ISEP - Departamento de Matemática
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Browsing ISEP - Departamento de Matemática by Author "António, Carlos Conceição"
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- An approach for reliability-based robust design optimisation of angle-ply compositesPublication . António, Carlos Conceição; Hoffbauer, Luísa N.Variations of manufacturing process parameters and environmental aspects may affect the quality and performance of composite materials, which consequently affects their structural behaviour. Reliability-based design optimisation (RBDO) and robust design optimisation (RDO) searches for safe structural systems with minimal variability of response when subjected to uncertainties in material design parameters. An approach that simultaneously considers reliability and robustness is proposed in this paper. Depending on a given reliability index imposed on composite structures, a trade-off is established between the performance targets and robustness. Robustness is expressed in terms of the coefficient of variation of the constrained structural response weighted by its nominal value. The Pareto normed front is built and the nearest point to the origin is estimated as the best solution of the bi-objective optimisation problem.
- Bi-level dominance GA for minimum weight and maximum feasibility robustness of composite structuresPublication . António, Carlos Conceição; Hoffbauer, Luísa NatáliaIn the proposed approach the robust design optimization (RDO) of composite structures is addressed as a bi-objective optimization problem with following objective functions: (1) the weight of the structure which optimality is associated with performance robustness; and (2) the variability of structural response which is associated with feasibility robustness of design constraints. The determinant of the variance–covariance matrix of the response is adopted for feasibility robustness assessment, being the sensitivities calculated by the adjoint variable method. The design and uncertainty rules are controlled by the following classes of variables and parameters: the deterministic design variables, the random design variables, and the random parameters. To solve the RDO of composite structures an evolutionary algorithm, denoted by Bi-level Dominance Multi-Objective Genetic Algorithm (MOGA-2D) is proposed. The Pareto front is built using a hierarchical structure where evolution is based on the exchange data between two populations: a small population using local dominance and elitism and an enlarged population to store the non-dominated solutions. The numerical tests show the capabilities of the approach. Although the optimal Pareto front establishes the trade-off between performance and robustness, knowledge on the importance of each uncertainty source can help the designer to make a decision on design space.
- From local to global importance measures of uncertainty propagation in composite structuresPublication . António, Carlos Conceição; Hoffbauer, Luísa N.The influence of uncertainties of input parameters on output response of composite structures is investigated in this paper. In particular, the effects of deviations in mechanical properties, ply angles, ply thickness and on applied loads are studied. The uncertainty propagation and the importance measure of input parameters are analysed using three different approaches: a first-order local method, a Global Sensitivity Analysis (GSA) supported by a variance-based method and an extension of local variance to estimate the global variance over the domain of inputs. Sample results are shown for a shell composite laminated structure built with different composite systems including multi-materials. The importance measures of input parameters on structural response based on numerical results are established and discussed as a function of the anisotropy of composite materials. Needs for global variance methods are discussed by comparing the results obtained from different proposed methodologies. The objective of this paper is to contribute for the use of GSA techniques together with low expensive local importance measures.
- Optimal design of composite shells based on minimum weight and maximum feasibility robustnessPublication . António, Carlos Conceição; Hoffbauer, Luísa N.A robust design optimization (RDO) approach for minimum weight and safe shell composite structures with minimal variability into design constraints under uncertainties is proposed. A new concept of feasibility robustness associated to the variability of design constraints is considered. So, the feasibility robustness is defined through the determinant of variance–covariance matrix of constraint functions introducing in this way the joint effects of the uncertainty propagations on structural response. A new framework considering aleatory uncertainty into RDO of composite structures is proposed. So, three classes of variables and parameters are identified: deterministic design variables, random design variables and random parameters. The bi-objective optimization search is performed using on a new approach based on two levels of dominance denoted by Co- Dominance-based Genetic Algorithm (CoDGA). The use of evolutionary concepts together sensitivity analysis based on adjoint variable method is a new proposal. The examples with different sources of uncertainty show that the Pareto front definition depends on random design variables and/or random parameters considered in RDO. Furthermore, the importance to control the uncertainties on the feasibility of constraints is demonstrated. CoDGA approach is a powerfully tool to help designers to make decision establishing the priorities between performance and robustness.
- Uncertainty analysis based on sensitivity applied to angle-ply composite structuresPublication . António, Carlos Conceição; Hoffbauer, Luísa N.This article describes a finite element-based formulation for the statistical analysis of the response of stochastic structural composite systems whose material properties are described by random fields. A first-order technique is used to obtain the second-order statistics for the structural response considering means and variances of the displacement and stress fields of plate or shell composite structures. Propagation of uncertainties depends on sensitivities taken as measurement of variation effects. The adjoint variable method is used to obtain the sensitivity matrix. This method is appropriated for composite structures due to the large number of random input parameters. Dominant effects on the stochastic characteristics are studied analyzing the influence of different random parameters. In particular, a study of the anisotropy influence on uncertainties propagation of angle-ply composites is carried out based on the proposed approach.
- Uncertainty assessment approach for composite structures based on global sensitivity indicesPublication . António, Carlos Conceição; Hoffbauer, Luísa N.The problem of uncertainty propagation in composite laminate structures is studied. An approach based on the optimal design of composite structures to achieve a target reliability level is proposed. Using the Uniform Design Method (UDM), a set of design points is generated over a design domain centred at mean values of random variables, aimed at studying the space variability. The most critical Tsai number, the structural reliability index and the sensitivities are obtained for each UDM design point, using the maximum load obtained from optimal design search. Using the UDM design points as input/output patterns, an Artificial Neural Network (ANN) is developed based on supervised evolutionary learning. Finally, using the developed ANN a Monte Carlo simulation procedure is implemented and the variability of the structural response based on global sensitivity analysis (GSA) is studied. The GSA is based on the first order Sobol indices and relative sensitivities. An appropriate GSA algorithm aiming to obtain Sobol indices is proposed. The most important sources of uncertainty are identified.
- Uncertainty propagation in inverse reliability-based design of composite structuresPublication . António, Carlos Conceição; Hoffbauer, Luísa N.An approach for the analysis of uncertainty propagation in reliability-based design optimization of composite laminate structures is presented. Using the Uniform Design Method (UDM), a set of design points is generated over a domain centered on the mean reference values of the random variables. A methodology based on inverse optimal design of composite structures to achieve a specified reliability level is proposed, and the corresponding maximum load is outlined as a function of ply angle. Using the generated UDM design points as input/output patterns, an Artificial Neural Network (ANN) is developed based on an evolutionary learning process. Then, a Monte Carlo simulation using ANN development is performed to simulate the behavior of the critical Tsai number, structural reliability index, and their relative sensitivities as a function of the ply angle of laminates. The results are generated for uniformly distributed random variables on a domain centered on mean values. The statistical analysis of the results enables the study of the variability of the reliability index and its sensitivity relative to the ply angle. Numerical examples showing the utility of the approach for robust design of angle-ply laminates are presented.