The Neuromorphic Element: A Data-Driven Finite Element Formulation Using Self-Designing Neural Networks

Abstract

In this thesis, a new data-driven finite element is developed, which is referred to as a neuromorphic element (designated as NmT2). Its goal is to reduce the computational expense of FEA models with- out compromising solution accuracy by embedding a neural network, trained on an element level. The neural network is developed such that the traditional trial-and-error approach to determin- ing its hyperparameters may be bypassed. This is achieved through a multi-objective optimization algorithm that builds networks with random configurations and uses Latin Hypercube sampling to test them on a fraction of the overall data repository. Once the algorithm reaches a state of diminish- ing returns over the development of multiple networks, the program is halted and the best perform- ing neural network is saved. The resultant network is then trained over the entire data repository consisting of over half a million datasets. The entire process of a self-designing neural network is called a neuromorphic engine. The neuromorphic engine is designed to determine the local nodal force vector of a truss mem- ber based on the structure’s geometry and axial nodal displacements. Axial tension and compres- sion are the two modes of loading that are considered and are pushed to the nonlinear regimes by including post-buckling and material plasticity. In addition, the user is provided with the option of including structural defects in the truss members. Once trained, the neuromorphic engine can be inserted within a user-element subroutine and deployed in ABAQUS. The neuromorphic element is essentially a truss element which includes the deformation ca- pabilities of beam elements. Unlike traditional FEA methods requiring multiple beam elements, a single NmT2 element can be used when meshing a truss member to model complex behaviour such as post-buckling deformation. To test the capabilities of the neuromorphic element, three case studies are designed as a proof of concept, comparing the performance of NmT2 elements against traditional FEA elements (T2D2 or B22). Overall, the NmT2 elements managed to accel- erate the computing time of an FEA model by up to 1,000%, while maintaining solution accuracy within 5%. These results affirm the potential of neural networks within active FEA simulations in the field of data-driven computational mechanics as a means to define complex nonlinear element formulations.