A Method for Capturing Structural Behavior Variations in the Realization of Optimized Graph-Based Topologies for a Morphing Airfoil

With more efficient computational capabilities, the use of topology optimization is becoming more common for many different types of structural design problems. Rapid prototyping and testing is often used to analyze optimized designs, but depending on a design’s complexity, the structural behavior of physical models can vary significantly compared to that of their computational counterparts. For graph-based topologies, this difference is caused by a need to realize finite-thickness structures from the infinitely thin geometries described by graph theory. To determine the variation in structural behavior that occurs when generating thick geometry from thin graphs, studies are performed on graph-based topologies of supersonic, diamond-shaped morphing airfoils from prior studies. Structural behavior of finite element models using lower fidelity beam elements are compared to those using higher fidelity volume elements. The amount of overlap between neighboring members that occurs in regions of the volume element models is shown to serve as an indicator of locations where structural behavior, specifically stiffness and maximum stress, is expected to vary between element types. These differences occur in regions where member overlap exceeds 10%, and for the morphing airfoil designs considered, such locations are highly present. Results from this work show that corrections could potentially be made in the beam models for regions where member overlap of 30% or less occurs. It is recommended that regions with overlap greater than 30% should be avoided in the graph-based topology optimization when modeled with beams since stresses in the higher fidelity elements were not accurately predicted.