Mechanical Problems Research Articles

Overlapping finite elements for the Navier-Stokes equations

The purpose of this paper is to investigate the performance of a certain family of low-order quadrilateral finite elements in the solution of the stationary Navier-Stokes equations governing incompressible fluid flows. These finite elements are derived from the ‘overlapping finite elements’, first developed for the solution of problems in solid mechanics [5,9,48] and incorporate features of both meshfree and traditional finite element methods. One of their most remarkable properties is the insensitivity to mesh distortions. Also, since the Shepard functions are replaced by a suitable interpolation, the resulting basis functions are entirely polynomial, which allows the numerical integration of the weak forms to be performed with few integration points [6,49]. We also discuss the theoretical reasons for the stability of the solutions, that is, the absence of spurious pressure modes, and show that the proposed discretization scheme passes the relevant inf-sup test.

Marathon runner algorithm: theory and application in mathematical, mechanical and structural optimization problems

Abstract This study proposes a novel human-inspired metaheuristic search algorithm called marathon runner algorithm. This method mimics competitive behaviors observed in real marathon runners through mathematical modeling. Unlike classical elitist algorithms that prioritize position of the best agent, the marathon runner algorithm introduces a novel concept called vision point. This point considers the quality of the entire population, not just the leader. By guiding the population towards vision point, the risk of getting trapped in local optima is reduced. A two-part evaluation was conducted to thoroughly assess the search capabilities of the marathon runner algorithm. First, it is tested against a set of unconstrained benchmark mathematical functions and the algorithm’s quantitative attributes, such as complexity, accuracy, stability, diversity, sensitivity, and convergence rate are analyzed. Subsequently, the algorithm was applied to mechanical and structural optimization problems with both continuous and discrete variables. This application demonstrated the effectiveness of the algorithm in solving practical engineering challenges with constraints. The outcomes are compared with those obtained by six other well-established techniques. The obtained results indicate that the marathon runner algorithm yields promising and competitive solutions for both mathematical, mechanical, and structural problems.

Effect of using multiple representations in teaching mechanics problem-solving on engineering students’ academic performance in Rwanda

In recent years, the use of multiple representations in physics teaching and learning has become more common. This study sought to determine if engineering students’ performance in Rwanda might be improved by the use of numerous representations when solving mechanics problems. Multiple representations improve students’ comprehension and recall of mechanics ideas, supporting efficient teaching methods and critical thinking. This study employed a quasi-experimental research design with pre-and post-test control and experimental groups. A total of 100 students were enrolled in the study, divided into two groups: the experimental group consisted of 52 students who received instruction using multiple representations, and the control group consisted of 48 students who received instruction using traditional methods. In the study, students’ performance was measured before and after intervention using a mechanics test. The mechanics problem-solving pre-test findings indicated a p-value greater than 0.05 between the control and experimental groups, indicating no statistically significant differences between the two groups. A post-test revealed a p-value < 0.001 between the groups, indicating that the experimental group outperformed the control group significantly. According to the findings, engineering student’s academic performance in physics can be improved through the use of multiple representations in teaching and learning mechanics problem-solving. This study will support the development of Rwandan education policies, instructional approaches, and global pedagogy are all supported by this study.

Study on the microwave absorbing properties of SiC@Ni powders with core@shell structure

Hybridization of dielectric and magnetic materials is considered a promising option for the preparation of electromagnetic wave absorbing materials with excellent properties. In this paper, SiC@Ni powders were prepared by a surface heat-assisted process, in which SiC was first cleaned sequentially with anhydrous ethanol and NaOH solutions, and the samples were etched into a mixed solution of HF and HCl, the SiC@Ni powders were then mixed at high speed at 120 °C under argon atmosphere. The sample were characterized by Scanning electron microscopy (SEM) and vector network analyzer (VNA). It is found that the absorption characteristics of SiC@Ni in the 2–18 GHz band are significantly enhanced due to the introduction of the ni layer which enhances the loss of the sample to solve the problem of a single absorption mechanism and high impedance of SiC. The reflection loss value of SiC@Ni in the 8.7 GHz band decreases to − 22.45 dB when the material thickness is 2.5 mm, the effective absorption frequency width is 2.5 GHz, which is a significant advantage over the initial SiC. The experimental methodology of this work is simple and easy to follow, and provides some guidance for the large-scale production of SiC-based microwave absorbing materials.

