Topology optimization has become an effective tool for least-weight and performance design, especially in aeronautics and aerospace engineering. The purpose of this paper is to survey recent advances of topology optimization techniques applied in aircraft and aerospace structures design. This paper firstly reviews several existing applications: (1) standard material layout design for airframe structures, (2) layout design of stiffener ribs for aircraft panels, (3) multi-component layout design for aerospace structural systems, (4) multi-fasteners design for assembled aircraft structures. Secondly, potential applications of topology optimization in dynamic responses design, shape preserving design, smart structures design, structural features design and additive manufacturing are introduced to provide a forward-looking perspective.

Topology Optimization in Aircraft and Aerospace Structures Design

A review of topology optimization for additive manufacturing: Status and challenges

Three-dimensional printing offers varied possibilities of design that can be bridged to optimisation tools. In this review paper, a critical opinion on optimal design is delivered to show limits, benefits and ways of improvement in additive manufacturing. This review emphasises on design constrains related to additive manufacturing and differences that may appear between virtual and real design. These differences are explored based on 3D imaging techniques that are intended to show defect related processing. Guidelines of safe use of the term “optimal design” are derived based on 3D structural information.

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Challenges of additive manufacturing technologies from an optimisation perspective

Experimental validation of 3D printed patient-specific implants using digital image correlation and finite element analysis

This paper presents an approach to shape and topology optimization of fluid-structure interaction (FSI) problems at steady state. The overall approach builds on an immersed boundary method that couples a Lagrangian formulation of the structure to an Eulerian fluid model, discretized on a deforming mesh. The geometry of the fluid-structure boundary is manipulated by varying the nodal parameters of a discretized level set field. This approach allows for topological changes of the fluid-structure interface, but free-floating volumes of solid material can emerge in the course of the optimization process. The free-floating volumes are tracked and modeled as fluid in the FSI analysis. To sense the isolated solid volumes, an indicator field described by linear, isotropic diffusion is computed prior to analyzing the FSI response of a design. The fluid is modeled with the incompressible Navier-Stokes equations, and the structure is assumed linear elastic. The FSI model is discretized by an extended finite element method, and the fluid-structure coupling conditions are enforced weakly. The resulting nonlinear system of equations is solved monolithically with Newton's method. The design sensitivities are computed by the adjoint method and the optimization problem is solved by a gradient-based algorithm. The characteristics of this optimization framework are studied with two-dimensional problems at steady state. Numerical results indicate that the proposed treatment of free-floating volumes introduces a discontinuity in the design evolution, yet the method is still successful in converging to meaningful designs.

An immersed boundary approach for shape and topology optimization of stationary fluid-structure interaction problems

Topology optimisation has for a considerable time been applied successfully in the automotive industry, but still has not become a mainstream technology for the design of aircraft components. The explanation for this is partly to be sought in the larger problem sizes and in the often quite complicated support and loading conditions for aircraft components. Also, aircraft components are often stability designs and the compliance based topology optimisation method still lacks the ability to deal with any buckling criteria. The present paper considers the use of the compliance formulated topology optimisation method and detailed sizing/shape optimisation methods to the design of aircraft components but also discusses the difficulties in obtaining correct loading and boundary conditions for finite element based analysis/optimisation of components that are integral parts of a larger structure.

Application of Topology, Sizing and Shape Optimization Methods to Optimal Design of Aircraft Components

Structure optimization at airframe level is mainly focused on sizing design variables detailing the thin-walled properties of aircraft structures. Typical design variables are cross sectional dimensions for 1D and 2D elements with an additional complexity brought by composite materials with their directional and multi-layer aspects. Even if the scope of these design variables is clear and well understood, the vision of the structure behaviour is multi-criteria and encompasses various fidelity levels. Its design requires several stages from the future project to the detailed definition of structural parts using various analysis tools from different disciplines. These several stages require adequate structural optimization processes to offer the best response with the right level of details to answer questions being sought at each maturity level of the design. A review of methods & tools developed and applied at AIRBUS to deliver automated sizing for aircraft structures along their development will be presented. Ways forward and major stakes for the future will be discussed.

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Numerical Optimization applied to structure sizing at AIRBUS: A multi-step process

A method of designing a composite laminate, the laminate comprising a plurality of zones, each zone comprising a plurality of plies of composite material, each ply in each zone having a respective ply orientation angle. A global stacking sequence is determined for the laminate, the global stacking sequence comprising a sequence of stacking sequence elements. A local laminate thickness is determined for each zone. A local stacking sequence is then determined for each zone by extracting a subsequence of stacking sequence elements from the global stacking sequence. The global stacking sequence and the local laminate thicknesses are determined together in an optimisation process in which multiple sub-ply selection variables are assigned to each stacking sequence element, each sub-ply selection variable representing the density or sub-ply thickness for a respective candidate ply orientation angle. Optimal values are determined for the sub-ply selection variables and the local laminate thicknesses. A single one of the sub-ply selection variables is assigned to each stacking sequence element thereby forcing a discrete choice of global ply orientation angle for each stacking sequence element.

Method of designing a composite laminate

A method of designing a composite panel, the panel comprising a plurality of zones, each zone comprising a plurality of plies of composite material arranged in a stacking sequence, each ply in each stacking sequence having a respective orientation angle For each orientation angle a first layout matrix is created which identifies zones in the panel which contain at least one ply with that orientation angle A second layout matrix is also created which identifies zones in the panel which contain at least two plies with that orientation angle, and so on up to an Nth layout matrix which identifies zones in the panel which contain at least N plies with that orientation angle The layout matrices are arranged in a plurality of candidate sequences Selection criteria are then used to choose one or more of the candidate sequences and stacking sequences are assigned to the zones in accordance with the chosen candidate sequence(s)

Method of designing a composite panel

An aircraft fuselage has a hatch or door located in the vicinity of a load bearing structure that places loads on the zone around the door or hatch. The fuselage frame around the door or hatch is strengthened by a supplementary e.g. roughly rectangular intercostal frame with diagonal members. The diagonal spar (12) has a cruciform cross section.

Lars Krog

Papers

Application of Topology, Sizing and Shape Optimization Methods to Optimal Design of Aircraft Components

Numerical Optimization applied to structure sizing at AIRBUS: A multi-step process

Method of designing a composite laminate

Method of designing a composite panel

Strengthening frame for aircraft fuselage hatch or door surround has spars with cruciform cross section