Appl. Mech., Volume 3, Issue 2 (June 2022) – 21 articles

Locating bearing track rollers are used, for example, in monorail transport systems to enable relative movement between the rail and the shuttle. Due to the two-point contact, both radial and axial forces can be transmitted simultaneously. Since friction is involved, the state of the art does not provide any calculation rules for the dimensioning and design. The development of a calculation model with sophisticated commercial software brings its difficulties since no plausibility check is possible using existing models. For this reason, a model based on analytical descriptions including the Hertzian and the elastic half space theories is presented in this paper. It bridges the gap between very simple approaches and widely developed commercial software. With this model, the contact forces, friction forces, surface tensions, relative velocities and subsurface stresses can be calculated for both free and driven rolling. The main advantages are that the model is easy to apply, and thus comparisons between different track roller designs can be made quickly. Full article

The study presents a generalized analytical solution of the laminar, oscillatory, creeping flow of an incompressible Newtonian fluid in a porous circular pipe with spatiotemporally periodic suction/injection at the wall. The analytical solution is examined for a variety of values of the dimensionless parameters, namely the Womersley number and the dimensionless suction/injection number. Full article

In the finite element simulation process, it is very common to use simplified models to replace the original complex models to reduce the computational cost. To improve the accuracy of simulation with simplified numerical models in Abaqus Explicit, we propose an inverse identification procedure to evaluate the equivalent loading conditions to be applied to these simplified models. We construct an objective function to test the correlation between the final deformed shape obtained by simulation on the full models and the simplified models. A Python identification program using the Levenberg–Marquardt algorithm is implemented to optimize this objective function. In parallel to this approach, we propose a data processing step, validated by a dynamic tensile test, to obtain more accurate numerical responses, including data extraction and estimation. Full numerical models for the Taylor test, dynamic tensile test, and dynamic shear test were constructed using Abaqus Explicit FEM code. The complete models were then replaced by simplified models, in which some non-essential parts were removed and some boundary conditions were modified. In order to obtain the same results in terms of the final geometry, the proposed inverse identification procedure is then used to calculate the equivalent impact velocities for the simplified models. Full article

When a finger actively slides over a surface, contact conditions including the contact area, sliding speed, and finger moisture naturally fluctuate. These random fluctuations lead to an apparent change of frictional properties and influence tactile pleasantness. Nonetheless, this probabilistic behavior has not been explicitly analyzed in previous studies on human fingertips. This study investigates the dependence of the coefficients of kinetic friction on the normal force produced by sliding a bare finger over different artificial skins with seven levels of hardness. The coefficient of friction was modeled as a power function of the normal force. An experimental study that involved sliding a finger over artificial skin surfaces was carried out under two conditions: the fingertip being wiped by a dry cloth or a cloth soaked in ethanol. Although the exponential term was assumed to be nearly constant for identical tribological conditions, we observed that the exponent varied randomly and could be negative, zero, or positive. This can be attributed to the variation of gross finger deformation that was not controlled during the observation. The probability density function of the exponent depended on the moisture content of the finger and object hardness. The variability of the exponent was higher for a soft material than it was for a harder material. In other words, for the softer materials, the exponent appears more random. Furthermore, the exponent tended to be positive and the coefficient of friction increased with the normal force when the finger was wiped with ethanol. These findings play an important role in understanding the frictional forces produced during skin–skin contact in terms of determining the root cause of random variations in the dependence of the coefficient of friction on the normal force. Full article