Capture dynamics and driving method of origami capture mechanism in orbit

This article focuses on the dynamic problem of origami capture mechanism capturing space debris in orbit. It delves into the envelope characteristics of the origami capture mechanism, analyzing the motion laws of its axisymmetric folding state. Furthermore, it establishes a kinematic model for the axisymmetric envelope of the origami capture mechanism. A rigid body dynamic model of the origami capture mechanism and a generalized torque equation for the hinge at the crease were established based on the D–H parameter method and the Lagrange method. The enveloping process of the origami capture mechanism in the microgravity environment was simulated using ADAMS software, and the accuracy of the rigid body dynamics model of the origami capture mechanism and the generalized moment equation of the hinge at the crease was verified. Using Ls-Dyna software to simulate the capture process of space debris by force-driven and displacement-driven flexible origami capture mechanisms in microgravity environments, the results show that displacement-driven origami capture mechanisms can quickly capture space debris and are suitable for capturing large-sized space debris; The force-driven origami capture mechanism can quickly complete envelope capture of space debris, suitable for capturing small-sized space debris.

An approach to describe the twinning and detwinning processes of the martensitic structure in ferromagnetic alloy with shape memory in magnetic and force fields

In the article, based on the theory of micromagnetism, a special case of the moment theory of elasticity for an anisotropic material and the Hadamard compatibility condition for deformations, a microstructural model of the behavior of the Heusler alloy with shape memory in magnetic and force fields is constructed. The dynamics of the magnetic process is described by the Landau-Lifshitz-Gilbert equation. Using the Galerkin procedure, variational equations corresponding to the differential relations of the magnetic problem are written out and the finite element method is used for numerical realization of these equations. Considering the problems of the moment theory of elasticity we come to a special case of this theory in which, under the action of force and magnetic fields, the tensor of moment stresses initiated only by the magnetic field is zero. Using this result, the general expression for the state equation is constructed that describes, within the framework of small deformations, the behavior of an anisotropic material under force and magnetic influences. The stress tensor in this equation consists of a symmetric part and a skew-symmetric part, depending only on the magnetic field. For the problem of deformable solid mechanics with such a state equation, the Lagrange variational equation was constructed, which made it possible to reduce the requirements for the smoothness of the desired solution by an order of magnitude. The general expression for the state equation has been concretized for an anisotropic material having one axis of symmetry of the fourth order and two axes of symmetry of the second order. The solution of the Hadamard compatibility equation for deformations made it possible to determine the sliding surfaces and sliding directions in a tetragonal crystal cell of a ferromagnetic material in the martensitic state, along which a shift occurs, leading to the appearance and dissipation of a twinned structure. The microstructural model, constructed using all these positions, is used to describe experimental results on the combined action of magnetic and force fields on the Heusler alloy.

Fragmentation of Application of the Personal Law of a Legal Entity in the light of the Amended Law on International Companies

The new version of Federal Law No. 290‑FZ dated 03.08.2018 «On International Companies and International Foundations» adopted in August 2023 confirms the relevance of finding ways to regulate companies incorporated in the Russian Federation. The domestic approach has no analogues because under the Russian doctrine a foreign company can move not only with its rights and obligations, but also with its corporate law. Is it possible to call the foreign law applicable in this way a personal law? Why does the law on international companies not follow the logic of the Civil Code of the Russian Federation and does not directly indicate the application of foreign law to international companies and international foundations as a personal law? Can a foreign law partially encroach on the territory of the application of personal law? Is the personal law uniform and indivisible? To answer these questions, the paper analyzes the key characteristics, as well as the novelties of the institute of personal law in relation to international companies, problems arising in this area and ways to solve them. The author concludes that with the globalization of corporate relations, the fragmentation of the scope of personal law will continue. This actualizes the problem of finding mechanisms for the «seamless» application of the norms of different states in the field of application of personal law. The author emphasizes that legislation on international companies can become a regulatory sandbox and contribute to the inclusion of the most modern and effective institutions and approaches in Russian corporate law. Proposed in the paper amendments to the Civil Code of the Russian Federation and Law No. 290‑FZ preserve the logic of current regulation and reduce the uncertainty of regulation in the field of application of the personal law of an international company, the risks of subsequent changes in legislation for participants in international companies, as well as the likelihood of conflicts in the case of reference to foreign law.

