Acta Mechanica Sinica最新文献

The adjoint method is widely used in gradient-based optimization with high-dimensional design variables. However, the cost of solving the adjoint equations in each iteration is comparable to that of solving the flow field, resulting in expensive computational costs. To improve the efficiency of solving adjoint equations, we propose a physics-constrained graph neural networks for solving adjoint equations, named ADJ-PCGN. ADJ-PCGN establishes a mapping relationship between flow characteristics and adjoint vector based on data, serving as a replacement for the computationally expensive numerical solution of adjoint equations. A physics-based graph structure and message-passing mechanism are designed to endow its strong fitting and generalization capabilities. Taking transonic drag reduction and maximum lift-drag ratio of the airfoil as examples, results indicate that ADJ-PCGN attains a similar optimal shape as the classical direct adjoint loop method. In addition, ADJ-PCGN demonstrates strong generalization capabilities across different mesh topologies, mesh densities, and out-of-distribution conditions. It holds the potential to become a universal model for aerodynamic shape optimization involving states, geometries, and meshes.

Generalised reduced masses with a set of equations governing the three relative motions between two of 3-bodies in their gravitational field are established, of which the dynamic characteristics of 3-body dynamics, fundamental bases of this paper, are revealed. Based on these findings, an equivalent system is developed, which is a 2-body system with its total mass, constant angular momentum, kinetic and potential energies same as the total ones of three relative motions, so that it can be solved using the well-known theory of the 2-body system. From the solution of an equivalent system with the revealed characteristics of three relative motions, the general theoretical solutions of the 3-body system are obtained in the curve-integration forms along the orbits in the imaged radial motion space. The possible periodical orbits with generalised Kepler’s law are presented. Following the description and mathematical demonstrations of the proposed methods, the examples including Euler’s/Lagrange’s problems, and a reported numerical one are solved to validate the proposed methods. The methods derived from the 3-body system are extended to N-body problems.

Quasi-periodic solutions with multiple base frequencies exhibit the feature of 2π-periodicity with respect to each of the hyper-time variables. However, it remains a challenge work, due to the lack of effective solution methods, to solve and track the quasi-periodic solutions with multiple base frequencies until now. In this work, a multi-steps variable-coefficient formulation is proposed, which provides a unified framework to enable either harmonic balance method or collocation method or finite difference method to solve quasi-periodic solutions with multiple base frequencies. For this purpose, a method of alternating U and S domain is also developed to efficiently evaluate the nonlinear force terms. Furthermore, a new robust phase condition is presented for all of the three methods to make them track the quasi-periodic solutions with prior unknown multiple base frequencies, while the stability of the quasi-periodic solutions is assessed by mean of Lyapunov exponents. The feasibility of the constructed methods under the above framework is verified by application to three nonlinear systems.

The airflow mechanics in adult nasal airways, whether healthy or abnormal, are extensively studied and investigated, but the flow mechanics in child nasal airways remain underexplored. This study investigates the airflow mechanics in the child’s nasal upper airway with adenoid hypertrophy, with an adenoid nasopharyngeal ratio (AN of 0.9), under cyclic inhalation and exhalation. An inlet respiratory cycle with three different flow rates (3.2 L/min calm breathing, 8.6 L/min normal breathing, and 19.3 L/min intensive breathing) was simulated by using the computational fluid dynamics approach. To better capture the interaction between airflow and the flexible airway tissue, fluid-structure interaction analysis was performed at the normal breathing rate. Comparing the airflow dynamics during inhalation and exhalation, the pressure drops, nasal resistance, and wall shear stress show significant differences in the nasopharyngeal region for all different flow rates. This observation suggests that the inertial effect associated with the transient flow is important during exhalation and inhalation. Furthermore, the considerable temporal variation in flow rate distribution across a specific cross-section of the nasal airway highlights the critical role of transient data in virtual surgery planning and data for clinical decisions.

This paper proposes the analytical solutions involving damping effects for the dynamic response of a simply supported thin-walled curved beam under uniformly variable two-axle moving loads in four directions: vertical, torsional, radial, and axial. The warping stiffness and damping of the thin-walled beam were comprehensively considered in the vibration control equations. Unlike traditional one-axle load cases, this study employs a more realistic two-axle vehicle load model. Based on the modal superposition method, the control vibration equations for thin-walled curved beams in-plane and out-of-plane under variable speed moving loads were solved using a combination of the Fourier sine transform method, the Galerkin method, and the Laplace transform method. Analytical solutions for the dynamic responses were derived in integral form, facilitating direct numerical computation. The proposed computational method’s effectiveness and accuracy were validated against published research. Subsequently, the dynamic responses of the thin-walled curved beam under one-axle and two-axle moving load models were compared, and the effects of initial load velocity, load acceleration, and center angle of the curved beam on the dynamic responses were investigated through extensive parameter research. The research results provide valuable insights into the structural behavior of thin-walled curved beams under the moving loading with variable speed.