This paper presents a study based on wind tunnel research on biplane configurations. The objective of this research is to establish an experimental basis for relationships between the main geometrical parameters that define a biplane configuration (stagger, decalage, gap, and sweep angle) and the aerodynamic characteristics (C_L, C_D). This experimental study focuses on a 2D approach. This method is the first step towards dealing with the issue, and it allows the variables involved in the tests to be reduced. The biplane configuration has been compared with the monoplane configuration to analyze the viability for implementing the biplane configuration in the field of application for micro air vehicles (MAV). At present, the biplane and other unusual configurations have not been a common design for MAV; however, they do have unlimited future potential. A set of experimental tests were carried out on various biplane configurations at low Reynolds numbers, which allowed the criteria for selecting the best wing configuration to be defined. The results obtained here show that the biplane configuration provides a higher maximum lift coefficient (C_Lmax) than the planar wing (monoplane). Furthermore, it has a larger wetted surface than the planar configuration, so the parasitic drag increases for the biplane configuration. This research is focused on a drone flight regime (low Reynolds number), and in this case, the parasitic drag (profile drag) has an important role in the total drag of the airplane. This study considers whether the reduction in the induced drag due to three–dimensional configuration (biplanes, box–wings, and joined–wings) can reduce the total drag or if the increase in the parasitic drag is bigger. Additionally, the increase in lift and the decrease in parasitic drag (profile drag) will be studied to determine if they have a greater influence on the performance of the airplane than the increase in structural weight. Further research is planned to be performed on 3D prototypes, with the selected configurations, and applied to nonconventional wing planforms. Full article

Circular and spherical particle models are a class of discrete elements (DEM) that have been increasingly applied to fracture studies of quasi-brittle materials, such as rock and concrete, due to their proven ability to simulate fracture processes through random particle assemblies representing quasi-brittle materials at the grain scale. More recently, DEM models have been applied to old stone masonry fracture studies. In order to extend its applicability to structures of larger dimensions, an enhanced hybrid particle model is proposed here that allows finite elements with a given surface roughness, provided by the discretization of the element boundary with particles, to interact with the particulate media in which they are embedded. The performance of the hybrid model is compared with that of a traditional all-particle model under uniaxial testing. It is shown that similar results are obtained, namely, in the elastic phase, figures of rupture and pre-peak and post-peak behavior, while the hybrid model allows for a significant computational run time reduction of 20% to 25% in the coarse particle assemblies. Finally, the proposed hybrid model is applied in the simulation of shear tests of stone masonry walls and dry and mortared joints, providing reasonably good agreement with both the experimental results and predictions. For the rubble masonry tests, the hybrid model allows for a computation run time reduction of around 40% when compared with an all-particle model. Full article

This paper studies a cracked orthotropic solid under symmetric heat flow, and symmetric mechanical loading is studied. A modified partially impermeable crack model is employed to simulate thermal load transfer. With the application of the Fourier transform technique and superposition theory, the related physical quantities and fracture parameters are obtained in explicit forms. The advantage of this paper is that the obtained solutions are explicitly closed. As a result, the calculation of the stress intensity factors of various cracks with different lengths becomes very convenient and fast. Some simple examples are used to demonstrate the method provided in this paper. The analysis results show the dimensionless thermal resistance (${\varpi }_c$) between the upper and lower crack regions and the proposed coefficient ($\epsilon$) greatly influence the related physical quantities and fracture parameters. In addition, the numerical analysis results also revealed that the calculated results of fracture parameters at the crack tip will not be physically meaningful unless certain conditions are met. Full article

An expanding pin locks the pin assembly to its supports and bearings and prevents any relative movements between the surfaces in contact. In this study, the diameter changes of the bearing inner ring as a function of the expanding pin’s tightening torque were studied. In addition, the required rotational moment of a set of complete bearings locked to an expanding pin solution was studied by exposing the assembly to a combination of an increasing radially outwards directed load from the bolt torquing and a radially external inwards directed load from a hydraulic jack. The bearings were of type Radial Spherical Plain Bearings (RSPBs), GE 80 ES, steel/steel, and loaded externally up to their maximum dynamic limit of 400 kN. The results indicate a major reduction in the required rotation moment of the bearing when the bearing inner ring is expanded by use of an expanding pin. The reduction of rotation moment indicates reduced contact pressure and friction force between the two bearing rings, which ultimately can have a reduced effect on ring surface wear and a positive effect on the bearing operational lifetime. Full article

