Papers by Helder Carriço Rodrigues
This work deals with a one-dimensional mechanical system that contains precompressed spring eleme... more This work deals with a one-dimensional mechanical system that contains precompressed spring elements whereby exhibiting negative stiffness in certain region. Nonlinearity of the pre-compressed elements is the main concern here. Stationary points and their stability with respect to pre-compression and stiffness of a stabilizing element are investigated. The time domain response to harmonic kinematical loading as well as to harmonic force are computed numerically and compared. Steady state is computed for various combinations of parameters and the results are interpreted in view of using the system in passive vibration damping.
Lecture Notes in Computer Science, 2003
The method is developed for multi-objective optimization problems. Its purpose is to evolve an ev... more The method is developed for multi-objective optimization problems. Its purpose is to evolve an evenly distributed group of solutions to determine the optimum Pareto set for a given problem. The algorithm determines a set of solutions (a population), this population being sorted by its domination properties and a filter is defined in order to retain the Pareto solutions. In most topology design problem volume is in general a constraint of the problem. Due to this constraint, all chromosomes used in the genetic algorithm 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 to define these chromosomes and to create corresponding operators of crossover and mutation which preserve volume. To reduce computational effort, optimal solutions of each of the singleobjective problems are introduced in the initial population. Results obtained by the evolutionary and classical methods are compared.
Recent progress in material processing and manufacturing have motivated increased interest of the... more Recent progress in material processing and manufacturing have motivated increased interest of the scientific community in material optimization. Tailoring material properties to achieve the optimal response to a given solicitation provides an important input to the new materials development. This paper is focused on material model identification and posterior optimization of its material parameters in order to achieve zero dynamic reaction (zero transmissibility) in passive vibration one-dimensional controllers. Material models that allow for zero dynamic reaction are identified by analytical evaluation of transmissibility. Then parameters characterizing non-linear behaviour of selected components of the chosen material model are optimized by generic probabilistic metaheuristic algorithm simulated annealing. The optimization procedure is programmed within MATLAB environment. It is concluded that optimized designs have no distinguished feature and moreover the corresponding reaction suffer from high reaction peak in the initial transient region. Therefore optimization is extended to the transient region as well. Then plateau at the equilibrium force level is clearly identifiable.
Proceedings of the Ninth International Conference on Computational Structures Technology
The aim of this contribution is to extend the techniques of composite materials design to non-lin... more The aim of this contribution is to extend the techniques of composite materials design to non-linear material behaviour and apply it for design of new materials for passive vibration control. As a first step a computational tool allowing determination of macroscopic optimized one-dimensional isolator behaviour was developed. Voigt, Maxwell, standard and more complex material models can be implemented. Objective function considers minimization of the initial reaction and/or displacement peak as well as minimization of the steady-state amplitude of reaction and/or displacement. The complex stiffness approach is used to formulate the governing equations in an efficient way. Material stiffness parameters are assumed as non-linear functions of the displacement. The numerical solution is performed in the complex space. The steady-state solution in the complex space is obtained by an iterative process based on the shooting method which imposes the conditions of periodicity with respect to the known value of the period. Extension of the shooting method to the complex space is presented and verified. Non-linear behaviour of material parameters is then optimized by generic probabilistic meta-algorithm, simulated annealing. Dependence of the global optimum on several combinations of leading parameters of the simulated annealing procedure, like neighbourhood definition and annealing schedule, is also studied and analyzed. Procedure is programmed in MATLAB environment.
Structural and Multidisciplinary Optimization, 2009
Topology optimization consists in finding the spatial distribution of a given total volume of mat... more Topology optimization consists in finding the spatial distribution of a given total volume of material for the resulting structure to have some optimal property, for instance, maximization of structural stiffness or maximization of the fundamental eigenfrequency. In this paper a Genetic Algorithm (GA) employing a representation method based on trees is developed to generate initial feasible individuals that remain feasible upon crossover and mutation and as such do not require any repairing operator to ensure feasibility. Several application examples are studied involving the topology optimization of structures where the objective functions is the maximization of the stiffness and the maximization of the first and the second eigenfrequencies of a plate, all cases having a prescribed material volume constraint.
