Underbelly Fairing Composites Optimization VersionII

Altair Engineering: United States, Brazil, Canada, China, France, Germany, India, Italy, Japan, Korea, Sweden, United Kingdom

Optimization Driven Design of a Composite Underbelly Fairing with HyperWorks Altair Engineering, Inc June 2009 by Dr. Robert N. Yancey Warren Dias


Challenge: To reduce the weight of a composite underbelly fairing.

Introduction

Larger aircraft, longer flight ranges, higher fuel costs and increased overall operating expenses are some of the challenges that have been posed to the aerospace industry recently. This has resulted in a need for more efficient design processes and more innovative designs. Weight has always played a critical role in the design of aircraft which has led to increasing use of lighter weight materials such as composites. Composites do offer lighter weight but they pose many design challenges due to non-isotropic material properties, a large number of design variables, and unique failure modes. Computer based design optimization methods provide an efficient method to develop optimal designs while taking into account the many design and manufacturing variables that need to be considered.

Free-Size optimization is used to identify the optimal ply shapes and locations as well as the most efficient ply drop-off zones. Size optimization followed by a ply stacking sequence optimization is used to obtain the optimal laminate configuration in terms of ply angle thicknesses and stacking sequence. It is the unique combination of these optimization techniques strung together in a process that allows for more efficient and innovative composite design. This finite element based composite design and optimization process also incorporates manufacturing constraints thereby leading to better designs in shorter design cycle times.

Problem Definition

Composite optimization methods were employed for a composite underbelly fairing as shown in Figure 1.


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Figure 1. Depiction of an aircraft underbelly fairing

Process: Design Synthesis, Fine Tuning, and Stacking Sequence Definition

This paper discusses the ‘Optimization Driven Design’ approach for the design of an aircraft underbelly fairing using Altair OptiStruct. Applying this design paradigm is a 3-phase approach:

• Phase 1: Concept Design Synthesis though Free Size Optimization.

• Phase 2: Design Fine Tuning using Ply Sizing Optimization.

• Phase 3: Detailed Design through Ply Stacking Sequence Optimization.

The fairing has been designed considering two major performance criteria: 1) the 1st 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.

Design Process and Results

The 1st phase of this 3 phase design process is applying Free Sizing Optimization techniques to establish the optimal ply shapes for each angle orientation to be included. The user can define the ply angles to be used up front.

Free Size Optimization applied to shells works on the concept that the thickness of each designable element is defined as a design variable. Applying this concept to the design of composites implies that the design variables are now the thickness per fiber orientation, per element. Therefore, the thickness of a ‘Super-ply ’ (total designable thickness of a ply orientation) of allowable orientations is defined as the design variable in a free sizing optimization. This allows for a truly concept level design synthesis of composite laminates, generating ply shapes and optimizing ply drop-off zones per fiber orientation.

Free size optimization is also recommended to be used when trying to optimize material fiber orientation. While generating the starting/baseline laminate stack, all manufacturable orientations can be specified and the regions or zones of those orientations


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Design Synthesis: Determining the general make up of the laminate configuration

that aren’t structurally required will be removed (have their thicknesses sent to 0).

Phase 1 – Concept Design Synthesis – Free Size Optimization

The geometry of the fairing is shown in Figure 2. The idealized finite element representation of the underbelly fairing was generated using HyperMesh. The model also represented 2 equipment masses, weighing 2Kg and 3Kg each, which were connected to their mounting locations through the use of RBE3 elements.

Figure 2: Geometry model of the underbelly fairing

Material properties for carbon-fiber were considered and the same was represented using an orthotropic material model for two-dimensional elements (MAT8).

Four Super-Plies – 0, +/- 45 and 90 degrees – were defined on the PCOMP card with a thickness variable between 0 and 2mm each. 2 load cases were considered to drive the optimization at the concept design stage: 1) a load case representing a 6.75g loading and 2) an internal pressure loading of 0.02MPa.

The ‘SMEAR’ option was applied on the PCOMP card to make the behavior of the laminate independent of the ply stacking sequence. This is a mathematical approximation.

