Neural Network-Based Second Order Reliability Method(NNBSORM)for Laminated Composite Plates in Free Vibration

Monte Carlo Simulations(MCS),commonly used for reliability analysis,require a large amount of data points to obtain acceptable accuracy,even if the Subset Simulation with Importance Sampling(SS/IS)methods are used.The Second Order Reliability Method(SORM)has proved to be an excellent rapid tool in the stochastic analysis of laminated composite structures,when compared to the slower MCS techniques.However,SORM requires differentiating the performance function with respect to each of the random variables involved in the simulation.The most suitable approach to do this is to use a symbolic solver,which renders the simulations very slow,although still faster than MCS.Moreover,the inability to obtain the derivative of the performance function with respect to some parameters,such as ply thickness,limits the capabilities of the classical SORM.In this work,a Neural Network-Based Second Order Reliability Method(NNBSORM)is developed to replace the finite element algorithm in the stochastic analysis of laminated composite plates in free vibration.Because of the ability to obtain expressions for the first and second derivatives of the NN system outputs with respect to any of its inputs,such as material properties,ply thicknesses and orientation angles,the need for using a symbolic solver to calculate the derivatives of the performance function no longer exists.The proposed approach is accordingly much faster,and easily allows for the consideration of ply thickness uncertainty.The present analysis showed that dealing with ply thicknesses as random variables results in 37%increase in the laminate’s probability of failure.