Optimization of Laminate Composite Structures – Recent Advances and Applications

The use of fiber-reinforced composite material entered a new era when leading aircraft OEMs took an unprecedented step to design and manufacture essentially full composite airframes for commercial airliners. Composite structures offer unmatched design potential, since the laminate material properties can be tailored almost continuously throughout the structure. However, this increased design freedom also brings with it new challenges for the design process and software technology.


In recent years, Altair has developed a comprehensive framework for composite optimization. The process consists of three optimization phases. Phase 1 focuses on generating ply layout/shape concepts through free-size optimization; Phase 2 further refines the design by determining the number of plies for a given ply layout defined by Phase I, using size optimization techniques; then Phase 3 completes the final design details through ply stacking sequence optimization, satisfying all manufacturing and performance constraints. This three-phase process design methodology has seen increasing adoption among aerospace OEMs, among others, as demonstrated by the Bombardier application process described in this article.

Three-Phase Laminate Composite Design Optimization Process                                                      

Figure 1 illustrates the different phases of the optimization process.

Concept Design of material orientation and placement through Free-Size optimization

Figure 1.

Phase 1: Concept design of material orientation and placement through free-size optimization

The optimization problem can be stated mathematically as follows:

                  Optimization problem stated mathematically

Where f(x) represents the objective function, gj(x) and  represent the j-th constraint response and its upper bound, respectively. M is the total number of constraints, NE the number of elements and Np the number of super-plies; xik is the thickness of the i-th super-ply of the k-th element. The concept of a “super-ply” is introduced to allow arbitrary thickness variation of a given fiber orientation at a given stacking location. Typically only one super-ply is needed for each available fiber orientation. During this design phase, responses of a global nature are considered for both the objective and constraints. Typically, compliance or key displacement responses are used to formulate the design problem so that the overall structural stiffness is optimized. Manufacturing constraints are important for composite design and need to be address right at the beginning of the concept design phase. A couple of commonly used manufacturing constraints are the percentage of a given fiber orientation in the overall thickness and the total laminate thickness.

Phase 2: Design fine-tuning using ply-bundle sizing optimization

The free-size optimization described in Phase 1 leads to a continuous distribution of thickness for each fiber orientation. A discrete interpretation of the thickness defines the layout of ply-bundles with each bundle representing multiple plies of same orientation and layout/shape. The ply-bundle layout can be simply obtained by capturing different level-sets of the thickness field of each fiber orientation. The default method provides a good balance between the true representation of the thickness field and the complexity of the ply tailoring. These ply-bundles of different fiber orientations are then stacked together so as to be uniformly distributed in the global stack.

In this phase, the design variables are optionally discrete thicknesses at unit ply thickness increments. Also at this design stage, all detailed behavior constraints, including ply failure, should be considered. Manufacturing constraints, such as orientation percentage considered in Phase 1, are carried over during this design phase.

Phase 3: Detailed design through ply stacking sequence optimization

Though the design achieved in Phase 2 contained all ply shapes and stacking details, it is likely that detailed manufacturing constraints or ply book rules are not satisfied. Therefore, the stacking sequence of individual plies is optimized during this phase to satisfy manufacturing constraints while preserving all behavioral constraints. Important manufacturing constraints include: (a) limit on consecutive plies of the same orientation; (b) pairing of +/- angles; (c) pre-defined cover lay-ups; (d) pre-defined core lay-ups.

Draping modeling

When shell surfaces have bi-directional curvature, fiber orientation flow is rather complex and needs to be determined by draping analysis. Often cuts, called darts, need to be placed to eliminate excess cloth when a ply is placed over a curved surface. An example of draping is shown in Figure 2. In such cases, a correction of fiber orientation and thinning needs to be considered in the FEA model. The DRAPE card is implemented in OptiStruct to accommodate this correction information obtained by draping analysis software.

Zone-based free-sizing

This design/manufacturing requirement was driven by some commercial aircraft OEM. Their design process required constant ply thickness for each zone, defined by intersected stringers and ribs. Besides simplifying ply layout, the main reason for the requirement is to accommodate legacy design criteria where each aforementioned zone is a panel unit for strength and stability evaluation. Therefore constant thickness within each panel is required for accurate calculation of its properties. An illustrative example is shown in Figure 3 where free-size results with and without zone-based pattern grouping are compared.

Ply orientation draping on a half sphere

Figure 2: Ply orientation draping on a half sphere.

Thickness distribution of Free-Size results with and without pattern grouping

Figure 3: Thickness distribution of Free-Size results with and without pattern grouping.

