SplineNet: An Isogeometric Deep Learning Method for Complex Shells

We present a novel isogeometric deep learning method, termed SplineNet, for the seamless design and analysis of shell structures with complex geometries.

The proposed approach is built upon watertight spline representations, e.g., analysis-suitable unstructured T-splines, and features exact geometric descriptions of Computer-Aided Design (CAD) models in neural networks.

Bézier extraction is used to build the network architecture, where Bernstein polynomials serve as the nonlinear activation functions.

SplineNet can be applied in a data-free or data-driven way.

In the data-free case, energy-based formulations can be naturally incorporated as loss terms, which fulfill the need of Computer-Aided Engineering (CAE) and can be accurately calculated.

In particular, the Kirchhoff--Love (KL) model is adopted to solve for the mechanical behaviors of shell structures.

This way, CAD and CAE can be tightly integrated in a deep neural network without the time-consuming model/data exchange process.

In the data-driven case, SplineNet can be used as the trunk net of Deep Operator Networks (DeepONet) to provide interpretability.

Given such a trained network and unseen input data, results can be immediately obtained without retraining the network or repeatedly performing the traditional workflow for analysis.

In the end, a variety of numerical examples are studied to demonstrate the effectiveness of the proposed method, especially when real-world complex geometries are involved.