Design method of variable-stiffness composite helical springs based on ply angle optimization

Spring is an elastic body whose function is to store energy when deflected by force and return equivalent amount of energy on being released. Helical compression springs are widely used for suspension in light vehicle and locomotives worldwide. Automobile manufacturer are looking for replacing existing metal spring by composite spring due to its high strength to weight ratio. In this study the design parameters indicate that there is considerable weight saving is possible and increase the stiffness of the spring by reducing the number of coils and increasing the area of the spring. The filament winding technique is used to fabricate the continuous fiber reinforced composite helical spring. The weight of the composite spring obtained is 42.63 % less than the conventional metal spring. Stiffness of the composite spring is 43.76% less compared to conventional metal spring. Even though stiffness of the composite helical spring is less when compared to conventional metal spring, the spring is designed with less number of coils to increase the stiffness without sacrifice the strength or load carrying capacity of the spring.

Composite helical springs (CHSs) are mainly used in transportation and aerospace fields, such as automobile suspension, railway bogie and aircraft engine systems. It has become a trend to replace the traditional metal helical springs with CHSs with the advantage of energy conservation during service and emission reduction during manufacturing. The advantages of CHSs such as low weight, high specific strength, high specific modulus, corrosion resistance, fatigue resistance and high strain energy storage capacity mean that it has great development potential. The static and dynamic performances of CHSs together determine whether they can be used on a large scale in the engineering field. The static performance of the CHS determines their service-load range and the dynamic performance determines the service life and safety performance of CHSs under dynamic load environmental conditions. Therefore, it is an important task to optimize the static and dynamic performance of CHSs. To provide a reliable reference for the development of CHSs, this review analyzes the important factors affecting the static and dynamic performance optimization of CHSs from the perspectives of theory, finite element method (FEM), and experiment. In addition, the outlook in the research of CHSs are discussed.

A novel method based on a physics informed data driven model is developed to design an origami composite crash tube. The structure consists of two axially stacked basic components, called modules. Each module presents lower and upper square sections with an octagonal section in the middle. The parameters of the octagonal cross-section and the height of each module are optimized to maximize the energy absorption of the tube when subjected to an axial impact. In contrast to standard surrogate modelling techniques, whose accuracy only depends on the amount of available data, a Physics-informed Neural Network (PINN) scheme is adopted to correlate the crushing response of the single modules to that of the whole origami tube, constraining the data driven method to physically consistent predictions. The PINN is first trained on the results obtained with an experimentally validated Finite Element model and then used to optimize the structure. Results show that the PINN can accurately predict the crushing response of the origami tube, while consistently reducing the computational effort required to explore the whole design domain. Also, the comparison with a standard Feed Forward Neural Network (FFNN) shows that the PINN scheme leads to more accurate results.

Traffic state estimation (TSE) is a critical component of the efficient intelligent transportation systems (ITS) operations. In the literature, TSE methods are divided into model-driven methods and data-driven methods. Each approach has its limitations. The physics information-based neural network (PINN) framework emerges to mitigate the limitations of the traditional TSE methods, while the state-of-art of such a framework has focused on single road segments but can hardly deal with traffic networks. This paper introduces a PINN framework that can effectively make use of a small amount of observational speed data to obtain high-quality TSEs for a traffic network. Both model-driven and data-driven components are incorporated into PINNs to combine the advantages of both approaches and to overcome their disadvantages. Simulation data of simple traffic networks are used for studying the highway network TSE. This paper demonstrates how to solve the popular LWR physical traffic flow model with a PINN for a traffic network. Experimental results confirm that the proposed approach is promising for estimating network traffic accurately.

<p indent="0mm">Against the background of precision payload mounting plates with complex heat sources in high-precision and high-stability spacecraft, an intelligent design method for functionally graded structures based on physics-informed neural networks is presented. Independent of thermal control devices, the local temperature in the load installation area and the fundamental frequency of the structure are regulated by optimizing the material gradient distribution. A loss function is established that includes the heat-conduction governing equation, local temperature and fundamental frequency optimization objectives, and material volume fraction constraints, considering multiple heat source distributions. The inverse problem with material gradient distribution as a design variable is solved using physics-informed neural networks. The results show that a reasonable design of the material gradient distribution can accurately regulate the local temperature at specific locations and the fundamental frequency without relying on external thermal control devices. The proposed method is expected to reduce the need for thermal vibration control devices for spacecraft structures and improve structural thermal-mechanical stability.

