G-WING: A NOVEL SOFTWARE TOOL FOR TOOLPATH-CENTRIC DESIGN OF WINGS FOR MATERIAL EXTRUSION

A novel software tool for the design of small aircraft wings to be fabricated with material extrusion is presented where the key requirement of the tool is to minimize the time from identified need to realized capability. The tool, named G-Wing, uses rapid design algorithms based on lifting line theory to determine the outer-mold line of the wing based on desired aerodynamic behavior. The resulting wing shape and flight-load distribution are given to a structural design algorithm to determine the internal structure of the wing based on both expected flight loads and manufacturing constraints. Finally, manufacturing instructions in the form of G-Code are created directly from the wing shape and internal structure. This process removes explicit geometric modeling and slicing from the critical design path and directly converts airfoil coordinates to perimeter G-Code points, minimizing the introduction of geometric error. This process has been used to design and fabricate multiple small aircraft wings that have successfully flown. G-Code for an example wing section is shown to be lighter and require less build time compared to G-Code generated by a standard CAD-slicing toolchain.Mechanical Engineerin

Analysis of an Algorithm for Identifying Pareto Points in Multi-Dimensional Data Sets. 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization

In this paper we present results from analytical and experimental investigations into the performance of divide & conquer algorithms for determining Pareto points in multidimensional data sets of size n and dimension d. The focus in this work is on the worst-case, where all points are Pareto, but extends to problem sets where only a partial subset of the points is Pareto. Analysis supported by experiment shows that the number of comparisons is bounded by two different curves, one that is O(n (log n)^(d-2)), and the other that is O(n^log 3). Which one is active depends on the relative values of n and d. Also, the number of comparisons is very sensitive to the structure of the data, varying by orders of magnitude for data sets with the same number of Pareto points. Nomenclature n = number of points in a data set d = dimension of the data set TZ … , , = Table of n records, each record having d attributes tz … ,, = A record with d attributes ti, zi, … = The ith attribute in a record DC = Divide & Conquer algorithm pbf[n,d] = estimator for number of comparisons in DC algorithm, n points and dimension d mbf[n,d] = estimator for number of comparisons in marriage step of DC algorithm I I

Experimental Study of Wing Structure Geometry to Mitigate Process-Induced Deformation

Small uncrewed aerial vehicles that are fabricated with material extrusion additive manu- facturing often have wings that are single-perimeter structures with sparse internal structure. The large distance between internal supports creates an “unsupported-wall distance”, which leaves the wing skin prone to deformation during fabrication. This work explores and quan- tifies the relationship between the deformation of the wing skin and three geometric param- eters: (1) unsupported-wall distance, (2) local surface curvature, and (3) extrusion width. A three-level full factorial study was devised in which wing sections of varying surface curva- ture, unsupported-wall distance, and extrusion width were fabricated with polymer material extrusion additive manufacturing. The surfaces of the wing sections were then digitized into point clouds with a coordinate measuring machine, and the point cloud data were directly compared to the GCode used to print each wing section. The deformation data was analyzed to quantify the relationship between deformation and the experimental parameters. From the experiment, a non-dimensional term was identified that captures a bounding relationship between the geometric parameters and the deformation. Finally, a mathematical expression was developed to serve an upper bound on unsupported-wall distance based on extrusion width and surface curvature.Mechanical Engineerin

Using Mean Curvature of Implicitly Defined Minimal Surface Approximations to Generate New Unit Cells for Lattice Design

Triply Periodic Minimal Surfaces (TPMS) are smoothly varying surfaces that exhibit zero mean curvature at all points on the surface. TPMS can be modeled with high accuracy us- ing discrete differential geometry techniques. However, generating a useful number of unit cells with this approach would be computationally expensive, and variable lattices would be impossible. Level sets of Fourier series approximations are often used instead. While these approximations have continuous geometry, they no longer retain zero mean curvature like the exact TPMS. In this paper, we calculate the mean curvature of the commonly used approximations of the gyroid and D-surface TPMS. Using isosurfaces of the mean curvature from these approximates, we define, similar but unique surface topologies. The development of these surfaces expands the list of lattices available to designers, broadening the lattice design space. Application to other approximations and further study of the application of these new surfaces is discussed.Mechanical Engineerin

Algorithms to Identify Pareto Points in Multi-Dimensional Data Sets

*Signatures are on file in the Graduate School. ii The focus in this research is on developing a fast, efficient hybrid algorithm to identify the Pareto frontier in multi-dimensional data sets. The hybrid algorithm is a blend of two different base algorithms, the Simple Cull (SC) algorithm that has a low overhead but is of overall high computational complexity, and the Divide & Conquer (DC) algorithm that has a lower computational complexity but has a high overhead. The hybrid algorithm employs aspects of each of the two base algorithms, adapting in response to the properties of the data. Each of the two base algorithms perform better for different classes of data, with the SC algorithm performing best for data sets with few nondominated points, high dimensionality, or fewer total numbers of points, while the DC algorithm performs better otherwise. The general approach to the hybrid algorithm is to execute the following steps in order: 1. Execute one pass of the SC algorithm through the data if merited 2. Execute the DC algorithm, which recursively splits the data into smaller problem size