Optimization and mathematical modelling of multi-layer beam based on sinusoidal theory

The optimization conditions of the embedded nanocomposite multi-layer beams reinforced by ZnO nanoparticles are evaluated using a sinusoidal shear deformation theory. The adaptive improved harmony search (AIHS) optimization method is used as optimizer. Based on numerical method of differential quadrature, the buckling load is obtained. The optimum designs for nanocomposite reinforced sinusoidal multi-layer beams are evaluated using proposed AIHS based on the axial forces, applied voltage, volume fraction of ZnO nanoparticles, boundary conditions and geometrical parameters. The results demonstrated that optimum design conditions for a nanocomposite multi-layer beam under 50 GPa buckling constraint force are obtained as the length and thickness of multi-layer beam are 3.3326 m and 29.1125 cm. The applied voltage is the effective variables on the buckling of nanocomposite multi-layer beams.