The two-dimensional Rayleigh-Bénard convection under external vibration at varying orientations has been systematically studied using direct numerical simulations. The vibration angle (β) relative to the horizontal axis spans from 0° to 90°, and the Rayleigh number (Ra) ranges from 10⁶ to 10⁸ with the Prandtl number fixed at Pr = 4.38. The dimensionless vibration frequency (ω) varies from 0 to 1000, with the dimensionless amplitude fixed at A_m = 1.52 × 10⁻³. The dependence of the Nusselt number (Nu) and Reynolds number (Re) on the vibration angle (β) exhibits a non-monotonic relationship, with an optimal vibration direction identified that maximizes heat transport enhancement. At high vibration frequencies, a critical vibration angle of β_c demarcates the transition between vibration-induced enhancement and suppression of Nu. For β < β_c, the horizontal component of vibration is dominant, leading to the detachment of thermal plumes from the conducting plates due to vibration-induced boundary layer (BL) destabilization, thereby enhancing convective heat transport. In contrast, for β < β_c, the vertical component of vibration dominates, stabilizing the thermal BLs and suppressing turbulent fluctuations, which reduces the global heat transport. Additionally, the action of vibration modifies the shape of the large-scale circulation, making it more circular and generating new vortex structures in the bulk for intermediate β. Vibration also influences the growth of corner rolls, reducing their size at small β and potentially inducing the formation of new corner rolls along the opposite diagonal direction at large β.

Inspired by the walking, jumping, and running of quadrupeds, a novel vibration isolation-absorption (BVIA) platform is proposed by applying a bistratal X-shaped structure and a multi-vertebra structure. Based on the mechanical-constitutive relationship, the static and dynamic models of the BVIA platform are established, and the force/stiffness-displacement curves are applied to reveal the loading capacity and quasi-zero stiffness characteristics. The vibration suppression performances of different parameters are investigated by amplitude-frequency curve and displacement transmissibility, and the results are verified by numerical methods. From the results, it can be found that the resonance peak significantly decreases due to the mutual promotion of vibration isolation and vibration absorption. The vibration suppression performance of the BVIA structure can be tuned flexibly by initial installation angle, rod length ratio, layer number, absorbed mass, stiffness coefficient, horizontal spring length, and excitation amplitudes. The proposed BVIA structure provides a useful reference for reducing the resonance peak and improving the vibration suppression performance in practical engineering applications.

Although supplying extensive design space, the curse of dimensionality restricts the widespread application of large-scale topology optimization in practical engineering. Various acceleration techniques have been integrated with topology optimization, achieving significant attention and progress in large-scale problems. This work aims to investigate how much benefit can be obtained by combining parallel computing and machine learning techniques to enhance the efficiency of large-scale topology optimization algorithms. Accordingly, a parallel problem independent machine learning (PIML)-enhanced topology optimization method is proposed. The PIML model substantially reduces the dimension of the condensed stiffness matrix and its computational cost, and parallel computing reduces the workload per process and enables the application of a parallel multigrid solver. Besides, several techniques, such as matrix-free implementation, direct condensation of uniform coarse elements, and adjusting computational resource limits, have been developed to enhance computational efficiency. The weak scaling efficiency, strong scaling speedup, and maximum achievable efficiency of the proposed method are validated across multiple numerical examples, showing significant improvement in the tractable problem size and solution efficiency compared to traditional topology optimization algorithms.

This paper explores the use of sparse time-series data from flow systems, acquired through sensors or other means, to predict flow fields using deep learning techniques. This area of research holds substantial scientific significance and practical application value. The time-series data measured from different points typically contain spatial correlation and temporal features, which, when utilized effectively, can contribute to reconstructing flow fields. In this study, a convolutional autoencoder is applied to reduce the dimensionality of the flow field. Subsequently, an Informer neural network and a convolutional neural network are employed to extract low-dimensional representations of the flow field from the measurement data. A specially designed loss function bridges these latent features to establish a mapping between measurement point sequences and flow fields. The hybrid model is validated using data from both numerical simulations and experimental measurements. Results demonstrate that this method effectively predicts velocity and pressure fields from sparse data, showcasing its potential for practical flow field reconstruction tasks.

Threaded connection is a common structural form in mechanical engineering, with their complex nonlinear behavior under combined loading critically affecting structural performance. While existing simplified models and finite element analysis (FEA) methods describe force distribution under single loading conditions, accurately modeling threaded connections under complex loading remains challenging. This paper proposes a simplified theoretical model to efficiently predict contact forces and deformation distributions under tension, torsion, bending, and shear. The model treats bolt and nut bodies as Euler-Bernoulli beams and represents thread stiffness using equivalent trapezoidal cantilever beams, reducing computational complexity while retaining essential mechanical characteristics. The paper introduces reference helical curves and derives a deformation coordination relationship based on contact constraints. The model’s calculations are validated against FEA results, demonstrating both high precision and significant computational efficiency under complex loading conditions. This work provides an efficient and reliable tool for analyzing threaded connections, offering promising engineering applications.