An Energy‐Based Deep Learning Method for Shakedown Analysis of Elastoplastic Structures

ABSTRACT Traditional shakedown analysis frameworks typically rely on complex mathematical programming or mechanics‐based numerical formulations, requiring substantial domain‐specific expertise that limits broader engineering applications. To overcome these challenges, this study proposes a novel shakedown deep neural network (SDNN) that introduces energy‐based physics‐informed neural networks (PINNs) into shakedown analysis for the first time. Grounded in the upper bound theorem, SDNN constructs an unsupervised energy functional defined as the ratio of plastic dissipation to external work. This functional serves as the sole training loss, effectively eliminating the manual tuning of multiple penalty weights commonly required in physics‐informed learning. Beyond determining shakedown limits, SDNN allows for the direct identification of failure mechanisms from predicted cyclic strain increment fields, bypassing the need for costly incremental simulations. To reduce the computational burden of training, this study proposes a strain‐guided adaptive importance sampling (SAIS) strategy that dynamically refines sampling distributions. This approach achieves an order‐of‐magnitude reduction in the required sample size while concurrently enhancing the computational accuracy. The robustness and broad applicability of the proposed method are demonstrated through extensive benchmarks, including complex cases involving combined thermo‐mechanical loading and multiple load vertices.