Structural and Multidisciplinary Optimization

, Volume 53, Issue 3, pp 589–603 | Cite as

Matrix-free aerostructural optimization of aircraft wings

  • Andrew B. Lambe
  • Joaquim R. R. A. Martins


In structural optimization subject to failure constraints, computing the gradients of a large number of functions with respect to a large number of design variables may not be computationally practical. Often, the number of constraints in these optimization problems is reduced using constraint aggregation at the expense of a higher mass of the optimal structural design. This work presents results of structural and coupled aerodynamic and structural design optimization of aircraft wings using a novel matrix-free augmented Lagrangian optimizer. By using a matrix-free optimizer, the computation of the full constraint Jacobian at each iteration is replaced by the computation of a small number of Jacobian-vector products. The low cost of the Jacobian-vector products allows optimization problems with thousands of failure constraints to be solved directly, mitigating the effects of constraint aggregation. The results indicate that the matrix-free optimizer reduces the computational work of solving the optimization problem by an order of magnitude compared to a traditional sequential quadratic programming optimizer. Furthermore, the use of a matrix-free optimizer makes the solution of large multidisciplinary design problems, in which gradient information must be obtained through iterative methods, computationally tractable.


Structural optimization Multidisciplinary design optimization Matrix-free Large-scale optimization Constraint aggregation 



Computations were performed on the GPC supercomputer at the SciNet HPC Consortium. SciNet is funded by: the Canada Foundation for Innovation under the auspices of Compute Canada; the Government of Ontario; and the University of Toronto.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Institute for Aerospace StudiesUniversity of TorontoTorontoCanada
  2. 2.Department of Aerospace EngineeringUniversity of MichiganAnn ArborUSA

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