# Multidisciplinary Optimisation of Aircraft Structures with Critical Non-Regular Areas: Current Practice and Challenges

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## Abstract

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## 1. Introduction

#### 1.1. The Design Process Paradox

#### 1.2. Aircraft Industry Strategies to Address the Paradox

- Working in parallel on multiple models during early design,
- Using a multidisciplinary approach to design.

#### 1.3. Ignoring Local Non-Regular Areas Potentially Thwarts MDO Benefits

#### 1.4. The Case for Global–Local MDO

#### 1.5. Structure of the Article

## 2. Current State-of-the-Art for MDO and Its Application to Airframe Sizing

#### 2.1. General Aspects of Multidisciplinary Design Optimisation

#### 2.1.1. MDO Optimisation Problem

**g**and

**h**are the inequality and equality constraints, respectively,

**x**are the design variables and

**y**is the solution of the Multidisciplinary Analysis (MDA):

**g**,

**h**and their derivatives depend on

**y**, as represented in Figure 2.

#### 2.1.2. Internal Structure of the Multidisciplinary Analysis

#### 2.1.3. Difference between State and Coupling Variables

#### 2.1.4. Contributing Analyses Result from Disciplines or Substructures

#### 2.1.5. MDO Architecture

#### 2.2. Classification of MDO Architectures

#### 2.2.1. Multidisciplinary Feasible

#### 2.2.2. Individual Discipline Feasible

#### 2.2.3. All-at-Once

#### 2.2.4. Monolithic and Distributed Architectures

#### 2.3. Distributed Architectures

#### 2.3.1. Multilevel Optimisation by Linear Decomposition and CSSO

#### 2.3.2. Global Sensitivity Equations

#### 2.3.3. BLISS

#### 2.3.4. Collaborative Optimisation and Its Extension

#### 2.3.5. Quasi-Separable Decomposition

#### 2.3.6. Analytical Target Cascading

#### 2.3.7. Augmented Lagrangian Decomposition

#### 2.3.8. Use of Response Surface Methods with Distributed Architectures

#### 2.4. Choice of Architecture

#### 2.5. MDO Applications

#### 2.5.1. Alternate Execution of Global and Local Optimisation

#### 2.5.2. Nested Execution of Global and Local Optimisation

#### 2.5.3. Parallel Execution through Response Surfaces

#### 2.5.4. Comparison of the Three Approaches

## 3. Current Practice in Structural Aircraft Design

#### 3.1. Application of MDO in the Design Process

#### 3.1.1. Conceptual Design

#### 3.1.2. Preliminary Design

#### 3.1.3. Detailed Design

#### 3.1.4. The Role of MDO

#### 3.1.5. Where Is Airframe MDO Used?

#### 3.2. Non-Regular Areas in Aircraft Design

#### 3.2.1. MDO Relies on Coarse Models

#### 3.2.2. Presence of Non-Regular Areas

#### 3.2.3. Location of Non-Regular Areas

#### 3.2.4. FE-Modelling of Non-Regular Areas

#### 3.2.5. Handling of Non-Regular Areas in the Optimisation

## 4. Limitations of the Current State-of-the-Art

#### 4.1. Possible Consequences of Neglecting Local Areas

#### 4.1.1. Wrong Assessment of the Configuration Performance

#### 4.1.2. Inaccurate Representation of the Global Optimisation Problem

#### 4.1.3. Undetected Local Constraint Violations

#### 4.1.4. Sub-Optimal Overall Design

#### 4.2. Example

#### 4.2.1. MDO of an Aircraft with a Non-Regular Area

#### 4.2.2. Modelling of the Non-Regular Area

#### 4.2.3. Optimisation and Subsequent Detailed Analysis

#### 4.2.4. Constraint Violation

#### 4.2.5. On the Importance of Considering Local Sizing during Global MDO

## 5. Conclusions

- Inaccurate weight and stiffness estimations,
- The fact that non-regular areas are kept fixed during the optimisation,
- The lack of constraints defined over the non-regular areas.

- A wrong performance assessment, which affects the choice of the best design concept;
- A non-optimal design;or
- Constraint violations, both of which may force to repeat the MDO process and cause costly delays.

- The MDO procedure only requires detailed information about weight and stiffness,
- Detailed FE-models are mainly needed to evaluate constraint violations within non-regular areas for which not all disciplines must be solved.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

MDO | Multidisciplinary Design Optimisation |

MDA | Multidisciplinary Analysis |

CA | Contributing Analysis |

MDF | Multidisciplinary Feasible |

IDF | Individual Discipline Feasible |

AAO | All-At-Once |

SAND | Simultaneous Analysis and Design |

CSSO | Concurrent Subspace Optimisation |

GSE | Global Sensitivity Equation |

BLISS | Bilevel Integrated System Synthesis |

CO | Collaborative Optimisation |

ECO | Extended Collaborative Optimisation |

QSP | Quasi-Separable Problems |

QSD | Quasi-Separable Decomposition |

ATC | Analytical Target Cascading |

GFEM | Global Finite Element Model |

DFEM | Detailed Finite Element Model |

FE | Finite Element |

CLT | Classical Laminate Theory |

PSO | Particle Swarm Optimisation |

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**Figure 1.**Setbacks are normal in product development, but their opportunity cost increases as the design progresses, which leads to the design paradox. (

**a**) Product development is characterised by steps forward and setbacks due to the violation of design requirements. (

**b**) The design paradox: as designers gain knowledge on how to design the product, they lose the freedom to modify the design.

