Reliability analysis-based conjugate map of beams reinforced by ZnO nanoparticles using sinusoidal shear deformation theory

First-order reliability method (FORM) is enhanced based on the search direction using relaxed conjugate reliability (RCR) approach for the embedded nanocomposite beam under buckling failure mode. The RCR method is formulated using discrete conjugate map with a limited scalar factor. A dynamical relaxed factor is proposed to control instability of proposed RCR, which is adjusted using sufficient descent condition. The characteristic of equivalent materials for nanocomposite beam are obtained by micro-electro-mechanical model. The probabilistic model of nanocomposite beam is simulated using the sinusoidal shear deformation theory (SSDT). The beam is subjected to external applied voltage in thickness direction and the surrounding elastic medium is modeled by Pasternak foundation. The governing equations are derived in terms of energy method and Hamilton's principal. Using exact solution, the implicit buckling limit state function of nanocomposite beam is proposed, which is involved various random variables including thickness of beam, length of beam, spring constant of foundation, shear constant of foundation, applied voltage, and volume fraction of ZnO nanoparticles in polymer. The robustness, accuracy and efficiency of proposed RCR method are evaluated for this engineering structural reliability problem. The results demonstrate that proposed RCR method is more accurate and robust than the excising reliability methods-based FORM. The volume fraction of ZnO nanoparticles and the applied voltage are the sensitive variables on the reliable levels of the nanocomposite beams.