Reliability-based Design Optimization of Laminated Composite Structures under Delamination and Material Property Uncertainties

Abstract Delamination is a major type of defects from manufacturing process in laminated composite structures, exhibiting uncertain characteristics which are represented by mixed random variables of continuous in-plane position and delamination size, as well as discrete through-the-thickness position, which should be considered in the design phase of composite structures. Thus, this paper presents a reliability-based design framework for optimal design of composite stacking sequence, for the first time to consider both delamination and material property uncertainties from manufacturing process. Mixed continuous-discrete random variables are involved, and a reliability analysis method is newly proposed to tackle this mixed-variable problem, maintaining high levels of both accuracy and efficiency. The formula of total probability is first employed to formulate the reliability constraint so that discrete and continuous random variables are decoupled; Monte Carlo simulation is then used for reliability analysis with respect to continuous random variables, and a surrogate modelling approach based on Gaussian process regression model is adopted to reduce computation costs. As design variables of ply angles are limited to a discrete set, a genetic algorithm with some proposed improvements is used to handle discrete design variables. Consequently, an optimization framework is devised for composite laminate design under uncertainties from manufacturing process, which is verified via case studies of a cantilever composite plate and can also be extended as a general solution for other composite laminates. With integrated consideration of manufacturing limitations and imperfections as well as structural performances, the presented framework provides a valuable tool in composite structure design.