An isogeometric design-analysis-optimization workflow of stiffened thin-walled structures via multilevel NURBS-based free-form deformations (MNFFD)

Abstract

Stiffened thin-walled structures are widely used in various fields as load-carrying components, but the process of design, analysis and optimization still remains challenging. In this paper, a new design-analysis-optimization workflow is proposed based on isogeometric paradigms for stiffened structures, which is on the basis of a simpler and more efficient method, called multi-level NURBS-based free-form deformations (MNFFD). In terms of modeling, different from the single-level mapping of traditional FFD, MNFFD allows to establish multi-level and composite mapping, which provides strong flexibility for stiffened structures with complex assembly relationships. In terms of analysis, in order to achieve the integration of design and analysis, we propose a MNFFD-based IGA and derive a series of mapped elements. Furthermore, we implemented an isogeometric formulation of the 6-DOFs degenerated shell, and it is more convenient for the coupling of non-conforming NURBS surface patches in the frame of IGA, especially for the patches with kinks. In terms of optimization, all involved models, i.e., geometric models, analysis models, and optimization models, use the same geometric basis. We propose a simultaneous optimization framework of shape optimization and stiffener layout for lightweight design of stiffened thin-walled structures. Because the interaction between skin shape and stiffener layout is considered, the simultaneous optimization expands design space and may obtain better design Based on the proposed isogeometric design-analysis-optimization workflow, the integration of design-analysis-optimization for complex thin-walled structures is achieved. Several numerical examples demonstrate the accuracy, flexibility and robustness of the proposed design-through-analysis workflow centered on MNFFD.