@article{Martínez-Frutos2018b,

title = {Structural optimization under internal porosity constraints using topological derivatives},

author = {Jesús Martínez-Frutos and Grégoire Allaire and Charles Dapogny and Francisco Periago},

url = {https://hal.archives-ouvertes.fr/hal-01790472v1 

https://www.sciencedirect.com/science/article/pii/S0045782518305401},

doi = {https://doi.org/10.1016/j.cma.2018.10.036},

year  = {2019},

date = {2019-01-01},

urldate = {2019-01-01},

journal = {Computer Methods in Applied Mechanics and Engineering},

volume = {345},

pages = {1-25},

abstract = {Porosity is a well-known phenomenon occurring during various manufacturing processes (casting, welding, additive manufacturing) of solid structures, which undermines their reliability and mechanical performance. The main purpose of this article is to introduce a new constraint functional of the domain which controls the negative impact of porosity on elastic structures in the framework of shape and topology optimization. The main ingredient of our modeling is the notion of topological derivative, which is used in a slightly unusual way: instead of being an indicator of where to nucleate holes in the course of the optimization process, it is a component of a new constraint functional which assesses the influence of pores on the mechanical performance of structures. The shape derivative of this constraint is calculated and incorporated into a level set based shape optimization algorithm. Our approach is illustrated by several two- and three-dimensional numerical experiments of topology optimization problems constrained by a control on the porosity effect.},

keywords = {19274/PI/14},

pubstate = {published},

tppubtype = {article}

}

@article{Marín2018b,

title = {A polynomial chaos-based approach to risk-averse piezoelectric control of random vibrations of beams},

author = {Francisco J. Marín and Jesús Martínez-Frutos and Francisco Periago},

url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.5823},

issn = {1097-0207},

year  = {2018},

date = {2018-08-10},

urldate = {2018-08-10},

journal = {International Journal for Numerical Methods in Engineering},

volume = {115},

number = {6},

pages = {738-755},

abstract = {This paper proposes a risk-averse formulation for the problem of piezoelectric control of random vibrations of elastic structures. The proposed formulation, inspired by the notion of risk aversion in Economy, is applied to the piezoelectric control of a Bernoulli-Euler beam subjected to uncertainties in its input data. To address the high computational burden associated to the presence of random fields in the model and the discontinuities involved in the cost functional and its gradient, a combination of a non-intrusive anisotropic polynomial chaos approach for uncertainty propagation with a Monte Carlo sampling method is proposed. In a first part, the well-posedness of the control problem is established by proving the existence of optimal controls. In a second part, an adaptive gradient-based method is proposed for the numerical resolution of the problem. Several experiments illustrate the performance of the proposed approach and the significant differences that may occur between the classical deterministic formulation of the problem and its stochastic risk-averse counterpart.},

keywords = {19274/PI/14},

pubstate = {published},

tppubtype = {article}

}

@article{JMF_CMAME_2017,

title = {Risk-averse structural topology optimization under random fields using stochastic expansion methods},

author = {Jesús Martínez-Frutos and Mathieu Kessler and Francisco Periago},

url = {https://www.sciencedirect.com/science/article/pii/S0045782517306990 

http://www.upct.es/mc3/files/JMF/riskaverse_cmame.pdf},

issn = {0045-7825},

year  = {2018},

date = {2018-03-01},

urldate = {2018-03-01},

journal = {Computer Methods in Applied Mechanics and Engineering},

volume = {330},

pages = {180-206},

abstract = {This work proposes a level-set based approach for solving risk-averse structural topology optimization problems considering random field loading and material uncertainty. The use of random fields increases the dimensionality of the stochastic domain, which poses several computational challenges related to the minimization of the Excess Probability as a measure of risk awareness. This problem is addressed both from the theoretical and numerical viewpoints. First, an existence result under a typical geometrical constraint on the set of admissible shapes is proved. Second, a level-set continuous approach to find the numerical solution of the problem is proposed. Since the considered cost functional has a discontinuous integrand, the numerical approximation of the functional and its sensitivity combine an adaptive anisotropic Polynomial Chaos (PC) approach with a Monte-Carlo (MC) sampling method for uncertainty propagation. Furthermore, to address the increment of dimensionality induced by the random field, an anisotropic sparse grid stochastic collocation method is used for the efficient computation of the PC coefficients. A key point is that the non-intrusive nature of such an approach facilitates the use of High Performance Computing (HPC) to alleviate the computational burden of the problem. Several numerical experiments including random field loading and material uncertainty are presented to show the feasibility of the proposal.},

keywords = {19274/PI/14},

pubstate = {published},

tppubtype = {article}

}

@article{Marín2017,

title = {Robust Averaged Control of Vibrations for the Bernoulli-Euler Beam Equation},

