Search Results (94)

Collar monopile foundation is a new type of offshore wind power foundation. This paper explores the horizontal bearing performance of collar monopile foundation in saturated cohesive soil through a combination of physical experiments and numerical simulations. After analyzing the deformation characteristics of the pile–soil system under horizontal load through static load tests, horizontal cyclic loading tests were conducted at different cycles to study the cumulative deformation law of the collar monopile. Based on a stiffness degradation model for soft clay, a USDFLD subroutine was developed in Fortran and embedded in ABAQUS. Coupled with the Mohr–Coulomb criterion, it was used to simulate the deformation behavior of the collar monopile under horizontal cyclic loading. The numerical model employed the same geometric dimensions and boundary conditions as the physical test, and the simulated cumulative pile–head displacement under 4000 load cycles showed good agreement with the experimental results, thereby verifying the rationality and reliability of the proposed simulation method. Through numerical simulation, the distribution characteristics of bending moment and the shear force of collar monopile foundation were studied, and the influence of pile shaft and collar on the horizontal bearing capacity of collar monopile foundation at different loading stages was analyzed. The results show that as the horizontal load increases, cracks gradually appear at the bottom of the collar and in the surrounding soil. The soil disturbance caused by the sliding and rotation of the collar will gradually increase, leading to plastic failure of the surrounding soil and reducing the bearing capacity. The excess pore water pressure in shallow soil increases rapidly in the early cycle and then gradually decreases with the formation of drainage channels. Deep soil may experience negative pore pressure, indicating the presence of a suction effect. This paper can provide theoretical support for the design optimization and performance evaluation of collar monopile foundations in offshore wind power engineering applications. Full article

This paper analyzed the behavior of polymer composite materials reinforced with randomly oriented short natural fibers (hemp, flax, etc.) subjected to external stresses under quasistatic contact conditions with dry Coulomb friction. We presumed the composite body, a 2D flat rectangular plate, being in frictional contact with a rigid foundation for the quasistatic case. The manuscript proposes the finite element method approximation in space and the finite difference approximation in time. The problem of quasistatic frictional contact is described with a special finite element, which can analyze the state of the nodes in the contact area, and their modification, between open, sliding, and fixed contact states, in the analyzed time interval. This finite element also models the Coulomb friction law and controls the penetrability according to a power law. Moreover, the quasi-static case analyzed allows for the description of the load history using an incremental and iterative algorithm. The discrete problem will be a static and nonlinear one for each time increment, and in the case of sliding contact, the stiffness matrix becomes non-symmetric. The regularization of the non-differentiable term comes from the modulus of the normal contact stress, with a convex function and with the gradient in the sub-unit modulus. The non-penetration condition was achieved with the penalty method, and the linearization was conducted with the Newton–Raphson method. Full article

This study investigates the in-plane shear behavior of solid brick masonry walls, both unreinforced and retrofitted using Reinforced Khorasan Jacketing (RHJ), a traditional pozzolanic mortar technique rooted in Iranian and Ottoman architecture. Six one-block-thick English bond masonry walls were tested in three configurations: unreinforced with Horasan plaster (Group I), reinforced with steel mesh aligned to wall edges (Group II), and reinforced with mesh aligned diagonally (Group III). All the walls were plastered with 3.5 cm of Horasan mortar and tested after 18 months using diagonal compression, with load-displacement data recorded. A detailed 3D micro-modeling approach was employed in finite element simulations, with bricks and mortar modeled separately. The Horasan mortar was represented using an elastoplastic Mohr-Coulomb model with a custom softening law (parabolic-to-exponential), calibrated via inverse parameter fitting using the Nelder-Mead algorithm. The numerical predictions closely matched the experimental data. Reinforcement improved the shear strength significantly: Group II showed a 1.8 times increase, and Group III up to 2.7 times. Ductility, measured as post-peak deformation capacity, increased by factors of two (parallel) and three (diagonal). These enhancements transformed the brittle failure mode into a more ductile, energy-absorbing behavior. RHJ is shown to be a compatible, effective retrofit solution for historic masonry structures. Full article

