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- Multiobjective optimization for node adaptation in the analysis of composite plates using a meshless collocation methodPublication . Roque, C. M. C.; Madeira, JFA; Ferreira, A .J. M.The bending of simply supported composite plates is analyzed using a direct collocation meshless numerical method. In order to optimize node distribution the Direct MultiSearch (DMS) for multi-objective optimization method is applied. In addition, the method optimizes the shape parameter in radial basis functions. The optimization algorithm was able to find good solutions for a large variety of nodes distribution.
- Multiobjective optimization of cold-formed steel columnsPublication . Madeira, JFA; Dias, Joaquim; Silvestre, NunoThe optimal design of cold-formed steel columns is addressed in this paper, with two objectives: maximize the local-global buckling strength and maximize the distortional buckling strength. The design variables of the problem are the angles of orientation of cross-section wall elements the thickness and width of the steel sheet that forms the cross-section are fixed. The elastic local, distortional and global buckling loads are determined using Finite Strip Method (CUFSM) and the strength of cold-formed steel columns (with given length) is calculated using the Direct Strength Method (DSM). The bi-objective optimization problem is solved using the Direct MultiSearch (DMS) method, which does not use any derivatives of the objective functions. Trade-off Pareto optimal fronts are obtained separately for symmetric and anti-symmetric cross-section shapes. The results are analyzed and further discussed, and some interesting conclusions about the individual strengths (local-global and distortional) are found.
- Optimal distribution of active piezoelectric elements for noise attenuation in sandwich panelsPublication . Madeira, JFA; Araújo, A. L.In this paper, a multiobjective optimization approach for obtaining the optimal distribution of surface-bonded piezoelectric sensors and actuators for noise attenuation in sandwich panels is presented. The noise attenuation is achieved by using negative velocity feedback control with co-located sensors and actuators. The control gains are also optimized in order to obtain the most efficient noise attenuation in a given frequency band. An in-house implementation of a viscoelastic soft core sandwich plate finite element, including surface-bonded piezoelectric sensors and actuators with active control capabilities, is used for obtaining the frequency response of the panels. The sound transmission capability of the panels is evaluated using the radiated sound power, along with the Rayleigh integral approach, which is suitable for lightly coupled structural/acoustic problems. The Direct MultiSearch (DMS) optimization algorithm is used to minimize the added weight due to the piezoelectric material, minimizing also the number of required controllers and maximizing the noise attenuation. The total length of the radiated sound power curve is shown to be an effective measure of noise attenuation in a given frequency band. Trade-off Pareto fronts and the obtained optimal configurations are presented and discussed.
- Optimal multiobjective design of a vehicle restraint system using pre-acting control: A limiting performance analysisPublication . Moita, Paulo Jorge Pires; Madeira, Jose Firmino Aguilar; Valido, Aníbal; Cardoso, João BarradasPurpose – The purpose of this paper is to perform the limiting performance analysis of a vehicle restraint system (seat belt) in order to find the optimal control force, and its pre-acting time that minimizes the risk of injury. Design/methodology/approach – A discrete model of the human thorax is used. A multiobjective optimum design problem is formulated in order to minimize the risk of injuries in case of impact. Several injury criteria are minimized and are required to remain below a safety threshold value. Findings – The authors found which of the objectives are contradictory and which are not. Several of the optimal sets of design variables are analyzed and their performance compared to one another.The results are also compared to the case of not taking in account the pre-acting time. As expected,the results in this case are worse. Research limitations/implications – As with all limiting performance analysis, the technological implementation restraints of the control force are not taken into account. As such, the solutions must be considered a benchmark to which the actual solution can be compared to. Practical implications – The limiting performance analysis concept allows us to have a theoretical benchmark to which the real control performance can be compared to. Originality/value – As far as the authors know, the pre-acting time, and it simplications on the improvement of the performance of the control system, is an original contribution to the problem the authors tried to solve.
- Multiobjective topology optimization of structures using genetic algorithms with chromosome repairingPublication . Madeira, JFA; Rodrigues, H. C.; Pina, H.In this work, a genetic algorithm (GA) for multiobjective topology optimization of linear elastic structures is developed. Its purpose is to evolve an evenly distributed group of solutions to determine the optimum Pareto set for a given problem. The GA determines a set of solutions to be sorted by its domination properties and a filter is defined to retain the Pareto solutions. As an equality constraint on volume has to be enforced, all chromosomes used in the genetic GA must generate individuals with the same volume value; in the coding adopted, this means that they must preserve the same number of “ones” and, implicitly, the same number of “zeros” along the evolutionary process. It is thus necessary: (1) to define chromosomes satisfying this propriety and (2) to create corresponding crossover and mutation operators which preserve volume. Optimal solutions of each of the single-objective problems are introduced in the initial population to reduce computational effort and a repairing mechanism is developed to increase the number of admissible structures in the populations. Also, as the work of the external loads can be calculated independently for each individual, parallel processing was used in its evaluation. Numerical applications involving two and three objective functions in 2D and two objective functions in3Dare employed as tests for the computational model developed. Moreover, results obtained with and without chromosome repairing are compared.