**Figure 7.**Flowchart of multidisciplinary feasible architecture: detail of the analysis block from Figure 6.

**Figure 9.**Flowchart of the individual discipline feasibility architecture: detail of the analysis block from Figure 6.

**Figure 10.**Flowchart of the all-at-once architecture: details of the analysis block from Figure 6.

**Figure 12.**A response surface can be used to decouple a two-level architecture. (

**a**) Two-level architecture, with a nested optimisation loop. (

**b**) A response surface (RSM) can be substituted for the nested procedure. The RSM can be created and updated in parallel, effectively decoupling the two optimisation procedures.

**Figure 16.**Consequences of an inaccurate representation of the optimisation problem. (

**a**) Optimisation problem solved by the MDO procedure; (

**b**) Suboptimal solution: when accurately represented, the objective is different; (

**c**) Invalid solution: when accurately represented, the constraints are different.

**Figure 21.**Non-regular area (in yellow) as represented in the aircraft model. (

**a**) OptiMALE with the wing upper-skin removed; (

**b**) Zoom on the right wing (upper-skin removed); (

**c**) Zoom on the non-regular area (in yellow); (

**d**) Zoom on the non-regular area with surrounding spars and ribs removed.

Two-Level Approaches | Comparison |
---|---|

Alternate Global–LocalReferences: Ciampa et al. [42] | |

Advantages: reduced computational cost | |

Disadvantage: not always applicable, possible optimality or convergence issues | |

Nested LocalReferences: Noevere and Wilhite [43], Kapania et al. [44,45,46,47,48,49,50] | |

Advantages: accurate and always applicable | |

Disadvantages: computationally expensive | |

Nested Response SurfaceReferences: Liu et al. [54], Ragon et al. [56,57] | |

Advantages: reduced computational cost | |

Disadvantages: limited to the accuracy of the response surface |

Element ID | At 7 Iterations | At Convergence | Drop in RF | |||
---|---|---|---|---|---|---|

Allowable | Actual | RF | Actual | RF | ||

42403021 | 5.5 $\times {10}^{-3}$ | 4.830 $\times {10}^{-3}$ | 1.14 | 5.564 $\times {10}^{-3}$ | 0.99 | −0.15 |

42403023 | 5.5 $\times {10}^{-3}$ | 5.002 $\times {10}^{-3}$ | 1.10 | 5.757 $\times {10}^{-3}$ | 0.96 | −0.14 |

42403025 | 5.5 $\times {10}^{-3}$ | 5.126 $\times {10}^{-3}$ | 1.07 | 5.898 $\times {10}^{-3}$ | 0.93 | −0.14 |

42403027 | 5.5 $\times {10}^{-3}$ | 5.221 $\times {10}^{-3}$ | 1.05 | 6.003 $\times {10}^{-3}$ | 0.92 | −0.14 |

42403189 | 5.5 $\times {10}^{-3}$ | 5.247 $\times {10}^{-3}$ | 1.05 | 6.030 $\times {10}^{-3}$ | 0.91 | −0.14 |

42403191 | 5.5 $\times {10}^{-3}$ | 5.218 $\times {10}^{-3}$ | 1.05 | 5.993 $\times {10}^{-3}$ | 0.92 | −0.14 |

42403193 | 5.5 $\times {10}^{-3}$ | 5.154 $\times {10}^{-3}$ | 1.07 | 5.916 $\times {10}^{-3}$ | 0.93 | −0.14 |

42403195 | 5.5 $\times {10}^{-3}$ | 5.031 $\times {10}^{-3}$ | 1.09 | 5.772 $\times {10}^{-3}$ | 0.95 | −0.14 |

42403197 | 5.5 $\times {10}^{-3}$ | 4.835 $\times {10}^{-3}$ | 1.14 | 5.545 $\times {10}^{-3}$ | 0.99 | −0.15 |

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**MDPI and ACS Style**

Sferza, M.; Ninić, J.; Chronopoulos, D.; Glock, F.; Daoud, F.
Multidisciplinary Optimisation of Aircraft Structures with Critical Non-Regular Areas: Current Practice and Challenges. *Aerospace* **2021**, *8*, 223.
https://doi.org/10.3390/aerospace8080223

**AMA Style**

Sferza M, Ninić J, Chronopoulos D, Glock F, Daoud F.
Multidisciplinary Optimisation of Aircraft Structures with Critical Non-Regular Areas: Current Practice and Challenges. *Aerospace*. 2021; 8(8):223.
https://doi.org/10.3390/aerospace8080223

**Chicago/Turabian Style**

Sferza, Massimo, Jelena Ninić, Dimitrios Chronopoulos, Florian Glock, and Fernass Daoud.
2021. "Multidisciplinary Optimisation of Aircraft Structures with Critical Non-Regular Areas: Current Practice and Challenges" *Aerospace* 8, no. 8: 223.
https://doi.org/10.3390/aerospace8080223