 Application example

The three-phase composite design process is demonstrated through the design of the wing of a wide- body aircraft, shown in Figure 4. Nine load cases of key significance are considered. In this simplified exercise, only wing tip displacement constraints are considered, with upper bounds not exceeding those of a baseline aluminum wing under each load case. Only the carbon fiber composite top and bottom skins are optimized. Ply orientations available are 0, +45/-45, 90 plies, with the leading edge as reference.

Phase 1: Concept design – Free-size optimization

Manufacturing constraints considered include:

  • Maximum thickness of each fiber orientation ≤ 10 mm
  • +45/-45 plies to be balanced
  • 8 mm ≤ total laminate thickness ≤ 32 mm
  • Minimum percentage of available fiber orientations ≥ 10%

The thickness distribution of the four fiber orientations is shown for the upper skin in Figure 5. It can be seen that ply balancing constraints kept the thickness distribution of +45 and -45 orientations identical.

Composite wing model of a wide body aircraft under cruise loading

Figure 4: Composite wing model of a wide body aircraft under cruise loading.

Thickness distribution of the upper skin of the wing

Figure 5: Thickness distribution of the upper skin of the wing.

 Phase 2: Design fine-tuning – Ply bundle sizing optimization

The results shown in Figure 5 are interpreted into four ply layouts for each fiber orientation. The ply coverage area decreases as the thickness level-set increases. The first ply bundle covers the entire wing. Layouts of the second ply bundle of 0 degree orientations for both lower and upper skins are shown in Figure 6. Note that typically some manual editing of the raw level-set based ply shape is needed. For simplicity, this example simply adopted the automatically generated ply shapes defined by the thickness level-sets.

Second ply-bundle layouts of the 0 degree orientation

Figure 6: Second ply-bundle layouts of the 0 degree orientation.

In this study, the sizing optimization problem remained the same as in Phase 1. For more realistic applications, this optimization phase should consider all detailed design criteria, such as strength and stability constraints. The number of plies in groups of 0/+-45/90 ply-bundles is:  /15-3-1/1-10-5/15-15-9/15-15-13/, [JK1] which can be determined after the sizing optimization.  The total thickness contour of upper skin after sizing optimization is shown in Figure 7.

Total thickness contour of upper skin after size optimization

Figure 7: Total thickness contour of upper skin after size optimization.

 Phase III: Detailed design – Ply stacking sequence optimization

This optimization phase focuses on the laminate stacking sequence while preserving both manufacturing and performance constraints. Additionally, it is required that certain ply book rules be applied to guide the stacking of plies based on specific requirements. Some ply book rules that control the stacking sequence are:

           Maximum number of successive plies of a particular fiber orientation

           Pairing of the + and – 45s

           Identifying a sequence for the core and cover regions

For this example, the optimization problem as previously formulated in the sizing phase is retained, and the following additional ply book rules are applied: (a) the maximum successive number of plies does not exceed three plies; (b) the + and – 45s be reversed paired. Figure 8 illustrates the stacking sequence before and after stacking optimization. Through this proof-of-concept study, the three-phase optimization process has successfully demonstrated its capacity for maximizing utilization of the potential of composite material in the design of a laminate composite structure, while significantly shortening the design process.

Stacking optimization - initial and final stacking sequence

Figure 8: Stacking optimization – initial and final stacking sequence.

 Application of Altair’s composite design optimization process to aero-structure composite component development at Bombardier

This section outlines application of the Altair composite optimization technology to composite-component design at Bombardier.  As part of Bombardier’s ongoing technology development initiatives, application of the process was explored at single and multiple component levels. A description of the process and method of application inside a dynamic aerospace design environment is described.  Methods for incorporating structural and manufacturing constraints are introduced.  Also summarized are the interfaces developed between design and stress groups, which underpin the successful application of the technology in an environment where design requirements can frequently change.

 Integration of Altair’s composite design process

Integration of Altair’s composite optimization process with the design process and all of the necessary interfaces is shown schematically in Figure 9. The main additions to the process are interfaces accommodating inputs and outputs to and from the design team.  Notably, custom responses and constraints are needed to align the optimization with strength, stiffness and stability qualification requirements.  Export of the optimization solution is also required in a number of different formats, including CAD-format laminate descriptions, qualification report summaries and additional finite- element formats.

Schematic Summary of Integrating Design Optimization within the Structure Design Process

Figure 9: Schematic Summary of the Integration of Altair’s Composite Design Optimization Process with Bombardier’s Aero-Structure Design Process.

