A drag-free satellite is an important platform for space-borne gravitational wave (GW) observation. To achieve the high-precision control of a drag-free satellite in practical engineering, an accurate dynamic model is essential. This paper presents a nonlinear model of the electrostatic effect between a satellite and a test mass (TM), and designs a model predictive controller based on the drag-free satellite model with the nonlinear electrostatic effect. To determine the analytical form of the electrostatic effect, a comprehensive theoretical analysis is performed for gravitational reference sensors (GRSs). An electrostatic force and a torque are simulated with the displacement as a varying parameter through a commercial software. Then, the results are fitted to derive the nonlinear expressions of the electrostatic effect. The model predictive controllers based on the models with the nonlinear and linear electrostatic effects are designed in the capture mode. Finally, the control results are given to show the advantages of the nonlinear electrostatic effect.

Hard-magnetic soft materials exhibit significant shape morphing capabilities under non-contact magnetic actuation, yet their particulate composition tends to compromise material toughness. To quantify particle-matrix interactions, we present a mechanics model describing the energy functional of planar magnetic composites. Through the Fourier series, the analytical solutions for stress distribution and interfacial peeling length of a single particle-polymer unit are derived with the Rayleigh-Ritz method under uniaxial tension. The calculated results of stress fields without the magnetic field agree well with those of the finite element method. The effects of external magnetic field strength and particle content on the stress distribution and peeling length are fully explored, and the enhanced analytical outcomes are obtained through numerical prediction. These insights can be used to validate the reliability of engineering designs, including adaptive structures, micro-electro-mechanical sensors, and soft robotic systems.

Metamaterials with multistability have attracted much attention due to their extraordinary physical properties. In this paper, we report a novel multistable strategy that is reversible under external forces, based on the fact that a variational reversible locally resonant elastic metamaterial (LREM) with four configurations is proposed. Through a combination of theoretical analysis and numerical simulations, this newly designed metamaterial is proven to exhibit different bandgap ranges and vibration attenuation properties in each configuration. Especially, there is tunable anisotropy shown in these configurations, which enables the bandgaps in two directions to be separated or overlapped. A model with a bandgap shifting ratio (BSR) of 100% and an overlap ratio of 25% is set to validate the multistable strategy feasibility. The proposed design strategy demonstrates significant potentials for applications in versatile scenarios.

Belt conveyors are extensively utilized in mining and power industries. In a typical coal mine conveyor system, coal is transported over distances exceeding 2 km, involving more than 20 000 idlers, which far exceeds a reasonable manual inspection capacity. Given that idlers typically have a lifespan of 1–2 years, there is an urgent need for a rapid, cost-effective, and intelligent safety monitoring system. However, current embedded systems face prohibitive replacement costs, while conventional monitoring technologies suffer from inefficiency at low rotational speeds and lack systematic structural optimization frameworks for diverse idler types and parameters. To address these challenges, this paper introduces an integrated, on-site detachable self-powered idler condition monitoring system (ICMS). This system combines energy harvesting based on the magnetic modulation technology with wireless condition monitoring capabilities. Specifically, it develops a data-driven model integrating convolutional neural networks (CNNs) with genetic algorithms (GAs). The conventional testing results show that the data-driven model not only significantly accelerates the parameter response time, but also achieves a prediction accuracy of 92.95%. The in-situ experiments conducted in coal mines demonstrate the system's reliability and monitoring functionality under both no-load and full-load conditions. This research provides an innovative self-powered condition monitoring solution and develops an efficient data-driven model, offering feasible online monitoring approaches for smart mine construction.

This study proposes a pre-strain optimization strategy for carbon fiber structural lithium-ion battery (SLIB) composites to inhibit the interfacial debonding between carbon fibers and solid-state electrolytes due to fiber lithiation. Through an analytical shear-lag model and finite element simulations, it is demonstrated that applying tensile pre-strain to carbon fibers before electrode assembly effectively reduces the interfacial shear stress, thereby suppressing debonding. However, the excessive pre-strain can induce the interfacial damage in the unlithiated state, necessitating careful control of the pre-strain within a feasible range. This range is influenced by electrode material properties and geometric parameters. Specifically, the electrodes with the higher solid-state electrolyte elastic modulus and larger electrolyte volume fraction exhibit more significant interfacial damage, making pre-strain application increasingly critical. However, these conditions also impose stricter constraints on the feasible pre-strain range. By elucidating the interplay between pre-strain, material properties, and geometric factors, this study provides valuable insights for optimizing the design of carbon fiber SLIBs.

The purpose of this article is to provide, from the perspective of deformable solid mechanics, a correct justification for the expressions of all forces acting on the surface of a ferromagnetic material in a magnetic field, initiated only by this field. It is shown that the moment of force applied to any closed body surface S, corresponding to the asymmetric part T_{\text{A}} of the stress tensor T (denoted as the force p_{\text{A}}), balances the mass magnetic moment L_{\text{mag}} acting in the volume V bounded by the surface S. The emergence of the asymmetric part T_{\text{A}} of the stress tensor arises as a consequence of a special case within the moment theory of elasticity, the use of which is necessary for accurately describing the behavior of a ferromagnetic material in a magnetic field. The force p_{\text{A}} acts in a plane tangential to the surface S at any point, while, in addition to this force, the normal force p_n also acts on the body surface. It is shown in the article that the latter force arises as a result of a jump in the normal component of the magnetic field strength appearing at the body surface, and its expression is defined by the mass's (ponderomotive) magnetic forces F_{\text{mag}}. Usually, this force is introduced based on the Maxwell stress tensor, which is used in the classical electromagnetism to represent the interaction between electromagnetic forces and mechanical momentum. However, as we believe and justify this in the article, such an approach is unacceptable in deformable solid mechanics.