While running an optimization study, it is important to define certain manufacturing constraints in order to produce results that conform to manufacturing requirements. OptiStruct includes several different manufacturing constraints such as ply percentage, ply thickness balancing, ply thickness, and laminate thickness, that can be defined at the concept level free sizing


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Results: Optimized Thickness and Ply Distribution for Laminate

stage. For the underbelly fairing optimization discussed in this paper, 2 manufacturing constraints were incorporated:

1. Ply percentage for the 0s and 90s such that no less than 10% and no more than 60% exist.

2. A balance constraint that ensures an equal thickness distribution for the +45s and -45s.

An important point to note here is that the manufacturing constraints are carried through all phases of the design process, with additional constraints that can be defined at the ply shuffling phase.

The free size optimization problem was setup to use a 30% volume fraction constraint of the designable volume while minimizing the weighted compliance of the 2 load cases. An equal weight of 1 was considered for both load cases to eliminate any bias in the solution. This setup will try to identify the stiffest design for a given fraction of the material.

Figure 3 shows the result of the thickness distribution achieved from the free size optimization, post processed in HyperView:

Figure 3: Element thickness distribution from free size

optimization

The regions indicated in red or in colors tending towards red (from the legend) can be interpreted as thicker regions, while those in blue or tending towards blue are thinner regions. The contour plot above shows the total thickness distribution that includes contributions from each defined superply orientation, i.e. a thickness contribution from the 0s, +/-45s and the 90s. The overall thickness distribution can be post-processed into individual superply thicknesses as shown in the following figures.


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Angle Distributions: Determine how much of each angle ply is required throughout the laminate

Figure 4: Optimized thickness distribution of 0 degree superply

Figure 5: Optimized thickness distribution of ±45 degree superply

Figure 6: Optimized thickness distribution of 90 degree superply


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Multi-Step Approach: Superply sizing, ply bundle sizing, ply lay-up

Due to the balance manufacturing constraint, the thickness distribution of the +45 degree superply and the -45 degree superply are the same.

From a free size optimization, the thickness of a superply is optimized and subsequently subdivided into a user-defined set of ‘Ply Bundles’. Each ply bundle would have a specific pattern and the ply bundles for a given orientation would be built up to approximate the thickness distribution of the superply. More ply bundles will result in a final thickness profile of the superply that more closely matches the free size optimization results. On the other hand, more ply bundles increases the number of ply cut-out patterns which can increase manufacturing costs. An illustration of the concept of going from a superply to ply bundles to individual plies is shown in Figure 7. For this study, 4 ply bundles per fiber orientation (superply) are defined.

Figure 7. Illustration of Superply, Ply Bundles, and Individual Plies

These ply bundles represent the shape and location of the plies per fiber orientation. With 4 ply bundles per fiber orientation, this study produced a total of 16 ply bundles. Since the +45 and -45 angle orientations are constrained to be identical, the study produced a set of 12 unique ply cut-out patterns.

Figure 8 represents the results for one ply bundle. The left hand images show the optimized ply shape for each angle considered in the ply bundle sizing optimization and the right hand images show the interpretation of these results taking manufacturing constraints into consideration. The goal is to match the results as closely as possible in the context of the manufacturing operation. In this case, small patches of plies are not practical so the interpretation generates larger ply patches that resemble the raw optimization results.


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Results Interpretation: Intepret Results to meet other design or manufacturing requirements not considered in the optimization set up

Example of 0 Degree Ply

Example of ±45 Degree Ply

Example of 90 Degree Ply

Optimization Results Manufacturing Interpretation

Figure 8. Results and Interpretation for One Ply Bundle

This process is repeated for each ply bundle to come up with all 12 ply shapes required for the full laminate. This process is currently done manually by the user but this could be automated based on rules established by the manufacturer.

Phase 2 – Design Fine Tuning – Ply Bundle Sizing Optimization

Phase 2 of this process involves a sizing optimization of the ply bundles generated from phase 1 of the design process.

Having established the optimal ply shapes and patch locations, the next step is to fine tune this design for thickness. Phase 2 involves identifying the optimal thickness of each ply bundle. A choice of running the optimization with the thickness as discrete variables or continuous variables is available. A minimum manufacturable ply thickness can be specified, thereby running a discrete optimization and allowing for the calculated


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Ply Bundle Sizing: Determine how many plies of each pattern are needed to meet all performance requirements

optimal ply bundle thickness to be a multiple of the minimum ply thickness value. This helps in calculating the total number of plies required per fiber orientation.

