An advanced physics-informed neural network-based framework for nonlinear and complex topology optimization
Hyogu Jeong, Chanaka Batuwatta-Gamage, Jinshuai Bai, Charith Rathnayaka, Ying Zhou, Yuantong Gu
Abstract
In this present paper, we introduce an advanced Physics-Informed Neural Network (PINN) based Topology Optimization (TO) framework for addressing complex structural design challenges. Traditional applications of PINN-based TO have primarily focused on solving classical compliance minimization problems. However, to demonstrate its broad applicability, PINNs must be utilized to address wide range of TO challenges. Addressing this gap, this study developed an advanced Complete Physics-Informed Neural Network-based Topology Optimization (CPINNTO) framework, offering a viable approach for solving complex and nonlinear TO challenges. To do so, a Deep Energy Method (DEM) PINN structures and Sensitivity-analysis PINN (S-PINN) models are constructed to estimate the structure displacement and deriving objective function, respectively. Moreover, CPINNTO is adapted for various TO challenges including periodic, multi-scale, multi-material and geometrically nonlinear TO problems. The numerical experiments indicate that the CPINNTO is capable of obtaining optimal topologies for complex TO problems without labelled data for PINNs or with no involvement of Finite Element Analysis (FEA). Notably, CPINNTO effectively optimized nonlinear designs under geometrically nonlinear conditions using the proposed Saint Venant-Kirchhoff (SVK) DEM-PINN model. In summary, the proposed CPINNTO framework presents an innovative approach for a wide range of practical applications. • An advanced PINN-based TO for solving nonlinear and complex TO problem is proposed. • Two PINNs are employed to replace structural and sensitivity analyses. • The proposed framework does not rely on any labelled data nor FEA to train PINNs. • The PINNs can be modified to solve complex and nonlinear design problems in TO.