Analytical Mechanical Model Research Articles

Stress-deformation analysis of the cracked elastic body

A new analytical plane Elastic Fracture Mechanics (LEFM) model of the effective elastic moduli exhibited by an isotropic elastic cracked solid in tensile and compressive stress fields is presented. The effective Young’s modulus and Poisson’s ratio E¯,v¯, respectively, relate the stresses applied to the cracked solid with its macroscopic deformation. In the case of a compressive stress field the effective elastic moduli depend solely on properly oriented cracks that are either open or closed. This model is then used for the stress and displacement estimations around a circular axisymmetric hole under internal pressure and external hydrostatic stress. The creation of the hole alters the stresses in its neighborhood, and induces a deterioration of the elastic moduli. In this manner, the effective elastic moduli depend on the radial distance from the hole’s boundary. The validation of the algorithm was done against Kirsch’s analytical solution of the axisymmetric hole problem for nearly zero density of cracks as well as for large values of the friction angle. The model predicts a lower tangential stress concentration at the wall of the hole compared to that predicted by the constant linear elasticity solution and a maximum stress concentration that is not necessarily located at the wall of the hole. This apparent enhancement of rock strength adjacent to the wall is more pronounced for larger concentrations of open cracks.

Magneto-mechanical design of a high-speed machine for aeronautics

Electrical machines that can run at high speeds are more and more studied as they can respond to the increasing need of power onboard of aircrafts. However, to allow high-speed operability mechanical handling of the rotating parts need to be insured. In this paper an analytic design process of a novel high-speed induction machine is presented. The analytical magnetic and mechanical models developed are presented and validated with finite element simulations. The magnetic model is based on a classic equivalent electrical diagram of induction machine with a specific adaptation for the rotor leakage inductance as the squirrel cage is buried. The mechanical model is based on a field displacement approach leading to the stress tensor in all the rotating part. A four degrees of freedom vibration analysis model considering gyroscopic effects based on Euler–Lagrange equation allows to identify the critical speeds of the system. It is shown that some geometrical parameters will have opposed effects on the two physics. Thus, an optimization-based coupling between the different physics allows to design rapidly the desired machine regarding any technical specifications as analytical models are being used.

Viscoelasticity of hydrating shotcrete as key to realistic tunnel shell stress assessment with the New Austrian Tunneling Method

The New Austrian Tunneling Method (NATM) essentially rests on observational information concerning displacements measured in selected positions at the inner surface of shotcrete tunnel shells. The combination of these measurements with advanced material and structural mechanics, in the course of so-called hybrid methods, have successfully delivered, for more than 20 years, practically relevant estimations of internal and external forces and corresponding degrees of utilization. The reliability of the latter, however, may crucially depend on the used material model. Based on a recently proposed analytical structural mechanics model [Acta Mech 233, 2989–3019 (2022)], and focusing on the benchmark example of measurement cross section MC1452 of the Sieberg tunnel, driven in the 1990s in Miocene clay marl, the present paper compares the estimations of forces and degrees of utilization arising from differently refined constitutive concepts, namely (i) aging elasticity, (ii) aging linear viscoelasticity, and (iii) aging nonlinear viscoelasticity. It turns out that only the consideration of aging nonlinear viscoelastic material behavior provides access to realistic values for the degree of utilization, being lower than one. Simpler material models would indicate local material failure, which was not observed in situ.

Seismic Isolation Effects on Elevated and Ground-Supported Flexible Concrete Cylindrical Tanks Under Bi-Directional Excitation Using an Advanced Mechanical Model

In this paper, the effectiveness of seismic isolation using lead rubber bearings (LRBs) and friction pendulum systems (FPSs) for slender and broad, grounded and elevated tanks (two seat locations of isolation systems in elevated tanks) is investigated under bi-directional excitation of up to 10 records of earthquakes. An analytical mechanical model for a flexible, concrete cylindrical tank, taking into consideration the effect of wall mass and sloshing, is used. The assumptions underlying the mechanical model are basic equations of the motion according to the theory of fluid dynamics. So, the assumptions are more realistic and the results therefore are more accurate than the previous models. The results show that by selecting the best mechanical properties of base isolation systems, reductions of seismic base shear in the grounded broad tanks are around 35% and 30% and for the grounded slender tanks are around 55% and 58% in the x- and y-directions, respectively. Maximum total hydrodynamic pressure is reduced considerably by about 40% on average in all grounded and elevated models. As a result of isolation, elevated tanks are concluded to be better candidates in terms of more effective application of seismic isolation.

