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This paper presents a Monotonic Unbounded Schemes Transformer (MUST) approach to bound/monotonize (remove undershoots and overshoots) unbounded spatial differencing schemes automatically, and naturally. Automatically means the approach (1) captures the critical cell Peclet number when an unbounded scheme starts to produce physically unrealistic solution automatically, and (2) removes the undershoots and overshoots as part of the formulation without requiring human interventions. Naturally implies, all the terms in the discretization equation of the unbounded spatial differencing scheme are retained.

The authors do not formulate new higher-order scheme. MUST transforms an unbounded higher-order scheme into a bounded higher-order scheme.

The solutions obtained with MUST are identical to those without MUST when the cell Peclet number is smaller than the critical cell Peclet number. For cell Peclet numbers larger than the critical cell Peclet numbers, MUST sets the nodal values to the limiter value which can be derived for the problem at-hand. The authors propose a way to derive the limiter value. The authors tested MUST on the central differencing scheme, the second-order upwind differencing scheme and the QUICK differencing scheme. In all cases tested, MUST is able to (1) capture the critical cell Peclet numbers; the exact locations when overshoots and undershoots occur, and (2) limit the nodal value to the value of the limiter values. These are achieved by retaining all the discretization terms of the respective differencing schemes naturally and accomplished automatically as part of the discretization process. The authors demonstrated MUST using one-dimensional problems. Results for a two-dimensional convection–diffusion problem are shown in Appendix to show generality of MUST.

The authors present an original approach to convert any unbounded scheme to bounded scheme while retaining all the terms in the original discretization equation.

This paper aims to numerically examine the impact of gyrotactic microorganisms and radiation on heat transport features of magnetic nanoliquid within a closed cavity. Thermophoresis, chemical reaction and Brownian motion are also considered in flow geometry for the moment of nanoparticles.

Finite element method (FEM) was depleted to numerically approximate the temperature, momentum, concentration and microorganisms concentration of the nanoliquid. The present simulation was unsteady state, and the resulting transformed equations are simulated by FEM-based Mathematica algorithm.

It has been found that isotherm patterns get larger with increasing values of the magnetic field parameter. Additionally, numerical codes for rate of heat transport impedance inside the cavity with an increasing Brownian motion parameter values.

To the best of the authors’ knowledge, the research work carried out in this paper is new, and no part is copied from others’ works.

Heterogeneous and micro-structured materials have been the object of multiscale and homogenization techniques aimed at recognizing the elastic properties of the equivalent continuum. The proposed investigation deals with the mechanical characterization of the heterogeneous material structured metamaterials through analyzing the ultimate strength using the limit analysis of the Representative Volume Element (RVE). To get the desired material strength, a novel finite element formulation based on the derivation of self-equilibrated solutions through the finite elements devoted to calculating the lower bound theorem has been implemented together with the limit analysis in Melàn’s formulation.

The finite element formulation is based on discrete mapping of Volterra dislocations in the structure using isoparametric representation. Using standard finite element techniques, the linear operator V, which relates the self-equilibrated internal solicitation to displacement-like nodal parameters, has been built through finite element discretization of displacement and strain.

The proposed work presented an elastic homogenization of the mechanical properties of an elementary cell with a geometry known in the literature, the isotropic truss. The matrix of elastic constants was calculated by subjecting the RVE to numerical load tests, simulated with a commercial FEM calculation code. This step showed the dependence of the isotropy properties, verified with Zener theory, on the density of the RVE. The isotropy condition of the material is only achieved for certain section ratios between body-centered cubic (BCC) and face-centered cubic (FCC), neglecting flexural effects at the nodes. The density that satisfies Zener’s conditions represents the isotropic geomatics of the isotropic truss.

