Accelerated Computation of Large-Order and Nonlinear Finite Element Models

In this paper, we discuss a physics-based framework for accelerated computation of large-order linear and nonlinear finite element models. We utilize the word physics-based to differentiate from accelerated computation achieved via other means such as neural networks. The typical manner in which system-level finite element models are developed is by first constructing the sub-system level (hereafter referred to as component) finite element models and then imposing constraint equations along the connecting interfaces to impose displacement compatibility and force equilibrium. In this way, the finite element model of large complex systems can be constructed from its components in a systematic fashion. The resulting system-level finite element model will often be of large-order (100M+ degrees of freedoms) especially if high resolution stress calculations are desired. The solution of such large-order finite element models in either frequency- or time-domain can easily become infeasible even on cloud-based super-computers. However, high-speed computation can still be achieved algorithmically with a proper framework for computation. By utilizing methodologies such as Residual-Flexibility Mixed-Boundary (RFMB), reduced-order component level models which fully preserve the accuracy of the upstream component finite element model can be developed. From these reduced-order components, the system-level model can be constructed which can now compute any desired forcing function for the subject assessment, including long duration stochastics inputs. The deployment of this methodology and framework are demonstrated through application examples, which include irregular wave fatigue of flexible risers, dynamics of a floating structure topside/hull, random vibrations of cokers, and stresses in thermoplastic composite pipe.