(Georgia Institute of Technology, 2023-12-05)
Okegbu, Daniel O.
The goal of this study is to investigate the effects of large deflections in the energy release rate and mode partitioning of face/core debonds for the Single and Double Cantilever Beam Sandwich Composite testing configurations, which are loaded with an applied shear force and/or bending moment. Studies on this topic have been done by employing geometrically linear theories (either Euler-Bernoulli or Timoshenko beam theory). This assumes that the deflection at the tip of the loaded debonded part is small, which is not always the case. To address this effect, we employ the elastica theory, which is a non-linear theory, for the debonded part. An elastic foundation analysis and the linear Euler-Bernoulli theory are employed for the "joined" section where a series of springs is employed to represent the interfacial bond between the face and the substrate (core and bottom face). The derivation/solution is done for a general asymmetric sandwich construction. A $J$-integral approach is subsequently used to derive a closed-form expression for the energy release rate. Furthermore, in the context of this Elastic Foundation model, a mode partitioning measure is defined based on the transverse and axial displacements at the beginning of the elastic foundation. The results are compared with finite element results for a range of core materials and show very good agreement. Specifically, the results show that large deflection effects reduce the energy release rate but do not have a noteworthy effect on the mode partitioning. Conversely, a small deflection assumption can significantly overestimate the energy release rate.
(Georgia Institute of Technology, 2023-08-04)
Kraus, Julie Anne
Tensegrity structures are composed of bars and tethers that have a state where they can be stability stressed without outside constraints. This makes them pliable, controllable, and capable of large deformations. In order to use tensegrities in actual applications it is necessary to have the capability to model them. Current computational modeling methods involve finite element modeling (FEM). FEM is a very powerful tool that can analyze most systems given enough time and computational power. However, for certain applications related to tensegrity structures, the required computational power can become a limiting factor.
In this work we develop computational models to further improve our understanding of tensegrity structures. For the case of pin-jointed tensegrity structures, we use the Elastica theory to derive an analytical model of deformation in imperfect beams. Our model outperforms existing ones and is more accurate over a large range of deformations. We also then utilize finite element simulations to study the behavior of 3D-printed tensegrity meta-materials and demonstrate that the same type of response observed in pin-jointed structures is also held in the frame cases, and that tensegrities have strong potential as structures that can handle high strain prior to failure due to their ability to delocalize failure. Finally, by observing that these models are accurate but computationally expensive, we develop a machine learning based reduced order model to predict the response of tensegrity structures. Our algorithm is based on a frame-indifferent neural network architecture, allowing for the ability to predict the effects of large-scale deformation on tensegrity structures.