For the isotropic case, the VFEM procedure was used to evaluate the isotropy of the limit domain and was compared with the Mises–Schleicher limit domain. The evaluation of residual ductility and dissipation energy allowed a measurement parameter for the limit anisotropy to be defined. The novelty of the proposal consisted in the formulation of both the linearized and the nonlinear limit locus of the material; hence, it furnished the starting point for further limit analysis of the structures whose elementary volume has been described through the proposed approach.

The purpose of this study is to investigate the strain rate effect on the problem of low-velocity impact (LVI) on a beam, including silicon nitride and stainless steel materials.

Based on the nonlinear Hertz impact mechanism, the energies related to the impactor and the beam are written, and motion equations are derived using the Lagrangian mechanics and Ritz method. The strain rate term is represented as a damping matrix in the equations of motion. In the issue of LVI on the silicon nitride and stainless steel beam, the effect of internal viscous damping coefficient in simply–simply and clamped–free boundary conditions are studied. Also, the influence of the volume fraction index in the range between zero and one and greater than one on the impact response is investigated.

The results make it clear that the strain rate parameter had little effect on the response in LVI. Also, an increase in the volume fraction index has led to a decrease in the contact force and an increase in the rebound velocity of the impactor.

The effect of strain rate on LVI is theoretically studied in this paper, while in most of the papers, this effect is investigated experimentally and numerically.

The “chiralisation” of Euclidean polygonal tessellations is a novel, recent method which has been used to design new auxetic metamaterials with complex topologies and improved geometric versatility over traditional chiral honeycombs. This paper aims to design and manufacture chiral honeycombs representative of four distinct classes of 2D Euclidean tessellations with hexagonal rotational symmetry using fused-deposition additive manufacturing and experimentally analysed the mechanical properties and failure modes of these metamaterials.

Finite Element simulations were also used to study the high-strain compressive performance of these systems under both periodic boundary conditions and realistic, finite conditions. Experimental uniaxial compressive loading tests were applied to additively manufactured prototypes and digital image correlation was used to measure the Poisson’s ratio and analyse the deformation behaviour of these systems.

The results obtained demonstrate that these systems have the ability to exhibit a wide range of Poisson’s ratios (positive, quasi-zero and negative values) and stiffnesses as well as unusual failure modes characterised by a sequential layer-by-layer collapse of specific, non-adjacent ligaments. These findings provide useful insights on the mechanical properties and deformation behaviours of this new class of metamaterials and indicate that these chiral honeycombs could potentially possess anomalous characteristics which are not commonly found in traditional chiral metamaterials based on regular monohedral tilings.

To the best of the authors’ knowledge, the authors have analysed for the first time the high strain behaviour and failure modes of chiral metamaterials based on Euclidean multi-polygonal tessellations.

This study aimed to analyze the free vibration of a radially graded Ni-Al2O3-based functionally graded (FG) disk with uniform thickness.

Using the energy method, natural frequencies of rotating and non-rotating disks were determined at the limit elastic angular speed. Material properties were estimated using a modified rule of mixture. Both even and uneven porosity variation effects were considered in the material modeling. Finite element analysis validated the analytical approach.

The study explored limit angular speeds and natural frequencies across various grading indices, investigating the impact of porosity types and grading indices on these parameters.

Insights from this research are valuable for researchers and design engineers involved in modeling and fabricating porous FG disks, aiding in more effective design and manufacturing processes.

This study contributes to the field by providing a comprehensive analysis of free vibration behavior in radially graded Ni-Al2O3-based FG disks. The incorporation of material modeling considering both even and uneven porosity variation adds originality to the research. Additionally, the validation through finite element analysis enhances the credibility of the findings.

The purpose of this study is to model the global dynamic hysteresis properties with an improved Jiles–Atherton (J-A) model through a unified set of parameters.

First, the waveform scaling parameters β, λ_k and λ_c are used to improve the calculation accuracy of hysteresis loops at low magnetic flux density. Second, the Riemann–Liouville (R-L) type fractional derivatives technique is applied to modified static inverse J-A model to compute the dynamic magnetic field considering the skin effect in wideband frequency magnetization conditions.