The Bohai Strait is a special tectonic region in North China, characterized by strong fault activity and frequent seismic events. In this study, we analyzed the stress state across the Bohai Strait in detail by integrating the stress data derived from the hydraulic fracturing measurements in four boreholes along the strait (i.e., Pingdu, Xiangli, Changdao, and Gaizhou from south to north) and evaluated its implications for seismicity. The results reveal that the gradient coefficients of the maximum (S_H) and minimum horizontal stresses (S_h) with depth in Xiangli and Changdao are over 1.59 and 1.87 times the corresponding stresses of the North China Block. However, the S_H and S_h in Pingdu and Gaizhou do not exceed 50.2% and 59.4% of those of the North China Block. The stress values increase as the distance approaches the interaction of the regional faults in the Bohai Strait. The S_H orientation in the Bohai Strait region is N68.67 ± 9.30° E, consistent with the prevailing NEE–E-W regional stress direction. According to the Coulomb friction failure criterion, the friction coefficients of the four boreholes range from 0.24 to 0.52, lower than the theoretically critical limit for inducing fault slip in the upper crust (i.e., Byerlee’s law). The faults in the strait region are considered to be contemporarily stable but need to be further evaluated, considering more influencing factors. This study provides a new, instructive understanding of the variations in the stress state in the Bohai Strait region. Full article

The multipole expansion on the basis of Spherical Harmonics is a multifaceted mathematical tool utilized in many disciplines of science and engineering. Regarding physics, in electromagnetism, the multipole expansion is exclusively focused on the scalar potential, $U\left(\mathit{r}\right)$, defined only in the so-called inside, $U_{in}\left(\mathit{r}\right)$, and outside, $U_{out}\left(\mathit{r}\right)$, spaces, separated by the middle space wherein the source resides, for both dielectric and magnetic materials. Intriguingly, though the middle space probably encloses more physics than the inside and outside spaces, it is never assessed in the literature, probably due to the rather complicated mathematics. Here, we investigate the middle space and introduce the multipole expansion of the scalar potential, $U_{mid}\left(\mathit{r}\right)$, in this, until now, unsurveyed area. This is achieved through the complementary superposition of the solutions of the inside, $U_{in}\left(\mathit{r}\right)$, and outside, $U_{out}\left(\mathit{r}\right)$, spaces when carefully adjusted at the interface of two appropriately defined subspaces of the middle space. Importantly, while the multipole expansion of $U_{in}\left(\mathit{r}\right)$ and $U_{out}\left(\mathit{r}\right)$ satisfies the Laplace equation, the expression of the middle space, $U_{mid}\left(\mathit{r}\right)$, introduced here satisfies the Poisson equation, as it should. Interestingly, this is mathematically proved by using the method of variation of parameters, which allows us to switch between the solution of the homogeneous Laplace equation to that of the nonhomogeneous Poisson one, thus completely bypassing the standard method in which the multipole expansion of ${|\mathit{r}-{\mathit{r}}^{\prime }|}^{-1}$ is used in the generalized law of Coulomb. Due to this characteristic, the notion of $U_{mid}\left(\mathit{r}\right)$ introduced here can be utilized on a general basis for the effective calculation of the scalar potential in spaces wherein sources reside. The proof of concept is documented for representative cases found in the literature. Though here we deal with the static and quasi-static limit of low frequencies, our concept can be easily developed to the fully dynamic case. At all instances, the exact mathematical modeling of $U_{mid}\left(\mathit{r}\right)$ introduced here can be very useful in applications of both homogeneous and nonhomogeneous, dielectric and magnetic materials. Full article

The self-foaming method offers a promising approach for producing AlCuFe metallic foams without the need for external foaming agents. Although it is well established that both alloy composition and heat treatment play a fundamental role in pore formation, the specific influence of annealing time on the resulting microstructure and physical properties remains insufficiently explored. In the present study, the effects of annealing time on the microstructure, phase evolution, and magnetic properties of self-foaming Al₅₈Cu₂₇Fe₁₅ alloys are investigated. Metallic foams were synthesized using the self-foaming method, heat-treating the samples at 850 °C for 6, 9, 15, and 24 h. X-ray diffraction (XRD), differential thermal analysis (DTA), and scanning electron microscopy (SEM) reveal that prolonged annealing increases porosity, reaching 64% and 61% after 15 and 24 h, respectively. The porosity formation mechanism was attributed to a peritectic reaction involving the liquid metastable τ phase and the solid λ and β phases. Magnetic measurements indicated complex behavior consistent with the Curie–Weiss law, influenced by phase composition and interactions between Coulomb forces, Hund’s rule exchange, and Fe 3d–Al s, p orbital hybridization. Full article

