Carbon fiber-reinforced plastics are used in various engineering fields because of a high specific strength and stiffness. Also, a creep is not nearly appeared, and dimensional stability is great because the coefficient of thermal expansion is quite small.
Furthermore, the sandwich structure helps us to satisfy various design requirements by combining advantages of different materials. When this composite sandwich structure is applied to the aerospace structures, materials of the facesheet and core which is suitable for structural and environmental should be considered. However, it is used to secondary structures restrictively at this present. The reason is many uncertainties caused by manufacturing process, along with the high production cost, low shear strength of core and complex failure modes. Also, this problem is for general composite laminates, and the mechanical strength and stiffness show a marked difference due to the thickness of ply, discontinuous space, temperature and humidity in curing, rate of resin impregnation and so on. Therefore, probabilistic structural design and optimization are required to consider the uncertainty quantitatively. This method that is based on reliability analysis is valid with considering the uncertainty in design stage, and can provide the effective design when applied to a professional experience and technique obtained from a specific system.
In this paper, a composite of sandwich structure is summarized, and the applicability to aerospace structure, design considerations and advantages and disadvantages are analyzed. To prevent from the structural failure by uncertainty, DO-PMS(Deterministic Optimization by Probabilistic Margin of Safety) is proposed in order to improve the typical design method based on the margin of safety. DO-PMS does not use the safety factor and A/B-basis value widely used in design process, and provides the design requirement not to happen the probability of failure under the uncertainty of random variables. The conservative design method used until recently can be improved by the simple concept and calculating process.
Next, RBDO-MPDF(Reliability-Based Design Optimization by Moving Probability Density Function) is proposed to improve a computation efficiency. Although the RBDO has many advantages, it is not easy to apply this method to many engineering fields because calculating the probabilistic constraint is complex and much computation time is required. RBDO-MPDF estimates the PDF(Probability Density Function) of structural response, and begins the optimization process with starting point that is selected by moving PDF to the probabilistic constraint. CMCS(Crude Monte-Carlo Simulation) method is used for calculating the probability of failure, and the reliability of result is guaranteed.
Also, the response surface model is generated and compared with the result using full analysis model to reduce a computation time in case that a finite element analysis is used to estimate the PDF. Based on this response surface model, the sensitivity of random variables is evaluated.
First, to verify the validity of proposed methods in this paper, these methods are applied to the simple cantilever problem. As a result, the failure happens in result of deterministic optimization based on margin of safety, and the safe structure without probability of failure is designed using DO-PMS. And then, it is confirmed that RBDO-MPDF is accurate and efficient by comparison with general RBDO method.
Next problem is the composite sandwich fuselage composed of Carbon/Epoxy facesheet and aluminum honeycomb core. The stiffness and strength of prepreg and four kinds of load are selected as a random variable. The probabilistic structural design and optimization is conducted in condition of the failure index calculated by Tsai-Wu criteria.
Like a previous problem, the probability of failure of the composite sandwich fuselage designed by deterministic optimization is calculated. And then, the margin of safety not to meet the failure is estimated using DO-PMS. The accuracy and efficiency of RBDO-MPDF is verified, and the thickness of ply with satisfying the probabilistic constraint is calculated under the minimized weight. The computation cost is consumed considerably because a finite element analysis is used in CMCS process. A computation time is reduced by using the response surface model, and the most sensitive variable is determined by efficient PSA(Probabilistic Sensitivity Analysis) method. Furthermore, RBDO-MPDF is applied to the multi-constraint condition efficiently and analyzed.
It is expected that the results of this paper using proposed methods can be used for improving the efficiency of RBDO method and applying the composite sandwich structure to the primary structure as a basic data.