Meccanica最新文献

This article explores certain limitations of some well-known methods employed in machine learning when applied for regression of mechanical models that might exhibit multiple solutions. Using the buckling of a beam as a prototypical example of a mechanical problem with multiple solutions, we show that neural networks, Bayesian methods, random forest, and similar forward techniques are ill-suited for approximating the solution to such problems. Instead, data-driven methods based on set projections are intrinsically capable of coping with multiple solution paths satisfactorily, incorporating in addition the stochasticity of the response.

The ability to design linear systems exhibiting non-reciprocal wave propagation would enable precise control of mechanical signals for filtering and vibration control. This study presents a macroscopic mechanical metamaterial with a time-varying radius based on crank-slider mechanisms. A hierarchical framework is established, formed by supercells, with each supercell comprising multiple subcells. Among configurations with varying numbers of subcells, the investigation focuses on a phase-modulated triatomic configuration designed to break time inversion symmetry to achieve non-reciprocity, which generates asymmetric bandgaps to selectively suppress wave propagation in positive wavenumber domains while permitting propagation in negative domains. The spatiotemporal field patterns with different modulation parameters are provided. Numerical simulations are also conducted to verify non-reciprocal wave propagation behavior. Furthermore, the influences of modulation amplitude, frequency, and initial phase on the bandgap structure are systematically examined, revealing their potential for precise asymmetric bandgap tuning wave propagation characteristics.

In this paper, a novel linear-driven parallel manipulator (PM) which has four identical PRPaR limbs and a simple moving platform is designed for high-speed pick-and-place motion. After proving that the robot can achieve Schönflies motion through Lie group theory, the kinematic model of it was established using the closed-loop vector method. By combining finite element analysis and the substructure method, the elastodynamic model was established, and the shape functions as well as the mass and stiffness matrices of the spatial beam element were derived. Then, the correctness and accuracy of the established elastodynamic model were verified using Ansys Workbench^®. Subsequently, the dynamic response analysis carried out using the Newmark method indicates that when the moving platform moves along a circular trajectory with a radius of 0.3m, its displacement error is sufficiently small. By analyzing the position error curves under different damping conditions, the optimal damping ratio of the mechanism was determined. To achieve the desired pick-and-place trajectory, the improved trapezoidal motion law was applied to ensure that the elastic displacement and angular displacement errors of the moving platform meet the practical requirements. Furthermore, dynamic stress analysis based on the fourth strength theory identifies the weakest components of the mechanism, providing a foundation for the optimization of the physical prototype. This paper offers new perspectives on the study of refined elastodynamic and dynamic response in parallel robots.

This work presents a finite-element (FE) framework for predicting the mechanical response of polymeric powders subjected to confined compaction. A contact-based FE formulation captures the deformation of individual microspheres, their evolving contact network, and the accompanying reduction in bulk porosity inside the mold. Two nonlinear constitutive descriptions, namely, an elastoplastic model with multilinear hardening and a Perzyna-type viscoplastic model, are implemented to assess both rate-independent and rate-dependent particle behavior. Representative-volume simulations of an epoxy-resin powder are carried out under multiple loading-unloading cycles to quantify how the mold-constrained effective Young’s modulus and porosity evolve with the compaction history. Because this effective modulus reflects both the intrinsic particle stiffness and the increasing confinement and densification of the packing, it can exceed the single-particle modulus as the contact network develops. The results show that the cumulative loading history, number of cycles, peak pressure, and loading rate, strongly influences densification and the apparent macroscopic stiffness of the compact. By providing a predictive tool for effective property estimation without costly trial manufacturing, the proposed approach can guide optimization of compression-molding parameters for polymer-based composites and other powder-processed components.

The onset of cavitation in hydraulic devices is caused by rapid pressure variations leading to the formation and collapse of vapor bubbles which can occasionally provoke severe damage. Shape optimizations for cavitation reduction, based on single-phase flow models, prevent static pressure from dropping below the vaporization pressure, but they do not account for the influence of vapor in the flow. In this article, a continuous adjoint-based optimization method for two-phase turbulent cavitating flows, using the Volume of Fluid method, is developed within an in-house GPU-enabled CFD solver. The adjoint accommodates new terms arising from the differentiation of the source terms modeling cavitation, the liquid–vapor mixture properties, as well as the turbulence model. The sensitivity derivatives are expressed in terms of surface integrals, using an adjoint formulation which, prior to this work, has been applied only to single-phase flows. The comparison of the sensitivity derivatives computed by the continuous adjoint method and finite differences shows that the differentiation of the turbulence model equations, frequently omitted in two-phase flows, is necessary to predict accurate gradients. After the validation of both the primal and adjoint solvers, gradient-based constrained shape optimizations are performed in three cavitation-dominated flows around a 2D isolated hydrofoil and a 3D hemispherical head body, as well as inside a 2D hydraulic poppet valve.

