Concurrent stringer topology and skin steered fiber pattern optimization for grid stiffened composite shell structures

Abstract

Abstract The use of fiber steering to improve composite plate behavior for aerospace applications is only feasible if the steered laminates can be effectively combined with a stiffening grid. In this paper, a methodology is presented for concurrent optimization of stringers topology and fiber pattern of grid stiffened tow steered composite structures. A finite element formulation is obtained through symbolic integration for tow steered composite panels and is extended to analyze grid stiffened composite panels. One of the challenges in the topology optimization of grid stiffened panels is the separation of the stringers’ discretization from the skin discretization. The meshing of a stiffened panel is tedious and time-consuming, and changing the topology of stringers may require re-meshing of the complete design domain. Based on a weak formulation of the continuity requirements between skin and stringers, the Lagrange multiplier approach is proposed to circumvent this problem. This approach allows the meshes of stringers and skin to be independent. The accuracy of the resulting finite element solver is compared to that of a conformal mesh based solver. The optimization design variables are defined to describe both the topology of the stringers and the fiber patterns in each of the panel’s plies. The fiber pattern parametrization is based on Lagrangian interpolation of nodal based fiber angles. The fiber angle distribution is mapped on the centroids of the composite plate elements used for the FE analysis. In this approach, a manufacturing mesh is used to define the nodes for the design variables, i.e., the nodal fiber angles, controlling the fiber pattern in the skin. The ground structure method is used to optimize the topology of the stringers. The heights of the stringers in the ground structure are defined as the stringer design variables. Therefore, the overall design vector includes the fiber angles at the manufacturing mesh nodes for each ply and the stringers’ height in the ground structure. The method is tested using a buckling load optimization with constraints on manufacturing aspects, such as minimum tow turn radius. The Lagrange multiplier based coupling of stiffener and plate models was shown to be accurate and effective. The results of the concurrent optimization of stiffener grid and fiber patterns showed that steering does improve the behavior of stiffened plates.