Uncertainty propagation in inverse reliability-based design of composite structures

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Uncertainty propagation in inverse reliability-based design of composite structures Carlos Conceic¸a˜o Anto´nio • Luı´sa N. Hoffbauer

Received: 1 December 2009 / Accepted: 31 March 2010 / Published online: 10 April 2010  Springer Science+Business Media, B.V. 2010

Abstract 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 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 e-mail: [email protected]

examples showing the utility of the approach for robust design of angle-ply laminates are presented. Keywords Composite structures  Uncertainty propagation  Inverse RBDO  Uniform Design Method  Artificial Neural Network  Monte Carlo simulation  Reliability index variability  Relative sensitivities

1 Introduction The most realistic failure analysis of structures under uncertainty is associated with the use of reliability analysis methods. Therefore, the need for reliability analysis associated with optimal design with respect to composite structures has increased in the last 15 years, and reliability-based design optimization (RBDO) of composite structures is currently a very important area of research (Adali et al. 2003; Boyer et al. 1997; Carbillet et al. 2009; Anto´nio et al. 1996, 2001; Rais-Rohani and Singh 2004; Salas and Venkataraman 2009; Teters and Kregers 1997). Approximate reliability methods, such as the first order (FORM) or second order (SORM) reliability methods, use the so-called most probable failure point (MPP) to estimate the failure probability (Melchers 1999). The applicability of approximate reliability methods depends on the number of uncertainty parameters involved and degree of nonlinearity of the system response. In the ladder case, it is necessary to

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use simulation techniques such as Mo