Elementary-level intrusive coupling of machine learning for efficient mechanical analysis of variable stiffness composite laminates: a spatially-adaptive fidelity-sensitive computational framework
Authors: Garg A. , Naskar S. , Mukhopadhyay T. 
Published: January 2025

Mechanical analysis of the complex configurations of composite laminates can be computationally prohibitive based on accurate higher-order theories, especially when the analyses involve multiple realizations corresponding to different sets of input parameters such as uncertainty quantification, optimization, reliability and sensitivity analysis. Efficient lower-order theories should not be adopted in such situations since the error accumulates with multiple realizations, leading to poor outcomes. We propose an elementary-level coupling of machine learning for efficient, yet accurate mechanical analysis of laminated composites based on finite element simulations coupled with gaussian process regression. The generic parameter space of material properties, mesh size, number of layers, and ply angle in composite laminates are accounted for forming an efficient mapping with the augmentation of lower-order theory-based elementary-level structural matrices. The computationally efficient machine learning models predict the difference in the elements of the stiffness matrix for higher-order zigzag theory (HOZT) and first-order shear deformation theory (FSDT) at the first stage. Based on such machine learning-based difference mapping, we augment the elementary stiffness matrices obtained using FSDT efficiently to the equivalent of HOZT theory without any additional computational expenses (referred to here as augmented FSDT, or aFSDT). However, it is not necessary to augment all the elements in the analysis domain which might otherwise lead to unnecessary computational expenses and loss in accuracy. To achieve an optimal level of computational efficiency and accuracy, we further propose spatially-adaptive fidelity-sensitive coupling of machine learning, only for the elements within the analysis domain where it is necessary to adopt higher-order theories. The selective augmentation strategy essentially brings in a scope of integrating physics-based insights of critical stress resultant distribution into the algorithm based on best theory diagram. Subsequently, the global structural matrices are computed exploiting such adaptive criteria containing a mixed set of elements formed using FSDT and aFSDT, which leads to an accuracy equivalent to HOZT in the mechanical analysis of composite laminates almost at the computational expense of FSDT. The proposed spatially-adaptive fidelity-sensitive scheme ensures optimal performance in terms of computational efficiency by augmenting selective elements while minimizing the loss of accuracy due to the involvement of surrogates. Detailed numerical results are presented for static, dynamic and stability characterization of composite laminates including the demonstration for variable stiffness composite configurations based on the efficient machine learning-assisted elementary-level intrusive computational framework, wherein the notion of engineering judgement is introduced concerning the trade-off between computational efficiency and required level of accuracy.