The incorporation of ceramic nanoinclusions in carbon nanocomposites can induce additional functionality in the field of magnetic properties, piezoelectricity, etc. In this study, series of nanocomposites, consisting of different carbon nanoinclusions (carbon black, MWCNTs, graphene nanoplatelets, nanodiamonds) and magnetite nanoparticles incorporated into a commercially available epoxy resin were developed varying the filler type and concentration. Experimental data from the static tensile tests and dynamic mechanical analysis (DMA) demonstrated that the elastic tensile modulus and storage modulus of hybrid nanocomposites increase with an increase in filler content up to almost 100% due to the inherent filler properties and the strong interactions at the interface between the epoxy matrix and the nanoinclusions. Strong interactions are implied by the increasing values of the glass transition temperature recorded by differential scanning calorimetry (DSC). On the contrary, tensile strength and fracture strain of the nanocomposites were found to decrease with filler content. The results highlight the potentials and capabilities of developing hybrid multifunctional nanocomposites with enriched properties while holding their structural integrity. Full article

Laser additive manufacturing enables economical production of complex lightweight structures. To realize the potential benefits of additive manufacturing technology in industrial applications, the fatigue performance of parts additively manufactured materials must be modelized. The aim of this paper is to present a new modeling approach combining plasticity and damage, and appropriate for as-built Laser-Powder Bed Fusion (LPBF) structures. The model presented is an extension of the Dang Van criterion, including damage, defined as porosity in the case of LPBF. Attention is focused on the integration of damage in a fatigue criterion using the concept of elastic shakedown. Finally, the case of 316L will illustrate the results of the model by fatigue tests with deterministic defects. Full article

The Updated Lagrangian method for nonlinear elasticity with contact is presented. First, we describe the Total Lagrangian for a compressible Neo-Hookean material. Next, we introduce the Updated Lagrangian formulation for Neo-Hookean and Ogden compressible materials with contact. An advantage of this approach is that at each iteration only a linear system is solved. The linear problem to be solved is written in the updated domain. Numerical results are presented: compression of a Hertz half ball and of a hyperelastic ring against a flat rigid foundation, and contact of an elastic cube and a ball. Full article

The main aim of the present paper is to assess the fatigue lifetime of ductile cast iron knuckles as one of the critical components of an automotive steering system. To this end, a real driving path, including various maneuvers, such as acceleration, braking, cornering, and moving on various types of road roughness, was considered. Different load histories, which are applied on various joints of the component (i.e., lower control arm, steering linkage, and Macpherson strut), were extracted through Multi-Body Dynamics (MBD) analysis of a full vehicle model. The achievements of previous studies have proved that the steering knuckle fails from the steering linkage and due to the rotational motion. Therefore, only this destructive load history was considered in future analyses of the present study. The CAD model was created using Coordinate Measuring Machine (CMM) data and some corrections in CATIA software. Furthermore, transient dynamic analysis was performed, and the time history of von Misses equivalent stress was obtained at the root of the steering linkage (which is exactly the location of failure based on the laboratory data as well as finite element simulations validated by the author in the previous studies). To predict the fatigue life of a component, two different methodologies were considered. Firstly, some well-known criteria were employed for equalization of load spectrum to a Constant Amplitude Loading (CAL). Then, fatigue analysis under sinusoidal loading was performed. Secondly, the fatigue life of the component considering Variable Amplitude Loading (VAL) was predicted using the Critical Plane Method (CPM), employing the Rain-flow cycle counting technique, and utilizing the Miner–Palmgren damage accumulation rule. Eventually, to evaluate the prediction accuracy of different methodologies, the obtained results were compared with the full-scale axial variable amplitude fatigue test which was performed by the corresponding author. The results indicated that the prediction of variable amplitude fatigue lifetime by Finite Element (FE) analysis in the time domain has about 21% error compared to reality. Additionally, the relative error between the results obtained from two different methodologies is about 20%, which is acceptable due to the scattering of the fatigue phenomenon results, the complex geometry of the part, and the complicated loading. Full article

