Optimal design of composite shells based on minimum weight and maximum feasibility robustness
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Optimal design of composite shells based on minimum weight and maximum feasibility robustness Carlos Conceic¸a˜o Anto´nio . Luı´sa Nata´lia Hoffbauer
Received: 27 October 2015 / Accepted: 15 November 2015 Springer Science+Business Media Dordrecht 2015
Abstract 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 CoDominance-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 C. C. Anto´nio (&) Faculdade de Engenharia, University of Porto, Rua Dr.Roberto Frias, 4200-465 Porto, Portugal e-mail: [email protected] L. N. Hoffbauer Instituto Superior de Engenharia do Porto, Polytechnic School of Porto, Porto, Portugal
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. Keywords Bi-objective optimization Composite structures Feasibility robustness Uncertainty sources Sensitivity Co-dominance
1 Introduction The robust design optimization (RDO) of composite structures is currently a very important area of research. Indeed, the principal objective of robust design is to improve product quality by minimising the uncertainty effects or stabilising variations in structural response without eliminating their causes. RDO applied to composite structures under probabilistic constraints is a very important field due to uncertainties associated with physical properties of fibrereinforced composites. Adali et al. (2003) developed a model aimed at the optimal design of composite laminates under buckling load uncertainty. In this model loads belong to a given uncertainty domain. Walker and Hamilton (2005) described a procedure to design symmetric laminates for maximum buckling load under manufacturing uncertainty in ply angle
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C. C. Anto´nio, L. N. Hoffbauer
design variable. Gumbert and Newman (2005) analysed the effect of geometric uncertainty in shape parameters in a 3-D fle
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