An Analytical Mechanics Model for the Rotary Sliding Triboelectric Nanogenerator.

In recent years, global attention towards new energy has surged due to increasing energy demand and environmental concerns. Researchers have intensified their focus on new energy, leading to advancements in technologies like triboelectrification, which harnesses energy from the environment. The invention of the triboelectric nanogenerator (TENG) has led to new possibilities, with the rotary sliding TENG standing out for its superior performance. However, understanding its mechanical behavior remains a challenge, potentially leading to structural issues. This paper introduces a novel analytical mechanics model to analyze the mechanical performance of the stator of the rotary sliding TENG, offering a new analytical solution. The solution also presents an innovative approach to solving axisymmetric problems in elasticity theory since it challenges a traditional assumption that the stress function depends solely on the radial coordinate, proposing a new stress function to derive a more general solution, supplementing the classical approach in the theory of elasticity. Through the obtained solutions, the mechanical characteristics of the rotary sliding TENG during operation are analyzed. A clearer relationship between mechanical characteristics and electrical output is expected to provide a theoretical basis for the design of the rotary sliding TENG.

Enhancing toughness through geometric control of the process zone

Material architecture provides an opportunity to alter and control the fracture process zone shape and volume by redistributing the local stresses at a crack tip. Properly designed structures can enlarge the plastic zone and enhance the effective toughness. Here, we use a pillar array as a model structure to demonstrate how variations in geometry at a crack tip control the size and shape of the plastic zone and can be used to engineer the effective toughness. Elastic–plastic finite element simulations are used to quantify how the pillar width, spacing, and height can be varied to tailor the size and shape of the plastic zone. A set of analytical mechanics models that accurately estimate the shape, volume, and resulting toughness as a function of the base material properties and geometry are also presented. A case study extends the analysis to sets of non-regular pillar arrays to illustrate how architecture can be used to alter toughness along the crack path.

Analytical investigation of hygrothermal effects on failure mechanisms of adhesively bonded corrugated sandwich structures under three-point bending

This research paper presents an analytical mechanics model for studying the degraded failure mechanics of an adhesively bonded corrugated sandwich structure (ABCSS) subjected to three-point bending and hygrothermal ageing loads. The model incorporates a detailed stress state model that considers the stress distribution of the adhesive layer, including the adhesive fillet, to more accurately reflect the failure mechanics of ABCSS. The Fickian Diffusion model and a degradation coefficient are used to describe the characteristics of water diffusion and hygrothermal mechanical degradation for the adhesive joint in ABCSS. The hygrothermal ageing experiments are conducted by immersing the ABCSS into deionized water and 5 wt% NaCl water, followed by three-point bending tests after hygrothermal ageing. The proposed two-step finite element (FE) method is developed to simulate both moisture diffusion and three-point bending test. The presented FE method is validated through comparison with corresponding experimental results, then it is utilized to demonstrate that the proposed analytical model is accurate enough in initial failure modes and initial failure loads predictions. At last, the hygrothermal effects on degraded stress distribution and degraded failure performance are investigated through analytical method, and the degraded failure mechanics maps are constructed to further visually demonstrate failure mechanics with the aid of the analytical model.

Mixed Bayesian Network for reliability assessment of RC structures subjected to environmental actions