Nonwovens are a type of textile that possess a wide range of unique properties, such as lightweight and damping characteristics, which make them suitable for many applications as in medicine and engineering. In this study, the focus lies on the mechanical response of nonwovens as a multiphase porous layer excited by an underlying vibrating plate. The material properties of the nonwovens are characterized via laboratory measurements applied to different samples. In particular, a dynamic analysis of the underlying thin plate is carried out to obtain its eigenmodes and, thus, the maximum response. These eigenmodes are then utilized in the boundary conditions in an advanced numerical porous media model to simulate the dynamic response of the anisotropic fibrous material. To understand the coupled processes in the fibrous textile material, a three-dimensional initial-boundary-value problem of porous media dynamics is introduced. The numerical results demonstrate the capability of the proposed model to realize the interplay between the pore-air pressure and the effective stresses during nonwovens vibration and, thus, the role of the pore air in vibration-induced fiber-fiber friction reduction as well as the effectiveness of the nonwovens in the dissipation of the kinetic energy, i.e., damping propagating acoustic waves. Full article

In this paper, the flow of concrete in a reinforced bored pile is analysed using computational simulations. In order to reduce the computational time, a porous medium that equally mimics the presence of the reinforcement is used. Experimental measurements are used as bounds on the material parameters describing the flow of fresh concrete. The influence of rheological properties of fresh concrete and the thickness of the porous medium that represents the reinforcements is analysed with a classical U-box simulation. Finally, casting of a bored pile is analysed using computational simulation implementing a porous medium representing the reinforcement cage. The concrete flow behavior and especially the filling of the concrete cover zone is analyzed for casting scenarios with different concretes varying in their rheological behavior. Simulations using the porous medium approach is 10x faster than simulations that explicitly model the reinforcements. Simulation results show that a good workability (low viscosity and low yield stress) of the initial batches of concrete must be maintained throughout pouring to avoid the risk of defect formation in the cover zone. Full article

In this paper, hierarchical studies based on both analytical and computational approaches have been employed to validate and improve current structural designs of mud holding tanks for hydraulic fracturing in petroleum industries. Through detailed comparisons at different levels of approximations for both real world complex structural design problem and a simplified stiffened plate with extreme geometrical aspect ratios, proper design procedures have been reiterated and validated. It is highly recommended that low-dimensional structures with emphasis on classical mechanics principles should be considered before full-fledged three-dimensional computational analyses. Both Castigliano’s Theorems and Galerkin methods are utilized along with simulation packages such as ADINA and Solidworks. The hierarchical approximation procedures reemphasize important subjects such as planes and shells, strength of materials, structural mechanics, asymptotic and perturbation analysis no longer required in some engineering programs, yet often necessary for the study of complex three-dimensional structural systems. Full article

The ‘diffraction in space’ and the ‘diffraction in time’ phenomena are considered in regard to a continuously open, and a closed shutter that is opened at an instant in time, respectively. The purpose of this is to provide a background to the principal theme of this article, which is to extend the ‘quantum shutter problem’ for the case when the wave function is determined by the fundamental solution to a partial differential equation with a fractional derivative of space or of time. This involves the development of Green’s function solutions for the space- and time-fractional Schrödinger equation and the time-fractional Klein–Gordon equation (for the semi-relativistic case). In each case, the focus is on the development of primarily one-dimensional solutions, subject to an initial condition which controls the dynamical behaviour of the wave function. Coupled with variations in the fractional order of the fractional derivatives, illustrative example results are provided that are based on presenting space-time maps of the wave function; specifically, the probability density of the wave function. In this context, the paper provides a case study of fractional quantum mechanics and control using fractional calculus. Full article