An ethnography of construction and characteristics of curriculum for inheritance of intangible cultural heritage martial arts in universities.

Inheriting excellent traditional Chinese culture is a prerequisite for ensuring the continuity of the cultural genes of the Chinese nation. However, with the historical mission of shaping the national character of the descendants of the Chinese nation, intangible cultural heritage martial arts face the problem of an unclear curriculum content construction mechanism in university inheritance and make it difficult for these martial arts to shoulder the responsibility of cultural inheritance in the era. Educational ethnography as a research method is conducive to the in-depth exploration of the mechanism of curriculum content construction in the inheritance of intangible cultural heritage martial arts in universities. Research suggests that the construction of curriculum content for the inheritance of intangible cultural heritage martial arts in universities relies on the form of cooperation between universities and inheritors, and form three models of curriculum content construction: off campus, on campus, and on-campus cooperation. The construction of curriculum content for off-campus inheritors belongs to the "attachment style" model, which is based on the actual needs of the inheritors and the selection of boxing types. The construction of curriculum content for inheritors on campus belongs to the "reshaping" model, which is the inheritor's "simplification and reorganization" based on traditional routines and subjective and objective conditions of inheritance. The construction of course content in school local cooperation belongs to the "integrated" model, which is the reintegration of course content by universities based on their own development characteristics and the characteristics of various martial arts. In the inheritance of intangible cultural heritage martial arts in universities, emphasis is placed on local knowledge, core skills, cultural traditions, and other characteristics, highlighting the excellence of its cultural inheritance. In the future, the focus of the inheritance of these martial arts in universities should be to cultivate innovative talents who are familiar with both traditional and modern martial arts.

Novel techniques to analyze dynamical properties of quantum chaos with peculiar evidence of hybrid systems confinement

Recent results demonstrate the dynamical peculiarities of the quantum chaos within the hybrid systems by chaotic parameters and probe the pattern formation under the influence of condensation. The complex dynamic behavior of the considered systems was determined with numerical simulation and presented an efficient technique that studied fractional systems comprising chaos-coherence fractions. The findings divulge the peculiar association between the coherence structure and the correlations at finite relative momenta. Thus the present study helps to explore the partially chaos hybrid systems in order to stimulate the experimental applications of nonlinear phenomena. The coherent-chaotic parameters can be measured by examining the chaos peculiarities that possess explicit relations with the condensations to demonstrate the environs of the physical systems. We investigate the influence of the multiplicities, chaos, momentum and temperature of the nonlinear system on the coherent-chaotic normalized correlations. The chaotic parameters are suppressed considerably with the coherence fraction and it appears numerically zero at maximum condensation and one at ideal chaos emissions. We procure that the meaningful parameters decrease significantly with the multiplicity of the nonlinear systems and increase with the momentum in the specified regimes. The identical multiplicity leads to contemplating the coherence and thus the normalized chaotic parameters within its spectacular influences exhibit significance worth contemplating in earnest. The findings underscore the significance of cogitating correlations in deciphering the nonlinear system characteristics and bestowing extraordinary perceptiveness into the convoluted essence of complex systems. The contemplated methodology can be applied to evaluating and analyzing the nonlinear systems and such an innovative approach computes the problems of celestial mechanics, heartbeats and chemical reactions in engineering and medical fields.

Recognition of local fiber orientation state in prepreg platelet molded composites via deep learning

This paper presents a novel deep learning approach for reconstruction of local through-the-thickness fiber orientation distribution (FOD) in discontinuous long-fiber, prepreg-platelet molded composites (PPMC). The thermal-residual strains on composite surfaces are used as inputs to train a fully convolutional neural network, named U-Net, to predict spatially varying, local FOD. High fidelity synthetic data was generated via computational simulation of PPMC with stochastic material orientation state and was used for training the deep learning model. The proposed U-Net model allowed for rapid recognition of PPMC morphology by solving the inverse structural mechanics problem of determining the average fiber orientation through the composite thickness based on the provided surface strain measurements. Upon training and validation, the U-Net deep learning model was deployed to rapidly predict complex distributions of the local through-the-thickness FOD in PPMC.

