The asymptotic-numerical method for the post-buckling response of curvilinearly stiffened panels

Abstract

Abstract In the present work, the asymptotic-numerical method is applied in conjunction with the Ritz method as a powerful mean for analysing the post-buckling response of panels with variable stiffness skin and curvilinear stringers. Main advantage of the proposed approach is the reduced computational time. The Ritz method guarantees an excellent ratio between accuracy and required degrees of freedom; the asymptotic-numerical method requires just one matrix inversion throughout the solution process. Moreover, the complete analytical representation of the non-linear equilibrium path is obtained, as opposed to the point-by-point representation of predictor-corrector algorithms. Several test cases are presented and compared with standard Newton-Raphson computations and commercial finite element simulations. The results show noticeable saving of computational time. For the test cases investigated, the asymptotic-numerical method requires about one third of the time required by a standard Newton-Raphson routine. These results demonstrate that the combination between Ritz and the asymptotic-numerical method is an excellent strategy for investigating the post-buckling response of innovative curvilinearly stiffened panels.