Reliability analysis of output electrical response performance of multi-state flexoelectric structures under single and multiple failure modes

Abstract This paper proposes a reliability model of flexoelectric beams in the electrical open and short circuit states when different failure modes and the multiple failure modes of the output electrical response performances are considered, respectively. The reliability indices of the flexoelectric beams in the two circuit states can be defined based on the output electrical response models. Sequentially, the importance sampling (IS) and the mixed importance sampling (IS) methods are respectively used to calculate the reliability of the flexoelectric beams in single and multiple failure modes. The reliability results of the flexoelectric beams are verified by comparing them with the results of the Monte Carlo Simulation (MCS). The numerical results show that the flexoelectric beam is entered into a relatively safe and reliable state when the critical value of the open circuit voltage of 0.235 V and the thickness of the flexoelectric beams of 1 mm are considered as well as the length-thickness ratio of 20.