Under environmental action, reinforced concrete (RC) structures might suffer from reinforcement corrosion caused by the surrounding environment, dramatically reducing structural reliability and threatening social development. However, most of the existing reliability assessment methods for RC structures only focused on the structural performance at the design stage given the original unchanged environment, ignoring the effects of realistic exposure conditions and inspection results on reliability evaluation. Thus, this paper develops a general reliability assessment framework based on a Mixed Bayesian network (MBN), incorporating three modules, i.e., durability assessment, load-bearing capacity analysis, and time-dependent reliability analysis. In MBN, separate sub-BNs are built based on different modules and connected by pinch point variables where probabilistic information is transmitted via soft evidence. Besides, this framework considers time-dependent environmental parameters and two-dimensional chloride transport and their effects on reliability. Meanwhile, adjustment coefficients are applied to improve the results of the analytical mechanical model with respect to different limit states through the finite element model (FEM). The proposed MBN framework is illustrated for a corroded RC beam under a marine atmospheric environment to investigate the effects of environmental modeling, chloride transport patterns, and concrete crack inspection on reliability assessment. The results indicate that under the assumed conditions in the case study, early inspection of large cracks may significantly overestimate the failure probability by about 500%. Besides, failure probability might be underestimated by about 95%, ignoring the time-variant environment and two-dimensional chloride transport.

Full [formula omitted]-space analysis of molecular dynamics effect on electron momentum profile of outer-valence orbitals of oxetane

The molecular dynamics effect on electron momentum profiles (EMPs) of outer-valence orbitals of oxetane was investigated theoretically by using the thermal sampling molecular dynamics (TSMD) method to prepare the initial condition of molecules at a certain temperature. A full Q-space sampling is achieved including both harmonic and anharmonic vibrations, particularly the ring-puckering vibration. The sampled conditions were testified by comparing the simulated electron binding spectrum with the photoelectron spectrum. The plane wave impulse approximation (PWIA) is adopted to calculate the EMPs. The results of outer valence orbitals of oxetane are compared with experiments adopting the asymmetric noncoplanar kinematics and theoretical results by ring-puckering model and the harmonic analytical quantum mechanical (HAQM) model. For 3b1 orbital, where the vibrational excitation and anharmonicity of ring-puckering mode cannot be ignored, the present model gives an improved description. For the other orbitals, the present results are similar to the predictions by the HAQM model.

Radio Frequency Cavity’s Analytical Model and Control Design

Reduction or suppression of microphonic interference in radio frequency (RF) cavities, such as those used in Electron Linear Accelerators, is necessary to precisely control accelerating fields. In this paper, we investigate modeling the cavity as a cylindrical shell and present its free vibration analysis along with an appropriate control scheme to suppress vibrations. To this end, we first obtain an analytical mechanical dynamic model of a nine-cell cavity using a modified Fourier-Ritz method that provides a unified solution for cylindrical shell systems with general boundary conditions. The model is then verified using the ANSYS software in terms of a comparison of eigenfrequencies which prove to be identical to the proposed model. We also present an active observer-based vibration control scheme to suppress the dominant mechanical modes of the cavity. The control system performance is investigated using simulations.

Numerical Simulation and Deformation Behavior of a Ti/Steel Clad Plate during the Rolling Process

The deformation mechanism is complex in the hot rolling process of clad plates, and head bending is a common defect. In this paper, an analytical computational mechanical model of a metal plate was established by the classical elastic mechanics method, and the relationship between uneven thickness extension and warpage was obtained. The hot rolling bonding process of dissimilar bimetallic plates of Ti/Steel was investigated. On this basis, the mechanical origins of the plate bending defects and the influence of various factors on the evolution of the plate bending defects of the metal plates were revealed. The results indicated that the rolling forces increased with the increase in reduction ratio and thickness ratio. As the total reduction ratios of the clad plates increased, the reduction ratio of each layer increased. Furthermore, it was found that the thickness reduction ratios of steel were larger than those of Ti at a certain total reduction ratio, which could reach up to 59.6%. When the reduction ratios were 0.4 and 0.45, the bending degree increased with the thickness ratio of the upper and lower plates increasing gradually. The maximum warpage could reach 0.349 m. The clad plate shape was better when the roll speed ratio was 1.02 and the reduction rate was 0.4. The present numerical results provide a valuable insight into the deformation behaviors and mechanisms involved in the hot rolling of clad plates.

