Composites offer a number of compelling advantages, but they also present some daunting design challenges. For example, the orthotropic nature of continuous-fiber-reinforced composites presents the designer with many more design variables to consider, such as ply angles, fiber volume fractions and stacking sequences. Finding an optimal design with so many design variables can be quite challenging. In addition, there is little design experience with composite structures, so often designers develop “quasi-isotropic” designs that look similar to their metal part-designs.

With the huge increase in material variables, there is often less material data available. Also, the failure mechanisms for composites are different from those for metals, leading to designs that are very conservative and do not take advantage of many of the unique properties of composites. When these advantages are desired, the design process is often very inefficient, and more physical testing is required to prove out design concepts. The design process becomes truly a “trial and error” process. Using Altair OptiStruct, one can optimize the composite panel design achieving significant weight savings and performance enhancements.

**Composite Optimization Process
**

The composite optimization process involves three steps: 1) ply shape optimization, 2) ply shape sizing, and 3) ply order optimization. Ply shape optimization uses a combination of topology and topography optimization methods known as composite free-size optimization. Once the composite panel geometry is defined, a finite-element shell mesh is applied to the geometry and the user selects the ply angles to be considered, defines the loads and boundary conditions on the panel, defines any structural constraints (e.g. buckling), defines any manufacturing constraints for the application, and selects the objective function (e.g., minimize mass). The manufacturing constraints can be a requirement to balance the laminate or ply pairs (e.g., ±45° plies), set a minimum or maximum thickness for any given angle, or set a minimum or maximum thickness of the laminate. The user also selects the number of ply shapes that are desired (e.g., four shapes per ply angle). The ply shape optimization routine then produces a set of ply shapes for each angle per the parameters set by the user.

From this step, the ply shape sizing is carried out. The user first determines if the ply shape optimization definitions are acceptable or if modifications are desired. In some cases, the designer may want to modify the ply shapes for manufacturing or other considerations. Once the final ply shapes are determined, the next step is to size the ply shapes. In this step, additional constraints can be applied to the problem (e.g., a strain constraint on the fiber) and the problem is re-run. Again, the objective function must be defined such as to minimize mass. The results of this step give the number of plies to cut for each shape.

The final step is to apply ply order optimization to the ply information to define the final lay-up definition of the structure. The ply order optimization method can take into account different requirements, such as a limit on the number of adjacent plies with the same angle, a constraint on which angle to have on the outside of the laminate and/or which stack to have in the core of the laminate.

**Optimization of Open-Hole Composite Panel**

The panel design used in this study is shown in Figure 1. The panel is 30.5 cm x 30.5 cm, with a 12.7 cm hole in the center. The x- and y-axes are shown in the figure. Three static load cases are applied as follows: 1) tension load of 44482 Newtons applied along the positive x-axis, 2) compressive load of 44482 Newtons applied along the negative x-axis, and 3) shear load of 6672 Newtons applied along the positive y-axis. Two buckling load cases are also monitored for the compression and shear applied load cases.

The panel will be constructed from carbon/epoxy material with 0°, ±45°, and 90° plies with 0° along the x-axis. The panel performance targets are as follows:

- Panel should not buckle under either of the buckling load cases (compression and shear)
- Strain along the fibers of any ply should not exceed 0.004 under all three static load cases (tension, compression, shear)
- Strain across the fibers of any ply should not exceed 0.0065 under all three static load cases (tension, compression, shear)

*Baseline Design*

A finite-element analysis was performed to size a standard 40/40/20 panel that meets the performance targets. That standard panel has 40% 0° plies, 40% ±45° plies, and 20% 90° plies. The result is a panel with the ply thicknesses shown in Table 1. The buckling eigenvalues and the fiber strains are shown in Figures 2 and 3 for this design, confirming that the design does not violate any of the constraints. For the buckling eigenvalue calculation, the value should be greater than 1.0 to ensure an unbuckled condition. The baseline panel mass is 0.879 kg.

**Table 1.** Ply Thickness Values for Baseline 40/40/20 Panel

Ply Angle |
Thickness (mm) |

0° | 2.82 |

+45° | 1.41 |

-45° | 1.41 |

90° | 1.41 |

**Table 2.** Buckling Eigenvalue Results for Baseline Panel

**Table 3.** Fiber Strain Results for Baseline Panel

*Optimized Panel Design*

Composite ply shape optimization on the panel is run to determine the location of ply drops in the panel. The objective is to minimize the mass of the panel with a constraint on buckling. The fiber strain constraints are neglected in this step. A symmetry constraint also was set to constrain the ply drops to be symmetrical along the x- and y-axes. The results are shown in Figure 2. Four ply shapes were specified for each ply angle, giving a total of 16 ply shapes for the panel. The ±45 degree plies were constrained to be identical and the first ply bundle of each angle is constrained to cover the entire panel geometry so a total of 10 unique shapes are defined.