author = {Francisco J. Marín and Jesús Martínez-Frutos and Francisco Periago},

url = {https://doi.org/10.1007/s10957-017-1128-x 

http://localhost/mc3/files/FPE/marin_17.pdf},

doi = {10.1007/s10957-017-1128-x},

issn = {1573-2878},

year  = {2017},

date = {2017-08-01},

urldate = {2017-08-01},

journal = {Journal of Optimization Theory and Applications},

volume = {174},

number = {2},

pages = {428–454},

abstract = {This paper proposes an approach for the robust averaged control of random vibrations for the Bernoulli–Euler beam equation under uncertainty in the flexural stiffness and in the initial conditions. The problem is formulated in the framework of optimal control theory and provides a functional setting, which is so general as to include different types of random variables and second-order random fields as sources of uncertainty. The second-order statistical moment of the random system response at the control time is incorporated in the cost functional as a measure of robustness. The numerical resolution method combines a classical descent method with an adaptive anisotropic stochastic collocation method for the numerical approximation of the statistics of interest. The direct and adjoint stochastic systems are uncoupled, which permits to exploit parallel computing architectures to solve the set of deterministic problem that arise from the stochastic collocation method. As a result, problems with a relative large number of random variables can be solved with a reasonable computational cost. Two numerical experiments illustrate both the performance of the proposed method and the significant differences that may occur when uncertainty is incorporated in this type of control problems.},

keywords = {19274/PI/14},

pubstate = {published},

tppubtype = {article}

}

@article{NME:NME5210,

title = {Robust optimal Robin boundary control for the transient heat equation with random input data},

author = {Jesús Martínez-Frutos and Mathieu Kessler and Arnaud Münch and Francisco Periago},

url = {http://dx.doi.org/10.1002/nme.5210 

http://localhost/mc3/files/FPE/ijnme_16.pdf},

doi = {10.1002/nme.5210},

issn = {1097-0207},

year  = {2016},

date = {2016-03-02},

urldate = {2016-03-02},

journal = {International Journal for Numerical Methods in Engineering},

volume = {108},

number = {2},

pages = {116–135},

abstract = {The problem of robust optimal Robin boundary control for a parabolic partial differential equation with uncertain input data is considered. As a measure of robustness, the variance of the random system response is included in two different cost functionals. Uncertainties in both the underlying state equation and the control variable are quantified through random fields. The paper is mainly concerned with the numerical resolution of the problem. To this end, a gradient-based method is proposed considering different functional costs to achieve the robustness of the system. An adaptive anisotropic sparse grid stochastic collocation method is used for the numerical resolution of the associated state and adjoint state equations. The different functional costs are analysed in terms of computational efficiency and its capability to provide robust solutions. Two numerical experiments illustrate the performance of the algorithm. Copyright © 2016 John Wiley & Sons, Ltd.},

keywords = {19274/PI/14},

pubstate = {published},

tppubtype = {article}

}

@article{MARTINEZFRUTOS2016271,

title = {Robust shape optimization of continuous structures via the level set method},

author = {Jesús Martínez-Frutos and Mathieu Kessler and Francisco Periago},

url = {http://www.sciencedirect.com/science/article/pii/S0045782516300834 

http://localhost/mc3/files/FPE/cmame16.pdf},

doi = {https://doi.org/10.1016/j.cma.2016.03.003},

issn = {0045-7825},

year  = {2016},

date = {2016-01-15},

urldate = {2016-01-15},

journal = {Computer Methods in Applied Mechanics and Engineering},

volume = {305},

number = {Supplement C},

pages = {271 - 291},

abstract = {Abstract This work proposes a stochastic shape optimization method for continuous structures using the level-set method. Such a method aims to minimize the expected compliance and its variance as measures of the structural robustness. The behavior of continuous structures is modeled by linear elasticity equations with uncertain loading and material. This uncertainty can be modeled using random variables with different probability distributions as well as random fields. The proper problem formulation is ensured by the proof of the existence colorrev of solution under certain geometrical constraints on the set of admissible shapes. The proposed method addresses the stochastic linear elasticity problem in its weak form obtaining the explicit expressions for the continuous shape derivatives. Some numerical examples are presented to show the effectiveness of the proposed approach.},

keywords = {19274/PI/14},

pubstate = {published},

tppubtype = {article}

}

@article{Martínez-Frutos2015,

title = {Robust optimal shape design for an elliptic PDE with uncertainty in its input data},

author = {Jesús Martínez-Frutos and Mathieu Kessler and Francisco Periago},

doi = {10.1051/cocv/2014049},

issn = {1262-3377},

year  = {2015},

date = {2015-05-20},

urldate = {2015-05-20},

journal = {ESAIM: COCV},

volume = {21},

number = {4},

pages = {901--923},

publisher = {EDP Sciences},

keywords = {19274/PI/14, Computational Mathematics, Control and Optimization, Control and Systems Engineering},

pubstate = {published},

tppubtype = {article}

}