Modeling of friction stir welding (FSW) is challenging, as there are large gradients in both strain rate and temperature (typically between 450 and 500 °C in aluminum alloys) that must be accounted for in the constitutive law of the material being joined. Constitutive laws are most often calibrated using flow stresses from hot compression or hot torsion testing, where strain rates are much lower than those seen in the stir zone of the FSW process. As such, the current work employed a recently developed method to measure flow stresses at high strain rates and temperatures in AA 2219-T67, and these data were used in the development of a finite element (FE) simulation of FSW. Because heat generation during FSW is primarily a function of friction between the rapidly spinning tool and the plate, the choice of friction law and associated parameters were also studied with respect to FE model predictions. It was found that the Norton viscoplastic friction law provided the most accurate modeling results, for both the transient and steady-state phases of an FSW plunge experiment. It is likely that the superior performance of the Norton law was its ability to account for temperature and rate sensitivity of the plate material sheared by the tool, while the Tresca-limited Coulomb law favored contact pressure, with essentially no temperature or rate dependence of the local material properties. With optimized friction parameters and more accurate flow stresses for the weld zone, as measured by a high-pressure shear test, a 65% overall reduction in model error was achieved, compared to a model that employed a material law calibrated with hot compression or hot torsion test results. Model error was calculated as an equally weighted comparison of temperatures, torques, and forces with experimentally measured values. Full article

The Kusaihu and Xidatan faults in the western part of the East Kunlun active fault present a miter compound relationship. The Quaternary activity of these two faults is vigorous and closely associated with potent and large earthquakes. The Ms 8.1 earthquake occurred on the Kusai Lake fault on 14 November 2001. To understand the current stress state and seismic hazard in the Kunlun pass region following the Ms 8.1 Earthquake in 2001, the in situ stress measurement work of four boreholes at two measuring points in this area is conducted through the hydraulic fracturing method, and the in situ stress accumulation level in this area is analyzed using the Coulomb fracture criterion, Byerlee’s law, and the fault friction parameter μ_m. It is found that the in situ stress accumulation level in the study area is not high, and the possibility of fault slip is low. Full article

We discuss applications of the Dirichlet $\eta \left(s\right)$ function in physics. To this end, we provide an introductory description of one-dimensional (1D) ionic crystals, which are well-known in the condensed matter physics literature, to illustrate the central issue of the paper: A generalization of the Coulomb interaction between alternating charges in such crystalline structures. The physical meaning of the proposed form, characterized by complex (in the mathematical sense) ion–ion interactions, is argued to have emerged in many-body systems, which may include effects from vacuum energy fluctuations. We first consider modifications to the bare Coulomb interaction by adding an imaginary component to the exponent of the Coulomb law of the form $s=1+ib$, where b is a real number. We then extend the results to slower-decaying interactions, where the exponent becomes $s=a+ib$, presenting numerical results for values $1/2\le a\le 2$, which include the critical strip relevant to the Riemann hypothesis scenario. Full article

This review analyzes numerical techniques for frictional contact problems, highlighting their strengths and limitations in addressing inherent nonlinearities and computational demands. Finite element methods (FEM), while dominant due to versatility, often require computationally expensive iterative solutions. Alternative methods, like boundary element methods (BEM) and meshless methods, offer potential advantages but require further exploration for broader applicability. The choice of contact algorithm significantly impacts accuracy and efficiency; penalty methods, though computationally efficient, can lack accuracy at high friction coefficients; whereas, Lagrange multiplier methods, while more accurate, are computationally more demanding. The selection of an appropriate friction constitutive model is crucial; while the Coulomb friction law is common, more sophisticated models are necessary to represent real-world complexities, including surface roughness and temperature dependence. This review paper delves into the future research that prioritizes developing computationally efficient algorithms and parallel computing strategies. Advancements in constitutive modelling are vital for improved accuracy, along with enhanced contact detection algorithms for complex geometries and large deformations. Integrating experimental data and multiphysics capabilities will further enhance the reliability and applicability of these numerical techniques across various engineering applications. These advancements will ultimately improve the predictive power of simulations in diverse fields. Full article

Nanoscale resonant devices based on optical tweezers are widely used in the field of precision sensing. In the process of driving the nanoresonator based on the Coulomb force, the real-time, precise regulation of the charge carried by the charged resonator is essential for continuous manipulation. However, the accuracy of the existing charge measurement methods for levitated particles is low, and these methods cannot meet the needs of precision sensing. In this study, a novel net charge measurement protocol for levitated particles based on spatial speed statistics is proposed. High-precision mass measurement based on Maxwell’s rate distribution law is the basis for improving the accuracy of charge measurement, and accurate measurement of net charge can be achieved by periodic electric field driving. The error of net charge measurement is less than 7.3% when the pressure is above 0.1 mbar, while it can be less than 0.76% at 10 mbar. This proposed method features real-time, high-precision, non-destructive, and in situ measurement of the net charge of particles in the medium vacuum, which provides new solutions for practical problems in the fields of high-precision sensing and nano-metrology based on levitated photodynamics. Full article