A novel gappy technology, gappy autoencoder with proper orthogonal decomposition (Gappy POD-AE), is proposed for reconstructing physical fields from sparse data. High-dimensional data are reduced via proper orthogonal decomposition (POD), and low-dimensional data are used to train an autoencoder (AE). By integrating the POD operator with the decoder, a nonlinear solution form is established and incorporated into a new maximum-a-posteriori (MAP)-based objective for online reconstruction. The numerical results on the two-dimensional (2D) Bhatnagar-Gross-Krook-Boltzmann (BGK-Boltzmann) equation, wave equation, shallow-water equation, and satellite data show that Gappy POD-AE achieves higher accuracy than gappy proper orthogonal decomposition (Gappy POD), especially for the data with slowly decaying singular values, and is more efficient in training than gappy autoencoder (Gappy AE). The MAP-based formulation and new gappy procedure further enhance the reconstruction accuracy.

The elliptic integral method (EIM) is an efficient analytical approach for analyzing large deformations of elastic beams. However, it faces the following challenges. First, the existing EIM can only handle cases with known deformation modes. Second, the existing EIM is only applicable to Euler beams, and there is no EIM available for higher-precision Timoshenko and Reissner beams in cases where both force and moment are applied at the end. This paper proposes a general EIM for Reissner beams under arbitrary boundary conditions. On this basis, an analytical equation for determining the sign of the elliptic integral is provided. Based on the equation, we discover a class of elliptic integral piecewise points that are distinct from inflection points. More importantly, we propose an algorithm that automatically calculates the number of inflection points and other piecewise points during the nonlinear solution process, which is crucial for beams with unknown or changing deformation modes.

This study generalizes the classical Taylor-Sedov framework to analyze finite-source spherical blast waves propagating through both uniform and power-law density media. Previous analyses have predominantly focused on the effects of varying initial conditions on blast dynamics. In contrast, this study investigates the primary shock wave evolution within different ambient gases, demonstrating the critical dependence on the initial density ratio between the blast sphere and the ambient medium, as well as the ambient density profile. We derive new scaling laws based on the density ratio, which accurately predict the dimensionless main shock distance. Furthermore, we systematically examine, for the first time, the conditions for uniform volume expansion, uniform surface area growth, and uniform shock wave propagation in power-law density media, revealing a key scaling relation associated with the power-law exponent. Numerical simulations validate these novel theoretical predictions, demonstrating excellent agreement with the normalized solutions. These findings provide new insights into blast wave dynamics in inhomogeneous media and have implications for astrophysical and laboratory plasma environments.

The pH-sensitive hydrogels play a crucial role in applications such as soft robotics, drug delivery, and biomedical sensors, as they require precise control of swelling behaviors and stress distributions. Traditional experimental methods struggle to capture stress distributions due to technical limitations, while numerical approaches are often computationally intensive. This study presents a hybrid framework combining analytical modeling and machine learning (ML) to overcome these challenges. An analytical model is used to simulate transient swelling behaviors and stress distributions, and is confirmed to be viable through the comparison of the obtained simulation results with the existing experimental swelling data. The predictions from this model are used to train neural networks, including a two-step augmented architecture. The initial neural network predicts hydration values, which are then fed into a second network to predict stress distributions, effectively capturing nonlinear interdependencies. This approach achieves mean absolute errors (MAEs) as low as 0.031, with average errors of 1.9% for the radial stress and 2.55% for the hoop stress. This framework significantly enhances the predictive accuracy and reduces the computational complexity, offering actionable insights for optimizing hydrogel-based systems.

This study explores the complex dynamics of unsteady convective flow in micropolar nanofluids over a rough conical surface, with a focus on the effects of triple diffusive transport and Arrhenius activation energy. The primary objective is to understand the interplay among nonlinear convection, micro-rotation effects, and species diffusion under the influence of thermal and electromagnetic forces. The analysis is motivated by practical applications of cryogenic fluids, specifically liquid hydrogen and liquid nitrogen, where precise control of heat and mass transport is critical. The conical surface roughness is mathematically modeled as a high-frequency, small-amplitude sinusoidal waveform. To address the non-similar nature of the boundary-layer equations, Mangler's transformations are employed, followed by the implementation of a finite difference scheme for numerical solutions. The methodology further integrates a machine learning-based neural network to predict the skin friction under the influence of roughness-induced perturbations, ensuring computational efficiency and improved generalization. The study yields several novel findings. Notably, the presence of surface roughness introduces the wave-like modulations in the local skin friction coefficient. It is also observed that nonlinear convective interactions, enhanced by temperature gradients and vortex viscosity parameters, significantly intensify near-wall velocity gradients. Moreover, key physical quantities are correlated with governing parameters using power-law relationships, providing generalized predictive models. The validation of the numerical results is achieved through consistency checks with the existing limiting solutions and convergence analysis, ensuring the reliability of the proposed computational framework.