Heavy-duty springs can be made lightweight by replacing metallic materials with polymer composite materials. Most existing studies mainly concentrate on the static performance of composite helical springs (CHSs), understanding the dynamic impact of CHSs is limited. In this study, the impact response of CHSs with multi-braided layers (MBLs-CHS) is investigated using drop-weight impact tests. Experimental results indicate a sequential improvement in the impact performance of CHSs with single, double, and triple braided layers (SCHS, DCHS, and TCHS). Specifically, TCHS demonstrates enhancements of up to 5.1%, 78.3%, and 34.1% in deformation resistance, F max , and E e , respectively, compared to SCHS. Subsequently, a virtual fiber model (VFM) elucidates the internal mechanism behind this improvement. The force-bearing contribution of the corresponding braided layers in SCHS, DCHS, and TCHS is similar, emphasising that the impact response difference is primarily attributed to the additional braided layer. Additionally, stress and motion responses of VFM revealed non-linear characteristics in stress, displacement, and velocity waves transitioning of MBLs-CHS. Finally, the impact mitigation ability of MBLs-CHS can be calculated based on velocity responses of VFM, highlighting that of TCHS improves by 111.6% and 42.0% compared to SCHS and DCHS, respectively. This research establishes a robust foundation for dynamic studies and offers valuable guidelines for the engineering design of CHSs. • Introduced VFM can precisely simulate the impact process of MBLs-CHS. • Impact performance of MBLs-CHS can be evaluated based on velocity response of VFM. • There is sequential improvement in the impact performance of SCHS, DCHS, and TCHS.

Despite advances in joint modelling, the ongoing demand for more efficient and sustainable steel structures calls for further improvements in the design of connections. This paper presents part of a broader research effort aimed at enhancing the design efficiency of steel joints by realistically capturing their behavior and enabling the development of more accurate and reliable design criteria. A novel application of Physics‐Informed Neural Networks (PINNs) is proposed to model the moment–rotation behaviour of welded beam‐to‐column joints. PINNs are trained on a parametric dataset generated from validated FEM models, embedding analytical expressions for initial stiffness as a physics constraint. The results show excellent agreement with FEM simulations in the elastic range and promising accuracy beyond it. By replacing FEM for large‐scale data generation, PINNs unlock the stochastic characterisation of joint behaviour within the probabilistic framework of EN 1990, supporting Monte Carlo simulations and the derivation of statistically robust resistance criteria. Future developments will extend the approach to other joint configurations and integrate the results into macroelements for system‐level digital workflows, supporting the advancement of the Direct Design Method.

Surrogate models leveraging Neural Networks (NNs) have demonstrated significant potential in accurately modeling the intricate dynamics of the injection molding process, enabling the prediction and optimization of process and material parameters on internal thermodynamics and final product quality. However, the substantial effort required for data collection remains a notable challenge. This study investigates the effectiveness of pretraining methods with varying fidelities for a two-dimensional cooling problem in injection molding. Specifically, NNs are pretrained using low-fidelity (LF) solutions derived from the Finite Element Method (FEM) and Physics-Informed Neural Networks (PINNs). These pretrained models are subsequently fine-tuned with high-fidelity (HF) simulation data to enhance prediction accuracy across previously untrained scenarios. While both FEM and PINNs provide approximations of the cooling process, PINNs offer a continuous solution space, however, at a higher computational cost compared to FEM. Respectively, FEM is more computationally efficient but less proficient at handling highly parameterized input spaces. Comparing different fidelities reveals that prioritizing the capture of main effects over detailed physical implementation during pretraining can be advantageous. The fine-tuned surrogate model demonstrates robust approximation capabilities with limited simulation runs, highlighting its data efficiency.

The physics‐informed neural network (PINN) method has been applied to solve water hammer equations in pipeline systems due to its ability of seamlessly integrate measurement data with conservation laws, offering advantages over traditional numerical method. However, existing PINN approaches require multiple neural networks to construct composite models for complex water distribution systems (WDS). This situation treats nodal information as boundary condition or labeled data during training, leading to a weaker robustness and a high demand for data. To address these issues, a hybrid water hammer model based on eXtended Physics‐Informed Neural Networks for WDS (WDS‐XPINN) is developed in this study. Unlike the standard PINN, WDS‐XPINN incorporates the nodal mechanistic model directly into the loss function, enabling to synchronously train a unified neural network jointly through sparse augmented measurement data for pipeline system. Additionally, an adaptive weights method is introduced to improve model robustness by balancing the contributions of flowrates and pressures. The proposed WDS‐XPINN is evaluated in two case studies: a series pipeline system with different operational events and noise perturbation, as well as a topological structure with looped and branched pipe. According to the simulation results and uncertainty analysis, the WDS‐XPINN model demonstrates its excellent capacity of modeling fluid transient accurately in pipeline system, even without exact operational conditions or true pipe parameters.