Magic in generalized Rokhsar-Kivelson wavefunctions

Magic is a property of a quantum state that characterizes its deviation from a stabilizer state, serving as a useful resource for achieving universal quantum computation e.g., within schemes that use Clifford operations. In this work, we study magic, as quantified by the stabilizer Renyi entropy, in a class of models known as generalized Rokhsar-Kivelson systems, i.e., Hamiltonians that allow a stochastic matrix form (SMF) decomposition. The ground state wavefunctions of these systems can be written explicitly throughout their phase diagram, and their properties can be related to associated classical statistical mechanics problems, thereby allowing powerful analytical and numerical approaches that are not usually available in conventional quantum many body settings. As a result, we are able to express the SRE in terms of wave function coefficients that can be understood as a free energy difference of related classical problems. We apply this insight to a range of quantum many body SMF Hamiltonians, which affords us to study numerically the SRE of large high-dimensional systems, and in some cases to obtain analytical results. We observe that the behaviour of the SRE is relatively featureless across quantum phase transitions in these systems, although it is indeed singular (in its first or higher order derivative, depending on the nature of the transition). On the contrary, we find that the maximum of the SRE generically occurs at a cusp away from the quantum critical point, where the derivative suddenly changes sign. Furthermore, we compare the SRE and the logarithm of overlaps with specific stabilizer states, asymptotically realised in the ground state phase diagrams of these systems. We find that they display strikingly similar behaviors, which in turn establish rigorous bounds on the min-relative entropy of magic.

Convergence Results for History-Dependent Variational Inequalities

We consider a history-dependent variational inequality in a real Hilbert space, for which we recall an existence and uniqueness result. We associate this inequality with a gap function, together with two additional problems: a nonlinear equation and a minimization problem. Then, we prove that solving these problems is equivalent to solving the original history-dependent variational inequality. Next, we state and prove a convergence criterion, i.e., we provide necessary and sufficient conditions which guarantee the convergence of a sequence of functions to the solution of the considered inequality. Based on the equivalence above, we deduce various consequences that present some interest on their own, and, moreover, we obtain convergence results for the two additional problems considered. Finally, we apply our abstract results to the study of an inequality problem in solid mechanics. It concerns the study of a viscoelastic constitutive law with long memory and unilateral constraints, for which we deduce a convergence result and provide the corresponding mechanical interpretations.

Minimization principle for hemivariational–variational inequality driven by uniformly monotone operators with application to problems in contact mechanics

In this paper, we consider hemivariational–variational inequalities driven by uniformly monotone or d-monotone operators in Banach spaces. We establish related minimization principles leading to the existence and uniqueness of solutions to the inequality considered as well as we suggest the Ritz type numerical approximations. The theoretical results obtained are next applied to some problems inspired by models from contact mechanics.

PLEIADES: A numerical framework dedicated to the multiphysics and multiscale nuclear fuel behavior simulation

The aim of this paper is to introduce the PLEIADES framework offering a set of services and numerical tools to model and simulate the behavior of nuclear fuels of different concepts of reactors. The framework provides in particular the following features: interfaces to manipulate meshes and fields, services to deal with different physical solvers, setup of coupling trees to realize multiphysics partitioned (accelerated) fixed point couplings, automated time-marching algorithm, checkpoint/restart strategies, capability to realize on-the-fly multiscale couplings. It is built with a permanent concern for sustainability, scalability and maintainability. PLEIADES framework supports multidimensional simulations, typically 1D, 2D and 3D, possibly multilayered. To date, this framework relies on the generic thermomechanical finite elements solver Cast3M to deal with partial derivative problems (mechanical, thermal or diffusion problems) at the scale of the structure or the (heterogeneous) microstructure. It also makes use of so-called point models (mainly based on ODE — ordinary differential equations) to describe the local (mesoscale) evolution of the material through the physics of irradiation. Several software applications are built on the PLEIADES framework, they can use its parallel features to use multiple processors. The multilayered calculation scheme provides a way to loosen the computations and access to a good parallel performance up to hundred cores. It is also possible to achieve efficient scalable concurrent multiscale simulations through finite element square (FE2) computational homogenization algorithms.

