# Optimization of structures & materials

## Aircraft structural mesh generation for high-fidelity design optimization

*Reference: [Hwang and Martins, AS&T, 2016]*

High-fidelity aircraft structural design optimization is performed using shell-element models of airframes. To perform aerostructural optimization combining CFD and FEA, the structural mesh must be parametrically linked to the geometry used for aerodynamic analysis and optimization. Here, we present an algorithm for constructing a structural mesh where the nodes can be computed as a linear combination of points on the geometry so that as the geometry changes during optimization, the structural mesh warps along with it. The algorithm uses a constrained Delaunay triangulation and elliptical smoothing.

Contours of derivatives of the structural mesh nodes with respect to the left root-chord length design variable. [Hwang et al., AIAA 2014-2041]

## Modular topology optimization

*Reference: [Chung et al., AIAA 2018-0653]*

Here, we demonstrate the benefits of solving a topology optimization problem using a modular approach, via MAUD and OpenMDAO. We implement both the solid isotropic material with penalization (SIMP) method, the parametric level-set method, and the level-set topology optimization method within OpenMDAO. In each method, the model is implemented as a set of components, so there is a high degree of code re-use between the three methods, and between SIMP and the parametric level-set method in particular.

Visualization of the OpenMDAO model for SIMP topology optimization. *[Chung et al., AIAA 2018-0653]*

Topology optimization of a cantilevered beam with a tip load. *[Chung et al., AIAA 2018-0653]*