Composite optimization interfaces

A review of the Bombardier aero-structure design process was performed to identify the inputs and outputs required for the composite optimization process.  Successful access to the technology in the overall design process is underpinned by these interfaces working efficiently and robustly.  The main focus areas for the interface development were:

i)                    Conversion of Bombardier FEM data to OptiStruct format suitable for optimization

ii)                   FEM export at the end of the process

iii)                 CAD format export of final designs

iv)                 Qualification analysis reporting in Bombardier format (spreadsheets and other digital documents)

Altair’s generic FEM and composite interfaces were modified to facilitate each of these requirements in the Bombardier design environment.  The resulting solution was a single integrated platform that facilitated passage of input and output data to and from the optimization between Bombardier and Altair.  Composite specific results visualization and report data could easily be shared and reviewed by all parties.

Optimization problem formulation

The optimization problems were typically defined to minimize mass subject to stiffness, allowable composite stresses and stability criteria.  Multiple load cases were defined and, where available, appropriate stiffness targets set for each, based on the baseline response.

In addition to the composite laminate sizing design variables for components, shape optimization of the stiffening members also was investigated through FREE SHAPE optimization in OptiStruct.  Greater design freedom is afforded with this approach, since it allows each stiffener height to change independently and freely in shape as well as size.  This is often advantageous where a balance between relative stiffness and stability must be maintained. To constrain the optimization to derive designs compatible with the design team requirements for some components, zone boundaries were defined over the surface.  OptiStruct can constrain the laminate solutions to respect these boundaries from the first free-sizing stage.  This is often a key manufacturability requirement and can be locked down at the concept stage.

Commonality between manufacturing constraints was maintained throughout the stages to enforce minimum percentages of cloths and uni-directional plies in the stack.  In the later stages, manufacturing rules were enforced limiting the maximum number of consecutive plies.

The structural constraints were implemented by direct sampling of finite-element results (stiffness and strain) or by custom calculations developed to correlate with qualification assessment methods (global and local stability, additional strength requirements).  The custom calculations were implemented through OptiStruct’s DRESP3 functionality, which ensures efficiency in the handling of custom calculation routines and response sensitivities.


The composite optimization process was applied successfully in a real-world aerospace design environment, allowing efficient exploration of designs and delivering weight-saving potential for a range of components and systems.

                The following major advantages were found from application of the process:

i)                     The free-form stage provided an efficient testing ground for design sensitivity to applied loads and design constraints.  The solutions were not influenced by previous designs and provided insight into methods for improving structural efficiency.  They provide a very efficient method for performing trade-off studies and rapid assessment of changes in design requirements.

ii)                   The process demonstrated the value of locking ply continuity into the optimization from early in the process.  In this way, manufacturability could be constrained with less impact on the structural efficiency.  Interfaces were developed between the OptiStruct ply-based output and design system carrying over ply continuity directly.

iii)                  Significant mass savings were predicted from application of the technology and a measure of the effect on weight of varying manufacturing constraints could be quantified.

iv)                 The input data and optimization solutions could be integrated with the current design practice at Bombardier, facilitating efficient communication and final design qualification.

Application of the optimization approach at Bombardier has led to a repeatable process, which accommodates the composite design qualification requirements and can be enhanced and applied at component and system level.

The three-phase design process starts with creating design concepts capable of fully utilizing the increased design potential of composite material. It finishes with a final design of ply-book-level details where manufacturing rules, together with all performance requirements, are satisfied. An aircraft wing case study is shown to demonstrate the optimization process. Then, a detailed description of the application within a real-world aircraft design environment at Bombardier Aerospace is given. It is particularly notable that customer-specific design constraints on panel strength and stability are incorporated through external responses (DRESP3). These factors demonstrate the versatility of OptiStruct that allows the optimization process to fit into an established complex environment of commercial-aircraft design.

This paper is written in collaboration with Ming Zhou, Vice President of Software Development.

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Warren Dias

Warren Dias

Business Development Manager - OptiStruct at Altair
Warren is the Business Development Manager for OptiStruct where his responsibilities include increasing the global footprint and usage of OptiStruct. He joined Altair in 2000, and now has nearly 15 years of experience in the field of finite element analysis and structural optimization. He holds a Bachelor Degree in Mechanical Engineering from Manipal Institute of Technology in India.
Warren Dias
Warren Dias

About Warren Dias

Warren is the Business Development Manager for OptiStruct where his responsibilities include increasing the global footprint and usage of OptiStruct. He joined Altair in 2000, and now has nearly 15 years of experience in the field of finite element analysis and structural optimization. He holds a Bachelor Degree in Mechanical Engineering from Manipal Institute of Technology in India.