Structural and Multidisciplinary Optimization, 2010
The contribution of optimization has been essential to the more recent developments in design of ... more The contribution of optimization has been essential to the more recent developments in design of new mechanical structures and materials. The objective of this work is to apply the models of material and structural optimization to the design of passive vibration isolators. A computational tool to identify the optimal viscoelastic characteristics of a nonlinear one-dimensional isolator was developed. The cost functional involves the minimization of a weighted average of the maximum transient and steady state response amplitudes for a set of predefined dynamic loads. The optimal isolator behaviour is obtained by a simulated annealing method. The solutions obtained are analyzed and discussed concerning their dependence on the applied forces and objective function selection. The results obtained can facilitate the design of elastomeric materials with improved behaviour in terms of dynamic stiffness for passive vibration control.
Multiobjective topology optimization of structures using genetic algorithms with chromosome repairing
Structural and Multidisciplinary Optimization, 2006
In this work, a genetic algorithm (GA) for multiobjective topology optimization of linear elastic... more 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
Engineering Optimization 2014, 2014
Engineering Computations, 2018
Purpose This study aims to achieve a “pseudo-ductile” behaviour in the response of hybrid fibre r... more Purpose This study aims to achieve a “pseudo-ductile” behaviour in the response of hybrid fibre reinforced composites under uniaxial traction by solving properly formulated optimization problems. Design/methodology/approach The composite material model is based on the combination of different types of fibres (with different failure strains or strengths) embedded in a polymer matrix. The composite failure under tensile load is predicted by analytical models. An optimization problem formulation is proposed and a Genetic Algorithm is used. Multi-objective optimization problems balancing failure strength and ductility criteria are solved providing optimal mixtures of fibres whose properties may come either from a pre-defined list of materials, currently available in the market, or simply assuming their continuum variation within predefined bounds, in an attempt to attain unprecedented performance levels. Findings Optimal solutions of hybrid fibre reinforced composites exhibiting pseudo-...
7th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, 1998
Structural Optimization, 1999
A method is presented for the prediction of optimal configurations for two-materiai composite con... more A method is presented for the prediction of optimal configurations for two-materiai composite continuum structures. In the model for this method, both local properties and topology for the stiffer of the two materials are to be predicted. The properties of the second, less stiff material are specified and remain fixed. At the start of the procedure for computational solution, material composition of the structure is represented as a pure mixture of the two materials. This design becomes modified in subsequent steps into a form comprised of a skeleton of concentrated stiffer material, together with a nonoverlapping distribution of the second material to fill the original domain. Computational solutions are presented for two example design problems. A comparison among solutions for different ratios of stiffness between the two materials gives an indication of how the distribution of concentrated stiffer material varies with this factor. An example is presented as well to show how the method can be used to predict an efficient layout for rib-reinforcement of a stamped sheet metal panel.
Engineering Optimization 2014, 2014
This paper has the aim of designing laminated composite structures to maximize vibration frequenc... more This paper has the aim of designing laminated composite structures to maximize vibration frequencies using concepts of hierarchical topology optimization, a structural optimization branch whose purpose is to simultaneously design the material distribution layout of a structure in two distinct levels: One macromechanical (or structural, global) and the other micro-mechanical (or material, local). In the macro-level, design in terms of optimal material distribution on the general layout of the structure is taken into account. In the microlevel, the constitutive properties optimal design is searched, in terms of defining the distribution of material phases in unit cells of microstructure. This general approach is here extended to the laminated composites of interest: At the macro-level, optimal orientations and fiber volume fractions are defined for unidirectional composite material layers and, at the micro-level, it is designed the shape of the reinforcement fibers. The objective is to maximize the first and second natural vibration frequencies of laminated plates subjected to constraints on the limit of total fiber volume fraction employed. In this problem multiple eigenvalues are possible, leading to non-differentiability.