The purpose of this work is to provide empirical design models for low-pressure, subsonic Venturi nozzles. Experimentally validated simulations were used to determine the effect of nozzle geometry and operating conditions on the suction ratio (ratio of suction mass flow rate to motive mass flow rate) of low-pressure, subsonic Venturi nozzles, over a wide range of geometries and operating conditions, through a parametric study. The results of the parametric study were used to develop seven empirical models, each with a different range of applicability or calculating a different indicator of nozzle performance (i.e., suction ratio, momentum ratio, or dynamic pressure ratio), of the Venturi nozzles using a constrained multi-variable global optimization method. Of the seven empirical models, the best models were found to be those for low- (less than one) and high-suction ratios (greater than one), with mean absolute percentage errors of 5% and 18%, respectively. These empirical models provide a design tool for subsonic, low-pressure Venturi nozzles that is more than an order of magnitude more accurate than a governing equation approach or conventional flow head calculations. These newly-developed empirical models can be applied for initial nozzle design when precise suction ratios are required. Full article

This paper presents a novel method for the design of purely elastic interference fits by exploiting the plastic properties of a material. In this process, the elastic potential of the material is expanded by the targeted application of residual stresses and material strengthening, in such a way that additional operational loads due to rotating bending moments, torsion, temperature changes, and centrifugal forces are absorbed by the hub in a purely elastic manner, and plastic deformations are avoided. In the ideal case, the performance shown by the connection can be almost doubled compared to conventional elastically joined interference fits. Compared with conventional elastically–plastically joined interference fits, a specifically defined additional safety against plastic deformation can be guaranteed. In addition to the prerequisites of plasticity theory, the fundamental aspects of the process are presented and investigated on the basis of two-dimensional numerical calculation models. Both ideal plastic and hardening material models were used. The results of this work showed that previous stress limits can be significantly increased up to full plastic loading and that the utilization of plastic material properties is also made possible by plastic conditioning for applications that were previously designed to be purely elastic. Full article

In this paper, a new methodology for the numerical simulation of the wheel–surface interaction has been presented. The finite-element method was combined with the discrete-element method, rigid body dynamics, and the advanced wheel–surface friction model. Compared to the current state-of-the-art, this novel approach can more realistically model the application of the traction force on the contact surface between the wheel and the soil. The rotation of a non-driven wheel is caused by the movement of the axis and the contact forces. The method that has been developed is able to assess both the longitudinal and lateral forces for a wide range of attack angles of the wheel; this is essential for calculating the traction effort of skid-steered vehicles. Full article

One group of losses that can considerably affect the performance of Free Piston Stirling Engines’ (FPSE) is the enthalpy pumping and the shuttle effect, which are due to the gap standing between the cylinder and the displacer. The shuttle effect is induced by the periodic displacer motion between the hot and the cold sources. The enthalpy pumping, which is the subject of the present study, is due to the short-circuit-like flow between the hot and cold spaces. To study these losses, first, a fine nonlinear dynamic model of the FPSE is developed and validated. Then, to study the enthalpy pumping based on that, a coupled model (for the first time) and a decoupled model are presented. The difference between the two models is that the first one provides a dynamic and a thermic linkage between the Stirling and loss model, while the second one studies them separately. The effect of the gap size on both loss models was investigated. The coupled and decoupled modeling results were quite different due to the considerable effect of the enthalpy pumping on the FPSE response. The results showed that the enthalpy pumping in the decoupled model exceeds the total output power when the gap exceeds $30 \mathsf{\mu }\mathrm{m}$, and when the gap exceeds $70 \mathsf{\mu }\mathrm{m}$, the enthalpy pumping is around ten times larger than the output power. In contrast, the enthalpy pumping in the coupled model is always less than the output power, which is logical. Thus, the coupled one was presented as the adapted model that should be considered for further FPSE studies. Full article