Reliability analysis of smart laminated composite plates under static loads using artificial neural networks

The applications of smart structures with integrated piezoelectric elements have been expanding in the last few decades due to the abilities of such structures to withstand mechanical loads and operate as sensors or actuators using their electromechanical coupling. The available manufacturing techniques can result in uncertainties in the structure's geometric parameters, which, coupled with uncertainties in material properties, can lead to unexpected failures or unreliable performance. This paper presents a reliability analysis of a smart laminated composite plate made of a graphite/epoxy cross-ply substrate with a piezoelectric fiber-reinforced composite (PFRC) actuator layer under static electrical and mechanical loads. A coupled finite element (FE) model was developed in COMSOL Multiphysics, from which nondimensional stresses and displacements were calculated. To investigate the effects of randomness in the material and geometric properties, an artificial neural network (ANN) model was developed and trained using generated FE data. Monte Carlo Simulation (MCS) and First- and Second-Order Reliability Methods (FORM/SORM) were then used to shed light on the significance of considering randomness in the various material and geometric parameters and the effect of such uncertainty on the resulting nondimensional stresses and displacements. A coefficient of variation (CV) study identified the piezoelectric stress coefficient as the most significant contributing factor to the variation of all nondimensional parameters. Variation in the nondimensional parameters also increases under the application of an electric load. ANN-based FORM, SORM, and MCS all indicate a pattern of low probability of failure until a threshold value of about 3% of input parameter variation is reached, beyond which there is a rapid nonlinear increase in failure probability with increasing input parameter variation.