Maintaining consistent part quality remains a critical challenge in industrial additive manufacturing, particularly in laser-based powder bed fusion of polymers (PBF-LB/P), where crystallization-driven thermal instabilities, governed by isothermal crystallization within a narrow sintering window, precipitate defects such as curling, warping, and delamination. In contrast to metal-based systems dominated by melt-pool hydrodynamics, polymer PBF-LB/P requires monitoring strategies capable of resolving subtle spatio-temporal thermal deviations under realistic industrial operating conditions. Although machine learning, particularly convolutional neural networks (CNNs), has demonstrated efficacy in defect detection, a structured evaluation of heterogeneous modeling paradigms and their deployment feasibility in polymer PBF-LB/P remains limited. This study presents a systematic cross-paradigm assessment of unsupervised anomaly detection (autoencoders and generative adversarial networks), supervised CNN classifiers (VGG-16, ResNet50, and Xception), hybrid CNN-LSTM architectures, and physics-informed neural networks (PINNs) using 76,450 synchronized thermal and RGB images acquired from a commercial industrial system operating under closed control constraints. CNN-based models enable frame- and sequence-level defect classification, whereas the PINN component complements detection by providing physically consistent thermal-field regression. The results reveal quantifiable trade-offs between detection performance, temporal robustness, physical consistency, and algorithmic complexity. Pre-trained CNNs achieve up to 99.09% frame-level accuracy but impose a substantial computational burden for edge deployment. The PINN model attains an RMSE of approximately 27 K under quasi-isothermal process conditions, supporting trend-level thermal monitoring. A lightweight hybrid CNN achieves 99.7% validation accuracy with 1860 parameters and a CPU-benchmarked forward-pass inference time of 1.6 ms (excluding sensor acquisition latency). Collectively, this study establishes a rigorously benchmarked, scalable, and resource-efficient deep-learning framework tailored to crystallization-dominated polymer PBF-LB/P, providing a technically grounded basis for real-time industrial quality monitoring.

Prediction of Kelvin–Helmholtz instability (KHI) is crucial across various fields, requiring extensive high-fidelity data. However, experimental data are often sparse and noisy, while simulated data may lack credibility due to discrepancies with real-world configurations and parameters. This underscores the need for field reconstruction and parameter inference from sparse, noisy data, which constitutes inverse problems. Based on the physics-informed neural networks (PINNs), the KH-PINN framework is established in this work to solve the inverse problems of KHI flows. By incorporating the governing physical equations, KH-PINN reconstructs continuous flow fields and infer unknown transport parameters from sparse, noisy observed data. The two-dimensional unsteady incompressible flows with both constant and variable densities are studied. To our knowledge, this is one of the first few applications of PINNs to unsteady incompressible flows with variable densities. To address the spatiotemporal multiscale issue and enhance the reconstruction accuracy of small-scale structures, the multiscale embedding (ME) strategy is adopted. To address the magnitude multiscale issue and enhance the reconstruction accuracy of small-magnitude velocities, which are critical for KHI problems, the small-velocity amplification (SVA) strategy is proposed. The results demonstrate that KH-PINN can accurately reconstruct the fields with complex, evolving vortices and infer unknown parameters across a broad range of Reynolds numbers. Additionally, the energy-decaying and entropy-increasing curves are accurately obtained. The effectiveness of ME and SVA is validated through comparative studies, and the anti-noise and few-shot learning capabilities of KH-PINN are also validated. The code for this work is available at https://github.com/CAME-THU/KH-PINN.