Fracture prediction on hydrogen-charge notched samples using a stress-state-dependent phenomenological model

There is a consensus for transitioning to clean energy sources to meet the world’s energy demands. Hydrogen is a candidate to supply green energy. However, hydrogen embrittlement (HE) in materials is an issue that needs to be assessed. Based on the damage concept, a straightforward and robust computational framework is presented to predict the harmful effects on material resistance caused by the HE phenomenon. The adopted model framework builds upon dealing with the coupled mechanical diffusion problem in a simplified approach by considering the local equilibrium between hydrogen concentration at interstitial sites and Cauchy stresses. A modified version of the Mohr–Coulomb criterion dependent on the stress triaxiality and Lode angle introduces a damage indicator parameter. The proposed model is applied to study the brittle intergranular fracture of a high-strength AISI 4135 steel. A detailed description of the stress state and hydrogen-driven failure parameters are presented for two specimens with different notch radii. The proposed model is implemented in a VUMAT subroutine and made available for download to the technical community for research and educational use. After calibrating the model parameters, the numerical results yield good agreements of the predicted fracture strength of notched hydrogen-charged samples compared to the experimental ones. Maximum differences of around 10% among experimental and numerical tests are observed.

Design a cross-linked film based on cellulose nanocrystals doping for enhancing the interfacial performance and desensitization of CL-20

Despite the extensive researches on CL-20 crystals, the mechanical safety issues and process problems of CL-20 applications have not been studied in-depth. Herein, the cellulose nanocrystals (CNC) was doped in microcrystalline wax (MW), oxidized microcrystalline wax (OMW) and hydrogel (PPC) to design and fabricate the cross-linked CL-20 composites by simple water-suspension melting and freeze-drying methods. The composites were characterized by SEM, XPS, TG-DSC, XRD, mechanical sensitivity device and inclined chute tester. It is found that the CNC@OMW composite film exhibits excellent coating effect (99.96%) on CL-20 due to the cross-linking results. The Ea of CL-20 is increased from 190.92 to 388.71 kJ/mol under the synergistic effect of the excellent compatibility between components and the compact coating structure of CNC@OMW. Additionally, the film enhances the Tp0 of CL-20 from 218.15 to 222.66 ℃ and Tb from 220.27 to 223.73 ℃, respectively. While, the PPC@CNC only promoted Ea, Tp0 and Tb of CL-20–292.89.71 kJ/mol, 224.22 ℃ and 225.66 ℃, respectively. Besides, the XRD results confirms that three composite films dose not cause a transformation of the ε-CL-20 crystal phase. Most importantly, the cross-linked film brings mechanical sensitivity of CL-20 from 60 N and 3.5 J to a level of over 360 N and 10.4 J, comparable to WO3/Al nanothermite with 5 wt% polyaniline (360 N) and composite with 95 wt% LLM-105 and 5 wt% ternary (11–12 J). This improvement enables the composite explosives to be handled using standard procedures. Furthermore, the ability of the particles to accumulate electrostatic charge after cross-linking coating is significantly reduced, and PVC is more suitable as the contact material of CL-20 and composite particles than copper for use in the transportation and packaging. These findings can serve as a reference for wide application of CL-20.

Weak-formulated physics-informed modeling and optimization for heterogeneous digital materials.

Numerical solutions to partial differential equations (PDEs) are instrumental for material structural design where extensive data screening is needed. However, traditional numerical methods demand significant computational resources, highlighting the need for innovative optimization algorithms to streamline design exploration. Direct gradient-based optimization algorithms, while effective, rely on design initialization and require complex, problem-specific sensitivity derivations. The advent of machine learning offers a promising alternative to handling large parameter spaces. To further mitigate data dependency, researchers have developed physics-informed neural networks (PINNs) to learn directly from PDEs. However, the intrinsic continuity requirement of PINNs restricts their application in structural mechanics problems, especially for composite materials. Our work addresses this discontinuity issue by substituting the PDE residual with a weak formulation in the physics-informed training process. The proposed approach is exemplified in modeling digital materials, which are mathematical representations of complex composites that possess extreme structural discontinuity. This article also introduces an interactive process that integrates physics-informed loss with design objectives, eliminating the need for pretrained surrogate models or analytical sensitivity derivations. The results demonstrate that our approach can preserve the physical accuracy in data-free material surrogate modeling but also accelerates the direct optimization process without model pretraining.

