Optimization of stiffened panels using a combination of FEM and a predictor-corrector interior point method

Structural optimization, first introduced by Schmidt in 1960, is a rapid growing factor in the development of new aerospace structures. This growth is established by the increase in numerical modelling techniques, cheaper computer power, the increasing cost of production and competition between companies. The combination of both structural optimization and finite element software allowed for the rise of new and more efficient optimization methods provided that the software can performsensitivity analysis. Many programs used in industry today such as BOSS Quattro , PASCO and VICONOPT restrict themselves to basic optimization methods. The goal now is to develop an optimizer for stiffened panels, using a combination of FEM and a more advanced optimization method. Interior point methods have been proven to be more efficient than primal-dual methods for solving sub-problems. Therefore Mehrotra’s predictor-corrector interior point method is used in the version of Zillober. To reach convergence convex approximations are required. The conservative approximation from Fleury’s ConLin provides the basis of many other more advance approximation methods. Therefore this method is chosen to form the initial optimizer. A 2D The FEM model is established using shell and bar elements for the panel and stiffeners respectively. This allows for easy adjustment of the geometry without the need to change the model itself. The bar element properties are defined by the PBAR card rather than the PBARL card in NASTRAN. This avoids the input of fixed NASTRAN specified cross sections with limited design freedom. The sensitivities with respect to stiffener properties are extracted from NASTRAN. These are then converted to the required sensitivities using analytical equations. With all the necessary information available, the inner loop of the optimization process is initiated. Approximations of the constraints, objective and sensitivities are produced. Based on the approximations, the predictor step establishes a maximum step size, which is then adjusted by the corrector step to a more feasible one. This is done iteratively until the duality gap is below a specified limit. Finally a new outer iteration can start if no convergence is reached. Three goals were achieved by analysing of 11 test cases. First the optimizer shows that it can handle different property sets for the stiffeners within the same panel. Secondly, the optimization works for different cross sections. Finally, when performed for similar panels with a different amount of stiffeners, an optimal number is found. The optimization is performed for minimum weight while limited by stress, buckling and design constraints. The results indicate that for 8 out of 11 cases convergence is reached within 12 cycles. Due oscillatory behaviour two other cases converged relatively slow and one did not converge at all. This happens due to the incapability of the optimizer to consider new buckling modes establishing with the adjustment of the parameters. In the end however all three statements were proven outside of the three oscillating cases. For the model that was defined, the optimal amount of stiffeners is 7. Additionally I-beam stiffener provided the most consistent performance with respect to convergence. Finally for this case, although optimizing for different stiffener properties per panel lead to a small reduction in weight, it is not worth the computational effort. So it can be concluded that the optimizer works. On top of this the restrictions on the cross-section defined by NASTRAN were eliminated by extracting a different set of sensitivities and adjusting them using analytical equations. This leads to an optimizer, which can perform size and shape optimization by use of NASTRAN analyses, analytical transformations and an interior point optimization method.Aerospace Structures and Computational MechanicsMechanics, Aerospace Structures & MaterialsAerospace Engineerin