Optimum design, nonlinear dynamic response and vibration of graphene-reinforced laminated composite with negative Poisson’s ratio under dynamic load in thermal environment

Material with a negative Poisson’s ratio, also known as auxetic materials with honeycomb and zigzag structures, is useful for reinforcing and protecting buildings, military structures, etc. However, the use of composite materials combining graphene-reinforced fibers and adjusting the laminated angle to create a material with a negative Poisson coefficient is a new problem. Thus, analysis of the nonlinear dynamic response and vibration of graphene-reinforced composite laminated (GRCL) plates with a negative Poisson’s ratio in a thermal environment that is supported by elastic foundations under moving loads is very valuable. To evaluate the effect of the misalignment angle, volume ratio, distribution of graphene, temperature, and geometry parameters, the third-order shear deformation theory is proposed with a Vor-Karman term. Based on the theory used, the deformation compatibility equation and motion equation are listed in detail. Besides, the natural frequency values of the graphene-reinforced laminated composite are also investigated in detail and highlighted. Furthermore, by utilizing the differential evolutionary optimization technique, we can identify the highest possible value of the natural frequency while also adhering to the limitations of the problem. These constraints involve a laminated plates with a negative Poisson's ratio, and the optimization is performed using angle variables.