- Multiobjective optimization solutions for noise reduction in composite sandwich panels using active controlPublication . Araújo, A. L.; Madeira, JFAIn this paper, optimal solutions for noise reduction in laminated viscoelastic soft core sandwich plates are obtained, using active control with surface bonded piezoelectric sensors and actuators. An in–house finite element implementation of the active laminated sandwich plate is used to obtain the frequency response of the panels. Since the structural/acoustic problem is lightly coupled, the sound transmission characteristics of the panels are evaluated by computing their radiated sound power, using the Rayleigh integral method. A negative velocity feedback control law has been used to implement the active damping. The optimal location of the surface co-located pairs of piezoelectric patches is then obtained, using the Direct MultiSearch (DMS) optimization algorithm to minimize simultaneously the added weight, the number of controllers and noise radiation. The minimization of noise radiation is accomplished by minimizing the total length of the radiated sound power frequency response curve. Trade-off Pareto fronts and the respective optimal active patch configurations are obtained and discussed.
- Multiobjective design optimization of laminated composite plates with piezoelectric layersPublication . Franco Correia, Victor; Madeira, JFA; Araújo, Aurélio L.; Mota Soares, Cristóvão ManuelA methodology of multiobjective design optimization of laminated composite plates with piezoelectric layers is presented in this paper. Constrained optimization is conducted for different behaviour objectives, like the maximization of buckling load or natural frequencies of specific vibration modes or prescribed displacements for example. Weight minimization can also be considered or the minimization of the electric voltages applied in the piezoelectric actuators. The optimization problems are constrained by stress based failure criteria and other structural response constraints like limits imposed on certain displacements, buckling characteristics and natural frequency constraints. The design variables considered in the present work are the fiber reinforcement orientations in the composite layers, thicknesses of individual layers and the electric potentials applied to the actuators. The optimization problems are solved with two direct search derivative-free algorithms: GLODS (Global and Local Optimization using Direct Search) and DMS (Direct MultiSearch). DMS, the multiobjective optimization solver, is started from a set of local minimizers which are initially determined by the global optimizer algorithm GLODS for each one of the objective functions.
- Optimal passive shunted damping configurations for noise reduction in sandwich panelsPublication . Araújo, Aurélio L.; Madeira, JFAThis article addresses the issue of vibration and noise reduction in laminated sandwich plates using piezoelectric patches with passive shunted damping. A finite element implementation of a laminated sandwich plate with viscoelastic core and surface bonded piezoelectric patches is used to obtain the frequency response of the panels. The sound transmission characteristics of the panels are evaluated by computing their radiated sound power using the Rayleigh integral method. Resistor and inductor shunt damping circuits are used to add damping to the sandwich panels. The optimal location of the surface-bonded piezoelectric patches is then obtained, along with the resistor and inductor circuits resistance and inductance, using direct multisearch optimization to minimize added weight, number of patches, and noise radiation. Tradeoff Pareto optimal fronts and the respective optimal patch configurations are obtained.
- Multiobjective optimization of viscoelastic laminated sandwich structures using the Direct MultiSearch methodPublication . Madeira, JFA; Araújo, A.L.; Mota Soares, C.M.; Mota Soares, C.A.A multiobjective approach for optimization of passive damping for vibration reduction in sandwich structures is presented in this paper. Constrained optimization is conducted for maximization of modal loss factors and minimization of weight of sandwich beams and plates with elastic laminated constraining layers and a viscoelastic core, with layer thickness and material and laminate layer ply orientation angles as design variables. The problem is solved using the Direct MultiSearch (DMS) solver for derivative-free multiobjective optimization and solutions are compared with alternative ones obtained using genetic algorithms.
- Optimal multiobjective design of a vehicle restraint system using pre-acting control: A limiting performance analysisPublication . Moita, Paulo Jorge Pires; Madeira, JFA; Valido, Aníbal J. J.; Cardoso, João BarradasPurpose – The purpose of this paper is to performthe limiting performance analysis of a vehicle restraint system (seat belt) in order to find the optimal control force, and its pre-acting time that minimizes the risk of injury. Design/methodology/approach – A discrete model of the human thorax is used. A multiobjective optimum design problem is formulated in order to minimize the risk of injuries in case of impact. Several injury criteria are minimized and are required to remain below a safety threshold value. Findings – The authors found which of the objectives are contradictory and which are not. Several of the optimal sets of design variables are analyzed and their performance compared to one another. The results are also compared to the case of not taking in account the pre-acting time. As expected, the results in this case are worse. Research limitations/implications – As with all limiting performance analysis, the technological implementation restraints of the control force are not taken into account. As such, the solutions must be considered a benchmark to which the actual solution can be compared to. Practical implications – The limiting performance analysis concept allows us to have a theoretical benchmark to which the real control performance can be compared to. Originality/value – As far as the authors know, the pre-acting time, and its implications on the improvement of the performance of the control system, is an original contribution to the problem the authors tried to solve.