Wrinkles are urgent problems to be solved in the process of hot diaphragm preforming. Inter-ply slipping resistance is one of the causes of wrinkles. In this paper, based on the vertical inter-ply slipping test system, the inter-ply slipping behaviors of carbon fiber-reinforced epoxy resin composite prepregs were characterized. The mechanism of wrinkles caused by inter-ply slipping resistance was analyzed. According to the different characteristics expressed by the fiber and resin during the slip process, the inter-ply slipping behaviors of the prepregs were divided into three stages. The effect of temperature on the inter-ply slipping stresses was shown. The temperature will affect the viscosity of the prepregs. When the viscosity of the prepregs is low, the inter-ply slipping resistance will decrease. Based on the Coulomb friction law and the hydrodynamic equation, the inter-ply slipping kinetic equation of the prepregs was established. The inter-ply slipping kinetic equation was introduced into the ABAQUS main program by the ‘vfriction’ subroutine. The introduction of inter-ply slipping dynamics improved the accuracy of predicting the shape and position of wrinkles. Full article

In this article, a simple and practical magnetic equivalent charge model is proposed to predict the torque of a slotted-type axial-flux magnetic coupler (SAMC) under conditions of radial misalignment, angle misalignment, and synthetic misalignment. The magnetic field generated by the permanent magnet (PM) disk and the induced magnetic field generated by the slotted conductor sheet (CS) are equivalent to the surface magnetic charge, respectively. Particularly, the induced magnetic field produced by eddy current considering skin depth in the conductor sheet is introduced into the magnetic equivalent charge model. Combined with Coulomb’s law of magnetic field, the formulas of torque and axial force are both derived. Using this method, the torques in three cases of misalignment are calculated. Finally, the effectiveness of the model is verified by the finite element method (FEM) and experiment; the results calculated by the magnetic equivalent charge model are basically consistent with those from the finite element method and experiment. The derived formula is suitable for small air gaps, small slip rates, and small radial deflection distances. Additionally, the limitations of the method proposed are discussed, which is of great help for understanding the torque transmission of the magnetic coupler in the misalignment state. Full article

This contribution shows a geometric optimal control procedure to solve the trajectory generation problem for the navigation (generic motion) of mechanical systems with revolute joints. The mechanical system is analyzed as a nonlinear Lagrangian system affected by dry friction at the joint level. Rayleigh’s dissipation function is used to model this dissipative effect of joint-level friction, and regarded as a potential. Rayleigh’s potential is an invariant scalar quantity from which friction forces derive and are represented by a smooth model that approaches the traditional Coulomb’s law in our proposal. For the optimal control procedure, an invariant cost function is formed with the motion equations and a Riemannian metric. The goal is to minimize the consumed energy per unit time of the system. Covariant control equations are obtained by applying Pontryagin’s principle, and time-integrated using a Finite Elements Method-based solver. The obtained solution is an optimal trajectory that is then applied to a mechanical system using a proportional–derivative plus feedforward controller to guarantee the trajectory tracking control problem. Simulations and experiments confirm that including joint-level friction forces at the modeling stage of the optimal control procedure increases performance, compared with scenarios where the friction is not taken into account, or when friction compensation is performed at the feedback level during motion control. Full article

The tribological phenomena concerning the lubrication regime change (LRC) during bulk metal forming are comprehensively studied. A multi-step cold forward extrusion process shows the evolution of LRC and reveals the shortcomings of the traditional Coulomb friction law. The previous works of the specific author’s research group on friction are reviewed, focusing on the LRC during bulk metal forming. Various LRC phenomena from various examples are revealed. It has been found that the drawing and forward extrusion processes are vulnerable to LRC because of significant sliding motion at the material–die interface, and that when the strain hardening of the material is slight, the influence of friction increases, and as a result, the influence of LRC increases excessively. The new findings also include the impact of LRC on the macroscopic phenomena of the process and the reason for the sharp increase in friction coefficient via LRC, which is validated by the work of Wilson. This paper aims to make engineers and researchers think much of the tribology with lubricant in bulk metal forming with a focus on the dependence of tribological phenomena on the state of the lubricants and the irrationality of traditional friction law, especially in the forging of materials with a low strain hardening capability. Full article