Thermal Network Modeling and Thermal Stress Evaluation for a High-Power Linear Ultrasonic Motor

This article presents a high-efficient thermal analysis methodology and outlines a set of useful design guidelines for high-power linear ultrasonic motors. A thermal network modeling technique is introduced to rapidly calculate the temperature rise for a typical high-power linear ultrasonic motor with a V-shaped stator. First, a six-terminal equivalent circuit for Langevin piezoelectric transducer considering the prestress bolt loss and all three losses in piezoelectrics is proposed to calculate the stator loss. Then, the calculated losses along with the friction loss are used as inputs into the developed thermal network model to calculate the temperature rise of critical parts of the motor. Furthermore, an analytical mechanical model combined with the proposed thermal network is established to calculate the temporal–spatial distribution of the stator thermal stress for evaluating its fatigue under the heating-up process. Finally, some experimental measurements and finite-element simulations are conducted to validate the theoretical analyses.

Data-driven analytical mechanics of aging viscoelastic shotcrete tunnel shells

Based on the principle of virtual power, equilibrium conditions are established for the forces within a cross section of a tunnel top heading driven according the New Austrian Tunneling Method (NATM). External forces, namely impost actions and ground pressure distributions following a third-order polynomial, are analytically linked with internal forces, such as axial forces and bending moments, arising as integrals over the shell thickness, of circumferential normal stresses. The latter are related, via an aging viscoelastic shotcrete material model, to circumferential normal strains, as well as to radial and circumferential displacement components. This allows for analytical transformation of displacement measurement data collected at the crown and the footings of the shell segment, into ground pressure and impost action evolutions, together with all the associated force and stress quantities. For the Sieberg tunnel, driven in Miocene clay marl, our data-driven analytical mechanics model evidences virtually uniform ground pressure distributions, leading to a first rapidly increasing, and then mildly decreasing utilization degree of the shotcrete shell.

Seismic performances assessment of heritage timber frame based on energy dissipation

Heritage timber structures in China have many connections of different forms in their construction which have a complex but significant contribution to the seismic resistance of the structure. An analytical mechanical model of a typical heritage timber frame with multiple nonlinear connections is developed in this paper for investigating its seismic performances in terms of energy transference within the structure. Analytical models of the mortise-tenon connections with gaps, free-standing column foot connections and Dougong-column head connections are introduced. Hybrid finite elements including these connections are then adopted for the dynamic analysis of this structure. The input seismic energy of a heritage timber frame is converted, in the loading process, to two types of recoverable and non-recoverable energies. The former consists of the kinetic energy, the elastic strain energy and the gravitational potential energy stored in the roof structure. The latter consists of the dissipated energy due to damping and that due to friction in the connections which correspond to 96.51% and 3.49% of the input energy in the timber frame studied.

Effect of speed ratio on shear angle and forces in elliptical vibration assisted machining

Elliptical vibration-assisted machining (EVAM) has been employed in manufacturing industries to improve the machining performance of metal alloys. The mechanics of EVAM is dependent on the critical process parameters, including the horizontal speed ratio (HSR) defined as the ratio between the original cutting speed and the horizontal vibration speed. This paper presents a new mechanics model of EVAM, which reveals that the primary reason for shear angle variation at different HSR values is the strain-hardening property of the workpiece material instead of the friction reversal phenomenon. The model quantitatively determines the effect of the HSR on the shear angle, friction reversal, and instantaneous cutting forces in EVAM. A 2-D vibration assistance stage driven is developed to perform EVAM experiments on aluminum alloy with evident strain-hardening property and Zirconium-based bulk metallic glass that is less sensitive to strain-hardening. The chip morphology is examined at various speed ratios and uncut chip thicknesses to validate the shear angle prediction from the mechanics model. In addition, the model predicts the time instance corresponding to the friction reversal, which is also dependent on the shear angle and HSR in EVAM. Finite element simulations are performed to validate the predicted instantaneous cutting forces and friction reversal from the analytical mechanics model.

Interfacial bonding properties of 3D printed permanent formwork with the post-casted concrete

The rapid construction of prefabricated components of reinforced concrete structures using 3D printing concrete as a permanent formwork is a promising way to organically combine 3D printing with traditional construction technology. The bonding property of the contact interface between the 3D-printed permanent formwork and internal post-cast concrete is crucial for the 3D-printed structure to maintain the overall mechanical performance. In this study, the roughness of 3D-printed formwork (10 mm, 15 mm, 20 mm) and the age difference between the formwork and post-cast concrete (1 d, 3 d, 7 d, and 14 d) were set as variables to investigate their influence on the interfacial tensile and shearing bonding properties. Additionally, computerised tomography (CT) scanning was used to visualise the meso-structure of the interfacial zones and the pore characteristics were quantified. The microstructure and hydration products of the bonding interface were detected, and the gradient structure of the interface transition zone of the 3D printing formwork was presented. A plastic limit analytical mechanical model of the interfacial shear strength was established. The results show that the tensile and shear properties of the bonding interface were the best when the layer height of the printing formwork was 20 mm, and it is recommended to cast internal concrete materials after 7 d of 3D printing formwork moulding.

