13:30
Aeroelastic optimisation 3
Chair: Héctor Climent
13:30
30 mins
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Aeroelastic reliability based optimisation of composite plates via surrogate modeling
Roger Ballester Claret, Nicolo Fabbiane, Christian Fagiano, Cédric Julien, Didier Lucor
Abstract: In aerospace engineering, optimizing composite laminates in aeronautical structures can be a complex problem which often results in intricate models that are computationally demanding. Addressing this, our work introduces a reduced model approach, employing a composite plate as a representative element of an aircraft wing [1]. The primary objective is to enhance aeroelastic behaviour in response to wind gusts, focusing on minimizing the bending moment generated by such gusts. Concurrently, flutter analysis is conducted, serving as the primary constraint in our optimization problem.
The optimization of composite materials presents unique challenges, particularly due to the non-convex nature of the stacking sequence design space and the presence of numerous local minima. Furthermore, the variable number of design parameters (angles of plies) adds to the complexity given that the possible stacking error must be considered within the optimisation process [2]. To navigate these challenges, our approach utilizes material homogenization, transforming the problem into one within a convex design space with a fixed number of variables.
Building upon this foundation, we implement a surrogate model-based optimization strategy. The surrogate models, are developed within the homogenized design space using constrained Efficient Global Optimization (C-EGO) [3]. Following the establishment of these models, a Genetic Algorithm (GA) is employed to determine the optimal stacking sequence [4]. The genetic algorithm attempts to find a stacking sequence that optimises the aeroelastic problem with a reliability-based approach. Considering the possible uncertainties in the ply orientation of the composite laminate the GA manages to tailor the composite to the aeroelastic constraints.
The results of this two-step optimization process, combined with the proposed dual design space approach, demonstrate the efficacy of surrogate models in exploring the full spectrum of optimal composite configurations. Moreover, the coupling of this methodology with the aeroelastic problem at hand permits for a cost-efficient optimisation reducing notably the number of calls to the aeroelastic solver compared to gradient based optimisation methods. This methodology not only streamlines the design process for composite aeroelastic structures but also showcases its possible applicability in more complex aeroelastic scenarios.
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14:00
30 mins
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Unified model of sandwich panel core and faces for aeroelastic optimization
Vladimír Hostinský, Jurij Sodja, Ivo Jebáček, Jan Navrátil
Abstract: Metamaterials show a considerable potential in the field of complex optimization
of aerospace structures. To fully exploit this potential, the authors present a novel approach to modeling the structural response of a sandwich panel with metamaterial core and CFRP skins that could be used within a single-step optimization process. The proposed approach is illustrated using a model of a panel with aluminum honeycomb core. Obtained results confirm the high potential of the inclusion of the core optimization into the optimization framework. Simple preliminary validation utilizing the finite element analysis presented in the closure of this study yielded a satisfactory agreement with the results of the proposed analytical model. The maximum reached difference of five percent can be attributed to a different shape of deformation of the honeycomb core within the sandwich as opposed to a deformation of the honeycomb core alone.
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14:30
30 mins
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A Panel-Free Aeroelastic Solver with Adjoint Sensitivities
Hollis Smith, Joshua Deaton
Abstract: The conventional approach to aeroelastic analysis with a panel method involves constructing a panel mesh of external surfaces and their wakes to estimate lifting pressures, constructing a finite-element mesh of the substructure to estimate deformations, and implementing a consistent and conservative interpolation scheme to simultaneously resolve the coupled state equations. Both the structural and the aero meshes are typically constructed from an explicit geometry that does not readily accommodate topological changes. When used in an optimization, the conventional approach requires an expensive re-meshing step for both analyses upon changes in the design, and expensive re-evaluation of topological operations like intersections, unions and subtractions.
In recent years, feature-mapping methods have been applied to solve structural displacements by mapping the geometric components in the design to an implicit field-representation (circumventing the need to re-mesh upon design changes). The implicit representation naturally and robustly transforms topological operations into inexpensive arithmetic operations. In contrast to conventional free-form topology optimization methods, the feature-based approach parameterizes the design in terms of high-level geometric features, resulting in optimized designs that are directly compatible with existing parametric CAD systems.
We present a novel panel-free approach to solve potential-based lifting pressures that is inspired by the feature-mapping approach used in structural topology optimization. The lifting surfaces and their wakes are mapped to a fixed analysis domain wherein an efficient multi-grid solver resolves the lifting pressures. In addition, we present a natural method to consistently and conservatively transfer loads and displacements between disciplines. Since all of the mappings are differentiable, we present an algorithm to adjointly compute the design-sensitivity of quantities depending on the coupled aeroelastic state, facilitating efficient gradient-based optimization.
The computational efficiency gained by circumventing the need to re-build and re-mesh the explicit geometry for each analysis, the topological design flexibility gained by mapping to an implicit representation, and the efficient adjoint computation of design-sensitivities make the proposed aeroelastic solver an attractive alternative to the conventional approach.
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15:00
30 mins
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Mathematical method for prediction aeroelastic phenomena and multidisciplinary optimization lifting surfaces of flight vehicle at preliminary stage design
Oleh Havaza, Vitalii Sukhov, Ruslan Nikitin
Abstract: Every year, the air transportation market increases the requirements for aircraft performance in order to obtain greater profits. Satisfaction of this requirement is the main purpose for aircraft manufacturer. One of the ways to achieve this purpose is improving the design process by developing and implementing new approaches and tools for modelling different phenomena (in considered case – Aeroelastic phenomena) inherent to flight vehicles.
The purpose of this report is to present a modern mathematical method that allows modelling static and dynamic Aeroelastic Phenomena by a symbolic operation, in contrast to the numerical methods that are widely used today.
The theory of this method based on science analogies approach which allow to present interaction (considering 6 DOF) between aeroelastic forces in analytical formulation, using modern Computer Algebra System tools and as results exclude iteration calculations which inherent inversing and eigenvalue extraction of large dimension matrixes.
Approach of this method based on reduced order modelling principle and main idea is presenting lifting surface (wing, blade, etc.) as a principal scheme which look as parallel, serial and star connection of three types of elements: aerodynamical, elastic and inertial. Each element describes by respective matrixes of parameters with maximum dimension of 6x6 for 6 DOFs (3 translations + 3 rotations).
Analysis is performing by transformation scheme (connection nodes condensation) and finding equivalent matrix of “Aeroelasticity” using recurrent equations for each type of connection (analogical with electrical circuit). Described method was validate by modelling: Wing load distribution, Divergence, Effectiveness of control surface and Flutter.
Finally, gotten Math model describes dependences between design variables and aeroelastic characteristic in explicit symbolic form which allow performs wide fast parametric investigation at preliminary stage design. Additional this model will be useful for structure optimization process using analytical methods and for machine learning and will allow expand using artificial intelligence in aerospace structure design.
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