137 research outputs found

    Solving the dual subproblem of the Method of Moving Asymptotes using a trust-region scheme

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    An alternative strategy to solve the subproblems of the Method of Moving Asymptotes (MMA) is presented, based on a trust-region scheme applied to the dual of the MMA subproblem. At each iteration, the objective function of the dual problem is approximated by a regularized spectral model. A globally convergent modification to the MMA is also suggested, in which the conservative condition is relaxed by means of a summable controlled forcing sequence. Another modification to the MMA previously proposed by the authors [Optim. Methods Softw., 25 (2010), pp. 883-893] is recalled to be used in the numerical tests. This modification is based on the spectral parameter for updating the MMA models, so as to improve their quality. The performed numerical experiments confirm the efficiency of the indicated modifications, especially when jointly combined.151170Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq

    Metamaterial filter design via surrogate optimization

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    Recently, an increasing research effort has been dedicated to analyse transmission and dispersion properties of periodic metamaterials containing resonators, and to optimize the amplitude of selected acoustic band gaps between consecutive dispersion curves in the Floquet-Bloch spectrum. Potential novel applications of this research are in the design of passive mechanical filters/diodes. The present work proposes a way to interpolate the objective functions in such band gap optimization problems, using Radial Basis Functions. The study is motivated by the high computational effort often needed for an exact evaluation of the original objective functions, when using iterative optimization algorithms. By replacing such functions with surrogate objective functions, well-performing suboptimal solutions can be obtained with a small computational effort. Numerical results demonstrate the feasibility of the approach

    Exploring the Method of Moving Asymptotes for Various Optimization Applications

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    The development of sequential explicit, convex approximation schemes has allowed for expansion of the size of optimization problems that can now be achieved. These approximation schemes use information from the original optimization statement to generate a series of approximate subproblems allowing for an efficient solution strategy. This thesis reviews established sequential explicit, convex approximations in the literature along with a brief overview of their associated solution schemes. A primary focus is placed on the theory and application of the Method of Moving Asymptotes (MMA) approximation due to its continued regard in the field of structural topology optimization. Numerical examples explore optimization problems solved by the MMA approximation in order to demonstrate the behavior of this method and impact of the prescribed empirical parameters. Other numerical examples study structural topology optimization problems in the 2D and 3D setting to compare with alternative, competitive update schemes such as the OC and to highlight the benefit of using the MMA in more complex settings.M.S

    A strictly feasible sequential convex programming method

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    Optimal design of low-frequency band gaps in anti-tetrachiral lattice meta-materials

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    The elastic wave propagation is investigated in the beam lattice material characterized by a square periodic cell with anti-tetrachiral microstructure. With reference to the Floquet-Bloch spectrum, focus is made on the band structure enrichments and modifications which can be achieved by equipping the cellular microstructure with tunable local resonators. By virtue of its composite mechanical nature, the so-built inertial meta-material gains enhanced capacities of passive frequency-band filtering. Indeed the number, placement and properties of the inertial resonators can be designed to open, shift and enlarge the band gaps between one or more pairs of consecutive branches in the frequency spectrum. In order to improve the meta-material performance, a nonlinear optimization problem is formulated. The maximum of the largest band gap amplitudes in the low-frequency range is selected as suited objective function. Proper inequality constraints are introduced to restrict the optimal solutions within a compact set of mechanical and geometric parameters, including only physically realistic properties of both the lattice and resonators. The optimization problems related to full and partial band gaps are solved independently, by means of a globally convergent version of the numerical method of moving asymptotes, combined with a quasi-Monte Carlo multi-start technique. The optimal solutions are discussed and compared from the qualitative and quantitative viewpoints, bringing to light the limits and potential of the meta-material performance. The clearest trends emerging from the numerical analyses are pointed out and interpreted from the physical viewpoint. Finally, some specific recommendations about the microstructural design of the meta-material are synthesized

    MINIMIZING THE ACOUSTIC COUPLING OF FLUID LOADED PLATES USING TOPOLOGY OPTIMIZATION

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    Optimization of the topology of a plate coupled with an acoustic cavity is investigated in an attempt to minimize the fluid-structure interactions at different structural frequencies. A mathematical model is developed to simulate such fluid-structure interactions based on the theory of finite elements. The model is integrated with a topology optimization approach which utilizes the Moving Asymptotes Method. The obtained results demonstrate the effectiveness of the proposed approach in simultaneously attenuating the structural vibration and the sound pressure inside the acoustic domain at several structural frequencies by proper redistribution of the plate material. Prototypes of plates with optimized topologies are manufactured at tested to validate the developed theoretical model. The performance characteristics of plates optimized for different frequency ranges are determined and compared with the theoretical predictions of the developed mathematical model. A close agreement is observed between theory and experiments. The presented topology optimization approach can be an invaluable tool in the design of a wide variety of critical structures which must operate quietly when subjected to fluid loading
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