Reliability analysis of smart composite structures using artificial neural networks

Composite structures are prevalent in many industries for their flexibility in design, and because they are relatively lightweight yet retain a high strength. This is achieved through the integration of two or more constituents in such a way as to achieve desirable properties unavailable to the constituents individually. The incorporation of smart materials, such as piezoelectrics, can greatly extend and enhance their already numerous practical advantages, albeit at the cost of increased complexity. When further considering the inherent uncertainty in their manufacturing, processing, and assembly, it is apparent that the efficient study of randomness in the material and geometric properties of smart composite structures is essential. This research focuses on the application of Artificial Neural Networks towards the efficient reliability analysis of hybrid laminated composite structures with piezoelectric layers - smart composite structures. A MATLAB code was written to perform an initial stochastic analysis of laminated composite plates without piezoelectric layers under unidirectional tensile loading. This first-ply failure analysis is performed using Classical Lamination Theory. The MATLAB code calculates the strength ratios using maximum stress, Tsai-Hill, and Tsai-Wu failure criteria for composite plates of three different materials of various stacking sequences. The coefficient of variation of the strength ratios with respect to the coefficients of variation of the input material properties and laminate geometry are explored and comparisons are made with deterministic predictions. To validate the MATLAB model, the first-ply failure loads output by the code were compared against literature for a cross-ply graphite/epoxy laminate as well as a converged finite element model created using commercial finite element analysis software (SolidWorks 2019 Simulation Package), which show excellent agreement. The analysis of laminated composite plates with piezoelectric layers is performed using a different commercial mathematical modeling software for the simulation of the coupled electrical and mechanical domains. Two smart composite structures are developed in COMSOL to investigate the effects of randomness in the material and geometric properties in both a static and dynamic analysis which assume perfect bonding at the interfaces. A static analysis of a three-ply graphite/epoxy cross-ply substrate with a piezoelectric fiber-reinforced composite (PFRC) actuator layer under sinusoidal electrical and mechanical loads is performed to determine the non-dimensional in-plane normal and in-plane shear stresses and displacements. A dynamic analysis on a two-ply graphite/epoxy core with polyvinylidene fluoride (PVDF) piezoelectric layers on both top and bottom surfaces is performed to determine the fundamental frequency of the smart composite plate in free vibration. The hybrid plate COMSOL models for both the static and dynamic analyses performed were validated against results reported in published research. Artificial Neural Networks (ANNs) are implemented in two ways: using the built -in MATLAB Deep Learning Toolbox, and a custom MATLAB ANN code which implements Levenberg-Marquardt backpropagation. A custom ANN code is used in order to compare results with commercially-available software. The custom MATLAB ANN code and MATLAB's Deep Learning Toolbox ANN are validated against published research, returning test set errors on the order of magnitude of 10-3 or less. Finally, the reliability analysis code written in MATLAB to perform First- and Second-Order Reliability Methods (FORM and SORM) and ANN-based Monte Carlo Simulation is validated against published research. For the static study of the non-dimensional stresses and displacements of the smart composite at the interface between the substrate and PFRC layer, a coefficient of variation study identified the piezoelectric stress coefficient as the most significant contributing factor to the variation of all non-dimensional parameters, with the non-dimensional in-plane normal stress the resulting in the most sensitivity with increasing input variation. It is shown that the absence of randomness in the piezoelectric stress coefficient can cause significant overestimation of the reliability of the smart composite. FORM, SORM, and ANN-based MCS all indicate a pattern of low probability of failure until a threshold value is reached, beyond which there is a rapid increase in failure probability with increasing input variation. The non-dimensional in-plane normal and in-plane shear stresses are respectively the least and most susceptible to input CV, with both non-dimensional displacements similarly sensitive to input variation. All non-dimensional parameters begin to exhibit failure for input variation as little as 3%. The ANN-based reliability techniques were effective in dealing with the 36 total input variables in the dynamic study, which was the highest number of input variables considered in this research. A coefficient of variation study showed that the mechanical properties of the PVDF layers were generally the most significant contributing factors to the variation of the smart composite plate fundamental frequency, although variation in the thickness of the piezoelectric PVDF layers plays a larger role as the side-to-thickness ratio decreases. The overall magnitude of variation in the plate fundamental frequency with respect to input variation is generally much less than that of the static case for the smart composite plate with a PFRC actuator layer. Plates of all side-to-thickness ratios exhibit failure to reach 99% of the deterministic fundamental frequency for input variation of even 1% of the mean, with SORM indicating a failure probability of 0.1253 for thin plates, which are generally more vulnerable to failure than thick and moderately thick plates.