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

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

Two dimensional composite structures are designed for maximum stiffness under multiple load cases. Both the topology and the fibre angle distribution are optimised simultaneous. To solve the topology optimisation, a density approach is used. The stiffness is parametrised in terms of lamination parameters, not directly in terms of the fibre angles. To force the fictitious density to either zero or one both implicit and explicit penalisation are used. Both penalisation approaches are implemented and both give a satisfactory result. Once the optimum lamination parameter and density distribution is found, some post-processing steps are necessary: the boundaries of the structure are determined by post-processing the density distribution. The fibre angle distribution is found by matching the lamination parameter distribution. Finally the fibre paths are determined. A number of examples are worked out to demonstrate the technique for balanced, unbalanced, single and multiple load case problems. The results show that the proposed technique is widely applicable and that there are considerable benefits in exten ding topology optimisation to handle composites.

Combining topology and lamination parameter optimisation

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.

Gerrit Rollema

Papers

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