Optimal stacking sequence design of stiffened composite panels with cutouts (1993)

The growing use of high performance composite materials has stimulated interest in the development of optimization procedures for the design of laminates. The design of composite structures against buckling presents two major challenges to the structural analyst and designer. First, the problem of laminate stacking sequence design is discrete in nature which complicates the solution process. Second, many local optima with comparable performance may be found. The present work addresses these challenges by investigating several techniques for designing stiffened composite panels. The specific focus is the minimum weight design of a compression-loaded blade-stiffened composite panel with a centrally located hole subject to stability, minimum gage and strain failure constraints. An efficient linked-plate analysis and design program PASCO is used to predict global response (buckling) of the stiffened panel. Since PASCO cannot model a hole, a finite element program, EAL, is used to model the local hole region and evaluate local strain response in the vicinity of the hole. A sequential approximate design procedure based on ply thicknesses as continuous variables is used to evaluate the relative efficiencies of softskin (designs· with no 0° plies) and stiff-skin designs (designs with 0° plies). The soft-skin design concept, which also has better damage tolerance, is found to be better for stiffened panels from weight and strength considerations. Addressing the discreteness of the problem with the continuous design procedure was found to be cumbersome leading to solutions that were not necessarily optimum. In order to address the limitations of the continuous optimization procedure, two integer programming procedures were investigated. A sequential linear integer programming procedure proved t o be less effective than a genetic algorithm (GA). The GA based discrete design approach provided results which were found to be about 5% lighter than results obtained previously with continuous optimization followed by rounding up of the ply thicknesses. Furthermore, many designs with similar performance were easily obtained, giving a choice of designs for the analyst. The integer programming formulations also permitted easy implementation of additional constraints such as ply contiguity (integer type constraints) that are difficult to enforce in continuous optimization based design procedures. Tests on optimal baseline designs were carried out in parallel with the analytical study to investigate the buckling and failure characteristics of stiffened quasi-static compression loaded panels with holes and to assess the validity of analytical models used for the design of such panels. Results from quasi-static tests indicate that the optimized designs without holes were susceptible to be imperfection sensitive. This is to be expected as the optimization process led to the coincidence of an overall and a local skin buckling modes. Quasi-static tests thus emphasized the need for the optimization process to include additional constraints on the separation of consecutive buckling modes in order to alleviate the tendency of the optimizer to produce designs which may be imperfection sensitive.