A Physics-informed Neural Network Approach for Robust Buckling Load Prediction and Reliability-Based Design of Thin Truncated Conical Shells

Physics-informed neural networks for predicting ultimate bearing capacity of layered soils under complex loading conditions

A Physics-Data Hybrid Model for Predicting Earth Pressure Evolution in Buried Horizontal Cylindrical Tanks

Buried horizontal cylindrical tanks are susceptible to stress instabilities, such as shell buckling and weld fatigue, under nonuniform ground settlement. Classical Terzaghi-based earth pressure theories simplify key parameters into static constants, rendering them inadequate for capturing the dynamic soil-tank interaction and parameter evolution induced by settlement. To address this limitation, a physics-data hybrid model (PDHM) is developed by embedding a genetic programming (GP) module into a three-dimensional (3D) analytical earth pressure framework for medium-dense sand conditions. This approach leverages the symbolic regression capability of GP to derive explicit nonlinear expressions for the dynamic load-bearing width B and lateral pressure coefficient K , thereby unifying data-driven adaptability with physical constraints. To ensure transparency and reproducibility, a standalone GP model is constructed as a purely data-driven baseline, utilizing identical feature inputs, preprocessing procedures, and training-testing protocols. Results demonstrate that the PDHM reduces prediction errors by 82.1% to 96.1% compared to the baseline, with decreases in RMSE and MAPE of 51.89% and 92.34%, respectively. Consequently, the PDHM offers an interpretable, generalizable, and computationally efficient tool for analyzing stress evolution and supporting the safety assessment of buried horizontal cylindrical tanks in medium-dense sand conditions.

Elasto-Plastic Optimization of Steel Trusses Under Geometric Nonlinearity and Imperfections via a Neural-Network-Assisted Genetic Algorithm

Elasto-plastic optimization of steel trusses accounting for geometric nonlinearity and initial imperfections poses a significant computational challenge, as each candidate configuration requires expensive nonlinear structural analysis. To address this, the present paper proposes a neural-network-assisted genetic algorithm (NNAGA)-based design framework, in which a deep neural network (DNN) model is progressively trained on data accumulated during the genetic algorithm (GA) search. A penalty-based objective function is constructed to minimize structural weight while enforcing constraints on plastic deformation, load-bearing capacity, and global stability, where the elasto-plastic response is characterized by complementary plastic work, and initial imperfections are introduced through scaled buckling mode shapes. The structural performance of each candidate is evaluated by geometrically and materially nonlinear finite element analysis with imperfections (GMNIA), coupled with linear buckling analysis (LBA). The framework is assessed using four established benchmark structures, namely a 10 bar, a 25 bar, and a 37 bar truss, as well as a double-layer space truss (DLST), and compared with a conventional GA under the same number of finite element evaluations. The NNAGA yields statistically significantly better designs in all four examples, with average fitness improvements of 42%, 21%, 77%, and 42%, respectively, reaching the solution quality of the best GA results using only 20–50% of the evaluation budget. A parametric study further supports the robustness of the penalty formulation and the algorithmic parameters, indicating additional achievable performance reserves.

A novel surrogate model for optimizing lattice for desired force-displacement response

Optimizing lattice structures for energy absorption and load-bearing applications necessitates accurately capturing their nonlinear mechanical response under large deformation. However, traditional nonlinear finite element analysis (NL-FEA) can often fail, particularly at higher compression, which creates numerical gaps in the design space, hindering gradient-based optimization algorithms, ultimately resulting in suboptimal designs. We propose here a neural network (NN) surrogate model that is trained on data generated using Abaqus, a commercial FEA solver. A unique feature of the model is that it exploits both fully and partially successful NL-FEA simulations. This significantly improves the surrogate model’s accuracy and predictive coverage across the design space. The resulting model enables efficient, gradient-driven optimization of lattice structures to match a desired force-displacement response. By replacing expensive NL-FEA evaluations, the surrogate model substantially reduces computational cost while maintaining a coefficient of determination (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R^2$$\end{document}) of 0.98 in prediction. The effectiveness and versatility of this framework are demonstrated by successfully optimizing \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3 \times 3$$\end{document} lattice structures under 40% compression, with the lattice radii as design variables.

Modal-Constrained Co-optimization Approach of Thermomechanical Performance and Weight for Straight-Ribbed Brake Discs Using Deep Learning

In this study, an efficient method for concurrent thermomechanical performance and weight optimization under modal constraints is proposed to address the coupled design challenges of thermomechanical characteristics (thermal capacity, thermal deformation, and modal) and structural weight in straight-ribbed brake discs. Based on high-fidelity computer-aided engineering (CAE) simulations of brake disc thermomechanical behavior, a neural network (NN)-based surrogate model and a ResNet-guided geometric feature recognition (RGFG) model for automatic modality recognition were developed, and integrated with a particle swarm optimization (PSO) framework for optimal solution exploration. When applied to a passenger vehicle brake disc case study, the surrogate model of NN demonstrates remarkable accuracy: it shows more than 95% agreement with the CAE results in thermal capacity prediction, the prediction accuracy of thermal deformation exceeds 90% compared to CAE results and 83.4% compared to test result, thereby validating the method’s effectiveness. Compared with conventional CAE approaches, the surrogate model of NN achieves a subsecond prediction speed, significantly reducing computational costs. The surrogate model of RGFG achieves a test accuracy exceeding 95%. Furthermore, the proposed optimization framework offers valuable insights for the inverse design of brake discs.

Computational modeling and multi-objective optimization of a thin-walled steel crash box for enhanced crashworthiness and failure mitigation

Thin-walled crash boxes are key energy-absorbing components whose geometry influences vehicle mass, impact-force transmission, and crash energy dissipation. Existing optimization approaches often rely on complex geometries or assess structural failure only indirectly, which limits their application to locally manufacturable steel components. In this study, an integrated framework that couples an ABAQUS/Explicit model with the non-dominated sorting genetic algorithm II (NSGA-II) is developed for a square steel crash box that can be produced with conventional manufacturing processes. Wall thickness, box length, trigger-hole diameter, and trigger-hole position were optimized to minimize mass and peak crushing force while maximizing specific energy absorption (SEA), subject to equivalent plastic-strain and connection-safety constraints. The baseline design had a mass of 4.25 kg, an SEA of 9.34 kJ/kg, and a peak force of 115.2 KN. The selected balanced Pareto-optimal design reduced the mass to 3.98 kg (6.4%), increased the SEA to 10.15 kJ/kg (8.7%), and lowered the peak force to 108.4 KN (5.9%). Its connection safety factor increased to 1.18, while the maximum equivalent plastic strain remained below the allowable limit of 0.35. Sensitivity analysis identified wall thickness and trigger-hole geometry as the dominant design variables. The proposed framework provides a practical route to improving crashworthiness using conventional steel and accessible manufacturing processes.