Li-ion batteries are garnering significant attention due to the electrification of critical sectors. High-fidelity battery cell models have proven effective in assessing performance and optimizing design, alleviating the financial burden associated with extensive experimental procedures. However, the computational costs associated with such simulations can become prohibitive, particularly when numerous iterations are required or when integration into small devices, such as battery management systems, is necessary. To address these challenges and provide an alternative to traditional methods such as finite element and finite volume solvers, we propose the development of an algorithm that utilizes Physics-Informed Neural Networks (PINNs) to solve the Single Particle Model across multiple parameter ranges. A notable advantage of this machine learning approach is its capacity to generate competitive solutions post-training by relying solely on the governing equations, without the necessity for experimental or simulation data. Additionally, the lightweight nature of the model indicates its potential for embedding within small-scale devices.

Magnetic resonance elastography (MRE) is a medical imaging modality that non-invasively quantifies tissue stiffness (elasticity) and is commonly used for diagnosing liver fibrosis. Constructing an elasticity map of tissue requires solving an inverse problem involving a partial differential equation (PDE). Current numerical techniques to solve the inverse problem are noise-sensitive and require explicit specification of physical relationships. In this work, we apply physics-informed neural networks to solve the inverse problem of tissue elasticity reconstruction. Our method does not rely on numerical differentiation and can be extended to learn relevant correlations from anatomical images while respecting physical constraints. We evaluate our approach on simulated data and in vivo data from a cohort of patients with non-alcoholic fatty liver disease (NAFLD). Compared to numerical baselines, our method is more robust to noise and more accurate on realistic data, and its performance is further enhanced by incorporating anatomical information.

Bearings are critical components in rotating machinery, and accurate prediction of their remaining useful life (RUL) is essential for prognostics and health management. However, complex and varying operating conditions in real industrial environments, together with the scarcity of full life-cycle failure data under target conditions, severely limit the small-sample prediction accuracy, cross-condition generalization capability, and practical applicability of existing RUL prediction models. To address these challenges, this paper proposes a hybrid RUL prediction framework that integrates unsupervised deep feature extraction with physics-driven modeling: the deep Boltzmann machine-physics-informed neural network (DBM-PINN). First, an unsupervised DBM is employed to automatically extract key degradation-related latent features from healthy data, effectively tracking the degradation trend while suppressing interference caused by varying operational conditions. Subsequently, an implicit PINN is constructed to embed degradation knowledge by modeling the intrinsic evolution of the degradation trajectory through nonlinear partial differential equations. Using DBM-extracted features together with time as inputs, the proposed framework overcomes the limitation of insufficient failure data and achieves high-precision, cross-condition RUL prediction from a single dataset. The effectiveness of the proposed DBM-PINN in terms of small-sample prediction accuracy and cross-condition generalization is validated using the XJTU-SY bearing dataset. Experimental results demonstrate that the proposed method enables the model to focus on the intrinsic degradation evolution, effectively capture essential degradation features, and reduce the influence of specific operating conditions, thereby achieving robust RUL prediction under complex and varying environments.

The Surface Water and Ocean Topography (SWOT) satellite mission, launched in December 2022, provides revolutionary measurements of the sea surface height (SSH) variations with unprecedented spatial resolution down to Ο(1 km). As a result, SWOT products have significant potential in monitoring ocean dynamics down to the submesoscale. However, the repeat cycle of 21 days introduces a barrier to fully capture these dynamics as they vary on the order of days. To fully exploit the potential of the satellite mission and simplify processing requirements for potential users, we propose a physics-informed neural network (PINN) to generate gridded SSH products from SWOT L3 along-track snapshots. The neural network has a U-Net-like architecture combined with residual learning to consider the spatial variations of the SSH field, and takes time, geolocations, and gridded SSH from conventional altimetry missions as input features, while the SWOT observations serve as ground truth. In addition to the classical data loss, the PINN model applies direct constraints on the model's trainable parameters by forcing them to fulfill the next-order correction of the quasi-geostrophic theory (SQG+1), which has been demonstrated to be able to capture cyclogeostrophic balance and frontogenesis attributed to submesoscale dynamics. To this end, the high resolution of SWOT observations is kept, while the velocities and pressure fields associated with the SQG+1 theory are predicted. We conducted experiments using both simulated data and real-world data. Both experiments demonstrate the benefits of incorporating physical loss to achieve higher generalizability, thereby filling the gaps between SWOT tracks reasonably. Based on the real-world data, 2-km gridded SSH products with a temporal resolution of five days are achieved. The proposed method shows promising potential for generating high-resolution gridded products while considering physical constraints. The product will be beneficial for the community to analyze mesoscale to submesoscale ocean dynamics, and compare with other sources of surface and in-situ data in the upper ocean.