Non-conventional tube shapes for lifetime extend of solar external receivers

In this work, several novel tube shapes of solar tubular receivers that differ from the classical circular shape are analysed aiming to reduce the stresses of the receiver tubes, without penalizing its thermal efficiency. The analysis is performed using analytical thermal and mechanical models of the literature adapted for their use with non-circular tube shapes, verifying the assumptions made with FEM simulations due to the lack of experimental data available.Among the geometries studied, the results show that oval cross-section tubes improve the thermal efficiency of the receiver at the expense of increasing the stresses considerably. Ovoidal tubes show worse thermal and mechanical behaviour when the frontal part becomes peakier. Semicircle tubes reduce the stress by 10.9%, while keeping constant or even slightly improving the thermal performance. The last ones, increase the lifetime of the receiver and reduces the receiver costs if the manufacturing of the new geometries does no overpass 3.5 times the present price of production of the circular tubes. Therefore, the use of asymmetric cross-section tubes with low rear-front surface ratios, and smooth front surfaces can be considered a good alternative for substituting traditional circular cross-section tubes in central receivers.

Orthogonal cutting mechanics of multi-directional carbon fiber reinforced polymer with interlaminar bonding effect

This paper determines the chip formation mechanism, fiber-matrix failure modes, and cutting forces in orthogonal cutting of multi-directional carbon fiber reinforced polymer (MD CFRP) with interlaminar bonding effect. The cutting experiments show that the varying chip formation angles with different fiber orientations in cutting unidirectional plies converge for MD CFRP. A new analytical mechanics model for cutting MD CFRP is developed to predict the chip formation angle and failure modes based on the minimum energy principle for all plies. The model with experimental validation reveals the different cutting mechanisms between UD and MD CFRPs.

A New Model to Calculate Stress Relaxation of Viscoelastic Material for Polyester-Wool-Spandex Yarn with Analytical Mechanics Approach

Many researchers have studied the mechanical properties of yarn in textile science because mechanical properties are the essential parameter in determining yarn quality. This research aims to make a new model and prediction of the material properties of textile yarns, especially for stress relaxation of viscoelastic textile yarn for polyester-wool-spandex yarn cases. In this research, a new approximation of the analytical mechanics model of stress relaxation using a system of four springs and a dashpot to determine viscoelastic yarn properties as polyester-wool-spandex has been studied. A yarn movement equation for viscoelastic yarn as polyester-wool-spandex having 36 yarn count number (in unit tex or g/km) has been formulated using analytical mechanics, and the model has been validated experimentally. The coefficient of determination R2 ranges from 0.82, which shows the closeness between the experimental results and the theoretical predictions. In this research, it is found that this model can be implemented to determine the viscoelastic material of yarn based on the properties of yarn as stress relaxation using the analytical mechanics approach.

A mechanical model for soil-rectangular tank interaction effects under seismic loading

In this paper, the dynamic behavior of concrete rectangular tanks subjected to motions caused by an earthquake considering the effects of soil-structure-fluid interaction is studied. An analytical mechanical model for a rectangular tank with flexible walls, taking into consideration the effects of rigid-base rocking motion and lateral translation, is developed. The model with a lumped-parameters idealization of foundation soil is used to evaluate the system's response to ground earthquake motions. Using this model, the soil-structure-fluid interaction effect can be taken into account in the seismic analysis of flexible rectangular tanks in a fast and practical manner. To verify the mechanical model, the numerical results of the fixed-base case are compared with the experimental results. The results show that dynamic soil-tank interaction under horizontal seismic excitations, depending on the type of soil, can cause a profound effect on the amplification of hydrodynamic forces and moments exerted on the tank structure.