Fig. 13: Basic vs. Novel Stringer Radii Design Fig. 14: FEM Setup Additional advantages of this approach include: - Avoids the knife-edge tooling required for a tight internal radius - Improves long-term durability (fatigue) versus a tight internal radius - Increased moment of inertia makes stringer more efficient in bending Note: Because this is not a failure analysis and absolute strain will vary according to input load, this model approach is only useful to compare the relative strains between the two configurations for a given load. A lower relative strain for an equivalent load corresponds to an increased relative strength. FEM results The FEM results for hoop and shear strain are depicted in Figure 15. FEM analysis predicts 58 % decrease in maximum hoop strain and 63 % decrease in maximum shear strain through the novel approach. The ~60 % decrease in strain through the novel approach predicted by the FEM corresponds to a ~60 % stronger radius configuration for vertical compression loads. The analysis is conservative due to clumping approximation of 0° plies in the corner of the novel approach FEM rather than distributed throughout the laminate (rightmost analysis in Figure 15) and the lack of support under the outside radius as the model deforms. Strength improvement validation The strength improvement of the novel approach is demonstrated by finite element modelling (FEM) and substantiated by element testing. The stringer configuration used for comparison in both the FEM and test is a 26-ply layup of sequence [90/0/90/45/-45]s[90/0]4s and thickness of ~3.6 mm (0.14 in). The basic approach stringers have external radii of 4.3 mm (0.17 in) and a constant-thickness corner, while the novel approach stringers have R = r = 1.5 mm (0.06 in). FEM analysis A NASTRAN 2D FEM was run to estimate the reduction in fibre and matrix stress for the novel approach vs. the basic approach. A vertical compression load was applied to each configuration and the relative hoop and shear strains calculated for relative strength capability comparison. FEM setup The FEM is a plane strain model and uses orthotropic plate elements to model both the basic and novel configurations. Element properties are rotated for plane strain. As depicted in Figure 14 below, the flange elements are constrained to the radius tangent points. The layup used in both configurations is [90/0/90/45/-45]s[90/0]4s, however the novel approach assumes that the additional cross-sectional area in the external radius is filled by 0° elements to approximate the tested stringer. A test-equivalent load is distributed over the top nodes to simulate the vertical compression load, and the models are run to generate maximum and minimum hoop and shear strains. Strains between the two models are then compared to evaluate the relative structural efficiency of the novel approach vs. the basic approach. Fig. 15: FEM Results No76 October - November 2012 / jec composites magazine 67