The proposed model is identified and verified by modeling the hysteresis loops whose maximum magnetic flux densities vary from 0.3 to 1.4 T up to 800 Hz using B30P105 electrical steel. Compared with the conventional J-A model, the global simulation ability of the proposed dynamic model is much improved.

Accurate modeling of the hysteresis properties of electrical steels is essential for analyzing the loss behavior of electrical equipment in finite element analysis (FEA). Nevertheless, the existing inverse Jiles–Atherton (J-A) model can only guarantee the simulation accuracy with higher magnetic flux densities, which cannot guarantee the analysis requirements of considering both low magnetic flux density and high magnetic flux density in FEA. This paper modifies the dynamic J-A model by introducing waveform scaling parameters and the R-L fractional derivative to improve the hysteresis loops’ simulation accuracy from low to high magnetic flux densities with the same set of parameters in a wide frequency range.

This study aims to introduce a predictive homogenization model incorporating electrical percolation considerations to forecast the electrical characteristics of unidirectional carbon-epoxy laminate composites.

This study presents a method for calculating the electrical conductivity tensor for various ply arrangement patterns to elucidate phenomena occurring around the interfaces between plies. These interface models are then integrated into a three-dimensional (3D) magneto-thermal model using the finite element method. A comparative study is conducted between different approaches, emphasizing the advantages of the new model through experimental measurements.

This research facilitates the innovative integration of electrical percolation considerations, resulting in substantial improvement in the prediction of electrical properties of composites. The validity of this improvement is established through comprehensive validation against existing approaches and experimentation.

The study primarily focuses on unidirectional carbon-epoxy laminate composites. Further research is needed to extend the model's applicability to other composite materials and configurations.

The proposed model offers a significant improvement in predicting the electrical properties of composite materials by incorporating electrical percolation considerations at inter-ply interfaces, which have not been addressed in previous studies. This research provides valuable information to improve the accuracy of predictions of the electrical properties of composites and offers a methodology for accounting for these properties in 3D magneto-thermal simulations.

Torque is one of the main parameters reflecting the operation status and detection of a mechanical rotation system. The use of quartz pillar to design torque sensors has advantage over the use of quartz disk, but research into the torsional effect of quartz pillar is rare. This paper aims to investigate a novel type of torque sensor based on piezoelectric torsional effect.

Based on the theory of anisotropic elasticity and the Maxwell electromagnetism, the torsion stress and distribution of surface charge of a rectangular quartz pillar are calculated. Using finite element analysis, the polarized electric field of the piezoelectric pillar is solved. According to the theoretical calculation of torsional effect of piezoelectric quartz pillar, detection electrodes are mounted on the surface of the quartz pillar and a new type of torque sensor is designed.

The calibration experimental results show that the bound charges are proportional to the torque applied, and the torque sensor has fully reached the dynamometer standard.

This paper shows that the torsional effect of the developed piezoelectric quartz pillar can be used to create a new type of piezoelectric torque sensor.

There are various uncertain and nonlinear problems in hydraulic legged robot systems, including parameter uncertainty, unmodeled dynamics and external disturbances. This study aims to eliminate uncertainties and improve the foot trajectory tracking control performance of hydraulic legged robots, a high-performance foot trajectory tracking control method based on fixed-time disturbance observers for hydraulic legged robots is proposed.

First, the robot leg mechanical system model and hydraulic system model of the hydraulic legged robot are established. Subsequently, two fixed-time disturbance observers are designed to address the unmatched lumped uncertainty and match lumped uncertainty in the system. Finally, the lumped uncertainties are compensated in the controller design, and the designed motion controller also achieves fixed-time stability.

Through simulation and experiments, it can be found that the proposed tracking control method based on fixed-time observers has better tracking control performance. The effectiveness and superiority of the proposed method have been verified.

Both the disturbance observers and the controller achieve fixed-time stability, effectively improving the performance of foot trajectory tracking control for hydraulic legged robots.