The next step is to carry out the ply bundle sizing optimization. The fiber strain constraints are applied in this step, along with the buckling constraints. The resulting thickness for each ply bundle is shown in Table 4. Using a standard ply thickness of 0.188 mm, the thickness is rounded up to calculate the number of plies required for each ply bundle shape. The buckling results are shown in Table 5, showing that the panel does not violate the buckling constraints. The fiber strains for each load case are shown in Figure 2, showing that the fiber strain constraints are also not violated. The final mass of the optimized panel is 0.639, a 27% reduction in weight over the baseline panel design. The optimized design meets the buckling constraints specified. Ply order optimization was not carried out with this study.

**Table 4.** Ply Bundle Sizing Results

Ply | Thickness (mm) | Number of Plies |

0° Bundle 1 | 0.94 | 5 |

0° Bundle 2 | 1.69 | 9 |

0° Bundle 3 | 0.75 | 4 |

0° Bundle 4 | 0.19 | 1 |

90° Bundle 1 | 0.19 | 1 |

90° Bundle 2 | 0.38 | 2 |

90° Bundle 3 | 0.56 | 3 |

90° Bundle 4 | 0.19 | 1 |

±45° Bundle 1 | 0.19 | 1 |

±45° Bundle 2 | 0.19 | 1 |

±45° Bundle 3 | 0.56 | 3 |

±45° Bundle 4 | 0.19 | 1 |

The results show that using composite free-size and gauge optimization methods, composite panels can be designed to meet performance targets while reducing weight, compared to standard designs. These techniques are best applied in consultation with manufacturing to make the appropriate trade-offs between design and manufacturing. In some cases, the number of ply bundle shapes needs to be minimized, resulting in higher weight but lower cost of manufacturing. In other cases, weight reduction is of great importance, so higher manufacturing costs are acceptable to achieve lower weight. These optimization methods provide the design and manufacturing engineer the tools to allow for better designs within the constraints of the application. Composite materials often are employed to reduce weight, and these methods allow the weight to be reduced even further over traditional panel designs.

**OPTIMIZATION FOR COMPOSITE IMPACT**

Composite optimization methods were employed for a composite underbelly fairing, as shown in Figure 3. The optimization process for static load cases follows the same three-phase approach discussed in the previous example:

**Phase 1:** Concept design synthesis though ply shape optimization.

**Phase 2:** Design fine tuning using ply shape thickness optimization.

**Phase 3:** Detailed design through ply order optimization.

The fairing has been designed considering two major performance criteria: 1) the first natural frequency is at least 20Hz, and 2) the maximum strain is less than 1000 micro-strain. The underbelly fairing is considered as a secondary structure and, unlike a primary aerospace structure, doesn’t serve any critical load-bearing requirements.

To represent operating conditions, different load cases were setup. These included an internal uniform pressure loading of 0.02MPa and an external gravity loading of 6.75g’s. Additionally, the fairing was considered to be riveted along its edges to the surrounding structure.

The composite optimization process was used as described earlier. For this study, the process involving an impact load case is discussed. The underbelly fairing is in an area of the airplane that could be subjected to a bird-strike event. Altair’s RADIOSS finite-element solver has a validated bird model based on Smooth Particle Hydrodynamics (SPH) theory that was used to simulate the effect of a bird strike on the fairing. The model was run in RADIOSS and the kinetic energy, velocity, deceleration information, together with the deformation limit desired, were calculated to estimate the static equivalent loads on the structure. The optimization run then was repeated with the additional impact load case. Figure 4 shows the ply shape optimization results (Phase 1), Figure 5 shows the ply shape thickness optimization results (Phase 2) and Figure 6 shows the ply order optimization results (Phase 3).

The bird-strike load case is just an illustration of how impact load cases can be included in the optimization. In an actual design, one would need to consider the most critical locations for a bird strike and add reinforcement to those areas. For example, sections of the fairing covering critical components (fuel tanks, flight control electronics, etc.) would need to have adequate reinforcement to withstand a bird-strike event. A potential approach would be to perform the worst-case-bird-strike analysis to come up with a minimum thickness in those areas to ensure flight safety and then use this minimum thickness constraint in those zones in the optimization run.

Composite optimization is a new technique that will allow composite structures to be designed more efficiently and with reduced weight. The main advantage of this optimization methodology is that the engineer now can take into account the increasing number of variables in the design efficiently and effectively. Without this tool, composite structures will continue to be designed by trial and error by a limited number of experienced composite design engineers. Composite optimization allows less experienced composite design engineers to get to an optimized design quickly, taking into account the various performance and manufacturing constraints for the given application. It provides useful information that can guide the engineer to know what the physics is dictating, how load is being distributed in the structure, and where material is needed. The number of variables to consider with composite structure design is too great for even the most experienced composite design engineer to manage effectively. Therefore, composite free-size optimization, which can account for these variables in a tractable way, will allow us to take full advantage of these unique and powerful material systems to design better-performing and lower-weight structures.

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### Bob Yancey

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