A novel method, energy method, for solving bearing stiffness in rotor system supported by multiple bearings is proposed. Energy method has no restrictions on bearing type, bearing arrangement, bearing number and load type in rotor bearing system and can significantly simplify the solution procedures involved in determining bearing displacements and bearing stiffness. The potential energy model of flexible rotor bearing system is derived by combining finite element method and bearing load–displacement relationship and can be expressed as the function of rotor shaft nodes’ displacements. Based on the principle of minimum potential energy, the true displacements of all nodes in the system are calculated by optimization algorithm, and then the stiffness for each bearing is obtained. The effectiveness of the proposed energy method is verified by comparing with the results of bearing displacements, loads and stiffness coefficients in published literatures. Based on the proposed energy method, the effects of the rotor shaft flexibility, bearing arrangement, load position, bearing radial clearance and initial angular misalignment of outer ring caused by installation error on bearing stiffness in the rotor bearing system are investigated.

The following paper focuses on structural displacement tracking that is a significant process, inter alia, for evaluating safety of structures, load classification, or structural control applications. The authors presented a method for the full-field displacement identification based on strain sensor measurements and machine learning. Using this method, it is possible to recreate full-field displacement maps of the entire structure or its parts, even for different load cases. An example is given in which a typical aerostructure (composite hat-stiffened panel) is subjected to displacement monitoring. Two neural networks were trained to identify full-field displacement maps of the panel, based on strain gauges measurements. The accuracy of the predictions was experimentally tested using digital image correlation (DIC). The predicted displacement maps were qualitatively and quantitively compared with the results of finite element simulation and experimental DIC measurements.

Gvirtzman et al. (Nature 637(8045):369–374, 2025) have made recently very interesting experiments showing how small shear cracks nucleate and then evolve at the interface between two rectangular blocks. They find essentially an approximate geometrical factor for confined cracks in plates in the condition for nucleation (threshold shear stress (tau _{thresh})) in a classical Griffith crack condition for quasi-static nucleation. However, they seem to suggest that slowly creeping patches approach the interface width and accelerate only when a topological transition takes place in which they become 1D through cracks. We observe that this second implication is due to the fact that the measured threshold shear stress (tau _{thresh}) is very close to the cohesive strength (tau _{coh}) in previously reported experiments by the same group in PMMA solids (about 1 MPa), which suggests the width of the specimen they have used may be rather special. The general model they have derived is entirely consistent with classical fracture mechanics, which doesn’t require cracks to accelerate at this topological change. Including the cohesive strength (tau _{coh}) crack nucleation in the model, and how cracks should behave when they are very small with respect to the plate width W, we provide a possible diagram of nucleation of cracks, depending on their shape and dimension, showing that we should take care when using their new formula, because deviations may be large if cracks are small—a full 3D numerical solution is to be preferred which is not difficult to obtain today.

The dynamics of a hanging chain pendulum, long treated as a textbook problem in classical mechanics, are revisited from a fresh and rigorous analytical perspective. By systematically deriving and comparing the continuum and discrete formulations, subtle but significant differences in the vibrational spectrum, particularly in the high-frequency regime are uncovered. Using asymptotic expansions, boundary layer theory, and matched scaling arguments, a comprehensive description of the eigenmodes and their scaling behavior is developed. In the discrete model, we reveal a striking two-regime structure: low-frequency modes governed by Bessel-type equations, and high-frequency modes localized near the free end, described by Airy-type asymptotics. The transition between these regimes emerges naturally from a balance of competing terms in the governing equations, yielding a characteristic crossover scaling. This analysis clarifies the limitations of discrete and continuum approximations and exposes the deeper mathematical structure underlying the system. Ultimately, the followed approach provides a dual perspective and case study, demonstrating how rigorous asymptotics bridge discrete and continuum models and yield fresh insight into seemingly well-understood mechanics of the chain pendulum.

A new method based on Berkovich nanoindentation is proposed to predict the stress–strain curve of hardened martensitic bearing steels. This method combines a theory for predicting yield strength with experimental Berkovich indentation. Kick’s constant has been identified as the most robust parameter derived from sharp nanoindentation tests. The yield limit is predicted using a screw-dislocation strengthening theory, while the steel hardening exponent is calculated using Kick’s constant derived from the nanoindentation data. This ’hybrid method’ shows good agreement with experimentally measured stress–strain curves of different bearing steels, combining the strengths of both experimental and theoretical approaches. The proposed model elegantly addresses the long-standing challenge of deriving a unique solution for the material stress–strain curve from nanoindentation test data.