies in hyperarid and dry environments.
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    Optimal design of Kirchhoff-Love plates under the low contrast assumption
    (2024) Burazin, Kresimir; Gutierrez, Sergio; Jankov, Jelena
    A method for the optimization of the distribution of two materials in a thin symmetric plate is presented. The model for the plate is the Kirchhoff-Love and the optimization method is based on the small amplitude, or low contrast, approximation for homogenization. Numerical results are presented for compliance minimization, i.e., maximizing the global stiffness of the plate, and for minimizing the integral of an even power of the deflection in a subset of the plate. The method arrives at classical designs without the need of penalization, which allows evaluating the exact performance of the proposed shapes and the comparison with some simple intuitive designs. This also gives insight in how small the contrast needs to be for the method to give designs which are better than some intuitive designs.
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    Optimal Strut-and-Tie Models Using Full Homogenization Optimization Method
    (2012) Pablo Herranz, Juan; Santa Maria, Hernan; Gutierrez, Sergio; Riddell, Rafael
    An optimization method based on homogenization is proposed for finding optimal strut-and-tie (ST) models for reinforced concrete (RC) elements. The method uses a layout that minimizes displacement for a given loading state in a linearly elastic regime by mixing two materials. Although this optimal layout might contain fine mixtures, one can still obtain a strongly resembling ST model without mixtures that performs closely to the optimal configuration through a penalization procedure. Two examples from the ST literature are used to illustrate the application of the method: the dapped beam and the beam on beam. The reinforcement layouts obtained make the element more efficient in terms of ultimate load divided by the weight of the steel used and having smaller deflections and crack widths. It is remarkable that the used optimization method, which considers the structure in the linearly elastic regime, gives a very good performance for the nonlinear regime.