Triaxial Load Cell for Ergonomic Risk Assessment: A Study Case of Applied Force of Thumb

To assess the ergonomic risk level in work systems involving tasks performed with hands or fingers, it is necessary to know the exerted triaxial forces. To address this need, a prototype of a triaxial load cell based on principles of linear elasticity theory and mechanical problems of torsion, bending and axial load is presented. This work includes an analytical strain model for each instrumented point and its solution regarding the applied force to a triaxial load cell. The proposed load cell was calibrated and validated by performing different static experimental tests. As a case study, the applied force in three directions while the thumb activates a cigarette lighter was measured. Triaxial forces and resultant forces were obtained and compared with the parameter of 10 N established by the ergonomic standards as reference values for pressing down with the thumb, finding that the applied forces in eight tests were 23.73 N, 43.51 N, 12.69 N, 14.50 N 20.35 N, 21.67 N, 39.74 N and 46.02 N, exceeding the reference values and establishing a direct relationship with Quervain syndrome. In conclusion, the developed load cell is a valid and reliable alternative to measure many forces that cannot be obtained with commercial devices, allowing the level of ergonomic risk to be determined with great precision.

Perturbative stability analysis of deformable charged bodies revealing the mathematical origin of Planck constant

This article considers elementary particles like electrons as finitely sized deformable bodies and analyzes the classical mechanics of their interior continuum. The consequent findings answer a long-standing question in physics by computing Planck constant mathematically. It also explains quantum phenomena like wave-particle duality, uncertainty principle and atomic stability without resorting to phenomenological relations like Planck’s law or Bohr’s postulates. The analysis introduces the criteria for perpetual stability under arbitrary perturbations to compensate for the lack of system-defining initial conditions typically available in a classical mechanics problem. Accordingly, unperturbed leading order field solutions are first constructed from steady rotation and axisymmetric electromagnetic potentials. Then, novel perturbation theories uniquely render the particulate geometry along with mass and charge distributions by exploiting the stability conditions. The approach reveals the perpetually stable body to have surface charges encapsulating a slender disk with a radius-to-thickness ratio 51.36 and a rim velocity of 0.09798c. The volumetric densities for rest-mass and charge are seen to vary with dimensionless radius (r) as (1−r2)−3/2 and (1−r2)−2 . The theory infers that the deformable system with many degrees of freedom would exhibit several pulsating modes. One such vibration, named quantum mode in this paper, causes spontaneous oscillation of the particulate center in the equatorial plane with a unique time period of oscillation. This wavy motion manifests wave-particle duality, whereas its probabilistic amplitude is identified as the reason behind quantum uncertainties. Moreover, in response to external fields, the charge deforms to create dipoles which can nullify radiation-inducing Poynting vector to ensure atomic stability. Finally, the Planck constant is retrieved after dividing the rest-energy by the frequency of the quantum mode. Thus, the paper concludes that a new detailed mechanics can potentially describe subatomic physics if charges are perceived as perpetually stable but readily deformable finite bodies, not rigid shape-less entities.

Axisymmetric virtual elements for problems of elasticity and plasticity

AbstractThe virtual element method (VEM) allows discretization of elasticity and plasticity problems with polygons in 2D and polyhedrals in 3D. The polygons (and polyhedrals) can have an arbitrary number of sides and can be concave or convex. These features, among others, are attractive for meshing complex geometries. However, to the author's knowledge axisymmetric virtual elements have not appeared before in the literature. Hence, in this work a novel first order consistent axisymmetric VEM is applied to problems of elasticity and plasticity. The VEM specific implementation details and adjustments needed to solve axisymmetric simulations are presented. Representative benchmark problems including pressure vessels and circular plates are illustrated. Examples also show that problems of near incompressibility are solved successfully. Consequently, this research demonstrates that the axisymmetric VEM formulation successfully solves certain classes of solid mechanics problems. The work concludes with a discussion of results for the current formulation and future research directions.