8th Symposium on Multidisciplinary Analysis and Optimization, 2000
A brief review of different strategies for designing simultaneously the global structural topolog... more A brief review of different strategies for designing simultaneously the global structural topology and the local material properties is presented. Different treatments have been developed in the last decade to design the stiffest continuum structure using the concept of material distribution introduced in 1988 by Bends0e and Kikuchi. The comparison of such treatments shows a trend towards simplification, as expected, and also towards unification of metrics that allows the expression of design variables, objective functions, and constraints in a single basis. Numerical examples are presented to show the capabilities of the 'natural basis' treatment introduced by Taylor in 1998.
Journal of Applied Physics, 2009
It is demonstrated based on continuum mechanics modeling and simulation that it is possible to ob... more It is demonstrated based on continuum mechanics modeling and simulation that it is possible to obtain polycrystalline ceramic ferroelectric (FE) materials which beggar single crystals in electromechanical properties. The local inhomogeneities at the FE domain-scale level due to spontaneous polarization and the underlying anisotropy are taken into consideration in the framework of mathematical homogenization of physical properties in FE materials. The intrinsic randomness of the spatial distribution of polarization is shown to be judiciously employed for the design of better polycrystalline FEs. The noncollinear rotation of the net polarization vectors embedded in crystallites of the ceramic FEs is demonstrated to play the key role in the enhancement of physical properties.
Composite Structures, 2014
The aim of this work is to perform hierarchical optimization in laminated composite structures, c... more The aim of this work is to perform hierarchical optimization in laminated composite structures, considering simultaneously macroscopic and microscopic levels in the design of structure and material. The macroscopic level takes into account orientations and fiber volume fractions of unidirectional composite layers. The microscopic level considers the cross-sectional size and shape of the reinforcement fibers, assuming them elliptical. Both levels are coupled by a resource constraint and exchange derivatives in a mathematically consistent manner. The objective is to minimize compliance under a total fiber volume fraction constraint. The variation of the fibers' size and shape is considered by response surfaces for constitutive parameters of a reinforced lamina. Such surfaces are built from data evaluated by asymptotic homogenization techniques. The plies orientations are chosen using the Discrete Material Optimization (DMO) approach. Results in laminated plates show the influence of the reinforcement fibers' shape and volume fraction in their global behavior. The optimal microstructures obtained vary with the loading conditions considered. It is shown that the present optimization procedure permits to increase structural stiffness when material microstructural characteristics are considered. Moreover, an assessment of layers' microstructural stresses is carried out in order to evaluate the fibers' shape influence on stress concentrations.
The focus of this paper is on the compliance minimization of composite structures. It assumes a m... more The focus of this paper is on the compliance minimization of composite structures. It assumes a mixed set of micro and macro independent design variables, to characterize the distribution of two materials to obtain the optimal composite microstructures at the micro design level as well as the optimal fiber orientation at the macro level.
Proceedings of the 4th International Conference on Engineering Optimization
This paper has the aim of designing laminated composite structures to maximize vibration frequenc... more This paper has the aim of designing laminated composite structures to maximize vibration frequencies using concepts of hierarchical topology optimization, a structural optimization branch whose purpose is to simultaneously design the material distribution layout of a structure in two distinct levels: one macro-mechanical (or structural, global) and the other micro-mechanical (or material, local). In the macro-level, design in terms of optimal material distribution on the general layout of the structure is taken into account. In the micro-level, the constitutive properties optimal design is searched, in terms of defining the distribution of material phases in unit cells of microstructure. This general approach is here extended to the laminated composites of interest: at the macro-level, optimal orientations and fiber volume fractions are defined for unidirectional composite material layers and, at the micro-level, it is designed the shape of the reinforcement fibers. The objective is to maximize the first and second natural vibration frequencies of laminated plates subjected to constraints on the limit of total fiber volume fraction employed. In this problem multiple eigenvalues are possible, leading to non-differentiability.
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Papers by Helder Carriço Rodrigues