**Applying the conservation of Gaussian curvature to predict the deformation of curved L-angle laminates**

In composites manufacturing, predicting the shape change in parts is vital for making sure part dimensions are properly compensated. Different factors in the manufacturing process, such as the temperature change throughout a thermoset cure cycle, can influence shape change. The compensation process becomes more difficult for geometries with double curvature, as interactions between the two radii of curvature can reduce the effectiveness of applying methodologies for single curvature geometries. Additionally, using finite element analysis (FEA) to predict shape change can be costly and time-consuming depending on part geometry.

This thesis studies an approach for predicting the shape change of a symmetric thermoset laminate with a double-curved L-angle section in its geometry. Specifically, the conservation of Gaussian curvature is applied to predict shape change. The geometry studied in this thesis can be broken down and analyzed as a segment of a torus, which is attached on one end by a cylinder and on the other end by a curved flange. Varying the length of the cylinder and flange sections, the effectiveness of Gauss’s theorem is determined for the different part geometries, with developed formulas compared against finite element simulations and experimental measurements.

By approximating torus segments with certain geometric criteria as cylinders, linear elasticity equations for a cylinder undergoing free thermal strain can be solved and the change in the larger arc length in the double-curved geometry is predicted after deformation. The integral form of Gauss’ theorem is then applied to determine the deformed angle of the larger arc, from which geometric relations can be applied to extract the deformed radius. Abaqus is used first to study the torus segment on its own, and then to see the effects of the cylinder and flange segments on the overall geometry. Experimental measurements are also used as a comparison.

Generally, the formula derived using Gauss’ theorem predicts shape change very well for the torus segment on its own. When cylinder and flange segments are included in the geometry, an empirical correction factor can be introduced to account for geometrically induced stiffening effects. Future developments and next steps in this research are discussed.

## History

## Degree Type

- Master of Science

## Department

- Aeronautics and Astronautics

## Campus location

- West Lafayette