Additional performance criteria can be incorporated into the problem formulation to ensure that the optimized design meets the necessary design requirements. In this case, an additional load case was added to calculate the natural frequency of the fairing under assembled conditions. The optimization setup was also modified to factor in these additional performance targets, among others. :

• Total designable volume

• Natural frequencies (1st – 5th modes)

• Composite strain

Constraints were defined on the frequencies and strain, i.e.

• Natural frequency > 20Hz

• Composite strain in the fairing < 1000 micro-strain

The objective of the problem was to minimize the volume

Manufacturing constraints previously defined in the free sizing phase are automatically carried over into phase 2, preserving manufacturability across the process. These include:

1. Ply percentage for the 0s and 90s such that no less than 10% and no more than 60% exist.

2. A balance constraint that ensures an equal thickness distribution for the +45s and -45s.

The results are presented in Figure 9 that shows the overall thickness distribution map of all 16 ply bundles before the ply bundle sizing optimization stage. Figure 10 shows the final ply bundle sizing results where each ply pattern is sized to achieve the overall performance specifications. The ply bundle size optimization yielded a design that led to a further weight reduction of 23% from the free size results, without violating any of the prescribed design constraints.


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Ply Bundle Sizing: Determine how many plies of each pattern are needed to meet all performance requirements

Figure 9: Element thickness contour before size optimization

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Figure 10: Element thickness contour after size optimization

Phase 3 – Detailed Design – Ply Stacking Sequence Optimization

While shuffling the stacking sequence it is important that behavioral and design constraints are preserved. Additionally, it is required that certain ply book rules be applied to guide the stacking of plies based on specific requirements. Some of the ply book rules that control the stacking sequence are:

• Maximum number of successive plies of a particular fiber orientation

• Pairing of plies

• Identification of a sequence for the core and cover regions


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Shuffling Optimization: Determine the optimal stacking sequence the meets ply book rules

For this case, the optimization problem as previously formulated in the sizing phase is retained and additional ply book rules are applied. They are:

• The maximum successive number of plies does not exceed 4 plies

• That the +45 and – 45 plies be reverse paired

Figure 11 shows the history of the shuffling optimization. 0 degree plies are represented in blue, 90 degree in red, +45 degree plies in green, and -45 degree plies in yellow.

Figure 11. History of Ply Shuffling Optimization


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Benefits: Design laminate structures in less time, achieve greater performance, and use less material

The final result produces a design with the following performance:

• Minimum natural frequency = 21.2Hz (>20Hz)

• Maximum strain = 9.5e-4 (<1e-3)

The design therefore meets its performance requirements, is feasible and manufacturable.

Summary and Conclusions The composite optimization process detailed in this paper expands upon advanced optimization techniques including

• Phase 1 - free size optimization to determine ply thickness per angle orientation

• Phase 2 - size optimization to determine ply bundle patterns and required number of plies per bundle

• Phase 3 – shuffling optimization to determine ply stacking sequence

By stringing these 3 techniques together, OptiStruct offers a unique and comprehensive process for the design and optimization of composite laminates. Free size optimization for composites allows a true concept level design synthesis of plies. A new PLY and STACK based modeling technique that simplifies laminate representation and facilitates the ply bundle sizing optimization followed by the ply shuffling optimization make the process unique. The process is automated and integrated in HyperWorks by generating the input data for a subsequent phase automatically from the previous design phase. The process also allows flexibility in case any modifications are required. Throughout the design process, manufacturability constraints and behavioral constraints are preserved to arrive at a feasible design and ensure a meaningful process.

Applying this process to the design and optimization of an aircraft underbelly fairing resulted in a design that made optimal use of material. Additionally, it resulted in a light weight design that met all prescribed design and manufacturing constraints. It is also important to note that the process was carried out in a short span of time (< 1 week). Incorporating an optimization driven design process (as described in this paper) can be a major enabler to a more efficient and less costly design process of composite structures.

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Underbelly Fairing Composites Optimization VersionII