Acta Mechanica Sinica最新文献

High-fidelity field reconstruction has been a focal point for many research studies, as the measured sensor data are often sparse and incomplete in both time and space. Physics-informed neural networks (PINNs) have been proposed to reconstruct fields using imperfect data, as they incorporate physical principles and thereby reduce reliance on the known sensor data. However, the placement of sensors remains crucial for optimizing PINNs, and existing studies have not sufficiently considered this aspect. Therefore, developing algorithms that intelligently improve sensor placement is of significant importance. In this study, we introduce a general approach that employs differentiable programming with attention modules to optimize sensor placement during the training of a PINNs model in order to improve field reconstruction. We evaluate our method using three distinct cases: the Allen-Cahn equation problem, the lid-driven cavity flow problem, and the cylinder flow problem to demonstrate our approach effectiveness in flow field inference, system identification, and its capability for multi-condition generalization. The results indicate that our method improves test scores and effectively learns the optimal layout of sensors for various Reynolds numbers, which advances our understanding of the relationship between sensor placement and reconstruction precision using PINNs.

The current study aims to look at the Darcy-Forchheimer and bioconvective flow of Casson blood-based trihybrid nanofluid (THNF) through an exponentially expanding surface. The three different nanoparticles, namely, cobalt ferrite (CoFe₂O₄), molybdenum disulfide (MoS₂), and zirconium dioxide (ZrO₂) are used to make the THNF. The impacts of viscous dissipation, magnetic field, thermal radiation, Brownian motion, thermophoresis, heat consumption/generation, and thermophoretic particle deposition are also included in this investigation. Using appropriate variables, the set of partial differential equations representing the fluid models are transformed into a system of ordinary differential equations and these equations are numerically solved using the ND solver and the bvp4c approach. Our outcomes are validated through the earlier publication results. Physical traits such as fluid velocity, temperature, nanofluid (NF) concentration, and motile microorganisms are shown graphically. The results show that improving the porosity parameter diminishes the velocity profile. The temperature profile decays when enhancing the value of the Casson parameter. The NF concentration profile suppresses as the thermophoretic particle deposition parameter enhances. The profile of microorganisms declines when enhancing the bioconvective Lewis number. Accelerating the magnetic field parameter makes a reduction in skin friction coefficient. The raise in the radiation parameter improves the heat transmission rate. The larger thermophoresis parameter declines the rate of mass transfer, and the motile microorganisms density diminishes when enlarging the value of the Peclet number. In addition, the long-short term memory model is used to optimize the heat transfer gradient data by training, validating, and testing to determine the data accuracy. The training mean square error (MSE) is 0.001089, 0.000195, 0.000236, and 0.000499, the validation MSE is 0.001665, 0.000647, 0.000629, and 0.000694, and the test MSE is 0.001779, 0.000158, 0.000154, and 0.000269 for Cattaneo-Christov heat and mass flux model (CCHMFM) with suction, CCHMFM with injection, Fourier heat and mass flux model (FHMFM) with suction, and FHMFM with injection, respectively.

Natural convection in enclosures containing nanofluids has attracted significant attention due to its relevance in thermal management systems. In this context, this study presents a comprehensive numerical investigation of flow and heat transfer in a square cavity saturated with water-based CuO nanofluid having a centrally placed sinusoidal-shaped heated element. All the enclosure walls satisfy the no-slip velocity condition. Thermally, the vertical walls are kept at a cold reference temperature, the lower wall is partially heated at its center, and the remaining portions of the lower and entire upper walls are adiabatic. The internal sinusoidal element is also uniformly heated. The flow dynamics and thermal fields are governed by the two-dimensional steady-state Navier-Stokes and energy equations, solved using the Galerkin finite element method. Additionally, a novel hybrid approach integrating multi-expression programming (MEP) technique with a convolutional neural network bidirectional gated recurrent unit (CNN-BiGRU) deep learning network is also applied to enhance flow and thermal prediction accuracy. This hybrid approach enables precise evaluation of how heater waviness, magnetic field orientation, and nanoparticle dispersion influence flow structure and heat transfer. Results reveal stronger convection at high Rayleigh numbers, magnetic damping at increased Hartmann numbers, and higher temperatures with reduced velocity at greater nanoparticle concentrations. Among the analyzed situations, increasing heater waviness improves heat-transfer performance. Both the MEP and CNN-BiGRU models accurately capture the key features of flow and heat transport trends, indicating that the hybrid approach provides enhanced predictive capability for complex convection-driven nanofluid systems.

Origami honeycombs exhibit excellent designability and mechanical properties, potentially improving the bending resistance and load-bearing capacity of beams in engineering applications. In this paper, a novel origami-enhanced honeycomb sandwich beam is proposed to improve the flexural toughness and load-bearing performance. The three-point bending behavior of the origami-enhanced honeycomb sandwich beam is systematically studied. Considering the influence of loading distance, loading position, thickness gradient, and cell size, the typical panel wrinkling deformation phenomenon is observed in the origami-enhanced honeycomb sandwich beam. The origami-enhanced core improves the flexural resistance and specific energy absorption compared to traditional re-entrant honeycomb sandwich beams. It is found that the panel wrinkling phenomenon is related to the stiffness of the unit cells: larger size and greater stiffness in unit cells are more likely to induce panel wrinkling in sandwich beams. The proposed origami-enhanced honeycomb sandwich beam provides new insights for the study of flexural resistance in sandwich beams and is expected to offer significant advantages in engineering applications.

The stiff problem within ordinary differential equations and partial differential equations presents numerous chal- lenges for the stability and convergence of numerical methodologies due to their significant differences in scale. While explicit time-marching schemes have their advantages, their need for extremely small time steps significantly sacrifices computational efficiency. Implicit time-marching schemes, on the other hand, allow for larger time steps with better stability properties, where traditional schemes such as the diagonally implicit Runge-Kutta method and the implicit-explicit Runge-Kutta scheme are al- ready widely used. However, when it comes to nonlinear problems, we still need to solve the nonlinear implicit equation, which is fundamentally difficult at high-order accuracy. To tackle this, the time-accurate and highly-stable explicit (TASE) operators were proposed. Differing from the traditional implicit time-marching schemes, TASE operators are preconditioners for existing explicit time-marching schemes, such as the explicit Runge-Kutta (RK) schemes, where their combination enables RK schemes to solve stiff problems with larger time steps and enhances stability. Furthermore, TASE operators are linear in nature, avoiding the need to solve non-linear problems, where the accuracy of TASE operators theoretically can also be of an arbitrarily high order through Richardson extrapolation. These inherent advantages have led to the rapid growth of the family of TASE-schemes recently, including theoretical analysis and algorithmic improvements. In this review, the TASE operators and their variants are summarised, highlighting their stability properties, parameter settings, comparisons with traditional implicit time-marching schemes, and promising future directions of the TASE family of operators.

A unique global strain approach based on the transition state theory was proposed to quantify the creep-recovery processes of metallic glasses, in which the structure of glasses is predominantly governed by the macroscopic strain. This methodology allows for the calculation of strain-dependent activation energy and activation volume for flow defects. The activation energy and volume of creep both increase linearly with the magnitude of strain. Upon the glass-to-liquid transition, they get large and strain-independent, which serves as a signature of the glass transition. During creep recovery, the cooperation of deformation units increases the activation volume but decreases activation energy due to the decrease in free volume. Notably, only a fraction of the anelasticity accumulated during creep persists in the recovery process; the rest is suppressed by structural relaxation. The results introduce physical insights into the deformation and relaxation of metastable solids that are not available in the usual rate-dependent theory developed for crystal plasticity.

Accurate prediction of crossflow-induced transition in hypersonic boundary layers remains a critical challenge, primarily due to the pronounced nonlinear evolution of stationary crossflow vortices. This study proposes a prediction method that establishes the saturation position of stationary vortices as a transition onset indicator, complemented by a saturation criterion derived from Mack’s linear amplitude. To validate the saturation-transition correlation, direct numerical simulations of the complete transition process were conducted on a hypersonic swept flat plate with two distinct nose radii and wall temperature conditions. Results reveal that despite an order-of-magnitude variation in background disturbance levels, the resultant transition location shift remains constrained within 2–3 nose radii—close to the identified saturation points. Furthermore, the linear amplitude method demonstrates that for given flow conditions, a single threshold value of the linear amplitude reliably determines saturation positions across broad spanwise wavenumbers and initial amplitudes of stationary vortices. This finding validates the effectiveness of linear stability theory based approaches for crossflow transition prediction.

This paper introduces a novel gradient-enhanced physics-informed neural network (gPINN) framework for analyzing Kirchhoff-Love plate bending under diverse boundary conditions. The approach marks a significant advancement in physics- informed machine learning by offering three key innovations: (1) a gradient-regularized loss function that enforces the biharmonic equation and boundary constraints concurrently; (2) a modular neural architecture featuring interconnected subnets for transverse and in-plane displacements; (3) an adaptive training algorithm with physics-informed sampling strategies. The proposed techni- cal framework integrates several pioneering elements. It augments the strain energy functional with higher-order gradient terms to accurately capture curvature effects near plate boundaries. Furthermore, it introduces edge-specific penalty functions that automatically accommodate various support conditions, such as clamped, simply supported, and free edges, without requiring geometric remeshing. The network design further integrates dedicated submodules for displacement gradients, utilizing shared weights for mixed partial derivatives critical to the bending moment formulation. Numerical validations across three benchmark cases (complex boundary conditions) highlight the framework’s superiority over traditional PINNs. Notable outcomes include: (I) a 72% average reduction in relative error at boundary transitions (p < 0.01); (II) convergence to engineering accuracy ( <% er- ror) in 38% fewer iterations; (III) robust generalization to untested boundary condition combinations. The gPINN solutions align closely with finite element benchmarks while eliminating meshing dependencies, demonstrating particular strength in high-stress concentration zones. This study sets a new benchmark for physics-informed deep learning in plate mechanics, offering immediate relevance for designing aerospace components, marine structures, and other thin-walled structures where precise deformation pre- diction under complex constraints is essential. The gradient enhancement methodology provides a scalable blueprint for applying physics-aware machine learning to other fourth-order boundary value problems in solid mechanics.

This study explores the nonlinear resonance of a rotating solar sail membrane exposed to time-varying solar thermal and solar radiation pressure. The sail membrane is modeled using a cantilever membrane, applying the von Kármán theory for membrane large deflection. The membrane’s nonlinear equation is derived by employing the Lagrange equation while accounting for excitations from solar thermal and radiation pressure. The equation is solved via the Rayleigh-Ritz method. The bifurcation diagram of membrane motion is applied to reveal membrane resonance responses under different solar sail rotating frequencies. The displacement time history, phase portrait, Poincaré map, frequency spectrum, and the largest Lyapunov exponent are used to study nonlinear vibrations that occur near resonance regions. The results indicate that time-varying thermal loading excites membrane motions with multiple natural frequencies by the parametric resonance mechanics, leading to the onset of membrane chaotic motion. The membrane’s primary resonance is stimulated in harmonic oscillation by the time-varying radiation pressure. The divergence instability caused by thermal excitation is also illustrated by comparing the membrane’s vibration amplitude with and without thermal excitation. The membrane’s nonlinear vibration characteristics vary significantly with solar illumination angles, the membrane’s thermal expansion coefficients, and structural damping.