A hybrid contact approach for modeling soil-structure interaction using the material point method

The grid-based multi-velocity field technique has become increasingly popular for simulating the Material Point Method(MPM)in contact problems.However,this traditional technique has some shortcomings,such as(1)early contact and contact penetration can occur when the contact conditions are unsuitable,and(2)the method is not available for contact problems involving rigid-nonrigid materials,which can cause numerical instability.This study presents a new hybrid contact approach for the MPM to address these limitations to simulate the soil and structure interactions.The approach combines the advantages of point-point and point-segment contacts to implement contact detection,satisfying the impenetrability condition and smoothing the corner contact problem.The proposed approach is first validated through a disk test on an inclined slope.Then,several typical cases,such as granular collapse,bearing capacity,and deformation of a flexible retaining wall,are simulated to demonstrate the robustness of the proposed approach compared with FEM or analytical solutions.Finally,the proposed method is used to simulate the impact of sand flow on a deformable structure.The results show that the proposed contact approach can well describe the phenomenon of soil-structure interaction problems.

FFT-Based Numerical Method for Nonlinear Elastic

In theoretical research pertaining to sealing, a contact model must be used to obtain the leakage channel. However, for elastoplastic contact, current numerical methods require a long calculation time. Hyperelastic contact is typically simplifed to a linear elastic contact problem, which must be improved in terms of calculation accuracy. Based on the fast Fourier transform, a numerical method suitable for elastoplastic and hyperelastic frictionless contact that can be used for solving two-dimensional and three-dimensional (3D) contact problems is proposed herein. The nonlinear elastic contact problem is converted into a linear elastic contact problem considering residual deformation (or the equivalent residual deformation). Results from numerical simulations for elastic, elastoplastic, and hyperelastic contact between a hemisphere and a rigid plane are compared with those obtained using the fnite element method to verify the accuracy of the numerical method. Compared with the existing elastoplastic contact numerical methods, the proposed method achieves a higher calculation efciency while ensuring a certain calculation accuracy (i.e., the pressure error does not exceed 15%, whereas the calculation time does not exceed 10 min in a 64 × 64 grid). For hyperelastic contact, the proposed method reduces the dependence of the approximation result on the load, as in a linear elastic approximation. Finally, using the sealing application as an example, the contact and leakage rates between complicated 3D rough surfaces are calculated. Despite a certain error, the simplifed numerical method yields a better approximation result than the linear elastic contact approximation. Additionally, the result can be used as fast solutions in engineering applications.

A METHOD FOR THE ANALYSIS OF DYNAMIC RESPONSE OF STRUCTURE CONTAINING NON-SMOOTH CONTACTABLE INTERFACES

A novel single-step method is proposed for the analysis of dynamic response of visco-elastic structures containing non-smooth contactable interfaces. In the method, a two-level algorithm is employed for dealing with a nonlinear boundary condition caused by the dynamic contact of interfaces. At the first level, an explicit method is adopted to calculate nodal displacements of global viscoelastic system without considering the effect of dynamic contact of interfaces and at the second level, by introducing contact conditions of interfaces, a group of equations of lower order is derived to calculate dynamic contact normal and shear forces on the interfaces. The method is convenient and efficient for the analysis of problems of dynamic contact. The accuracy of the method is of the second order and the numerical stability condition is wider than that of other explicit methods.

Power equipment vibration visualization using intelligent sensing method based on event-sensing principle

Vibration measurements can be used to evaluate the operation status of power equipment and are widely applied in equipment quality inspection and fault identification.Event-sensing technology can sense the change in surface light intensity caused by object vibration and provide a visual description of vibration behavior.Based on the analysis of the principle underlying the transformation of vibration behavior into event flow data by an event sensor,this paper proposes an algorithm to reconstruct event flow data into a relationship correlating vibration displacement and time to extract the amplitude-frequency characteristics of the vibration signal.A vibration measurement test platform is constructed,and feasibility and effectiveness tests are performed for the vibration motor and other power equipment.The results show that event-sensing technology can effectively perceive the surface vibration behavior of power and provide a wide dynamic range.Furthermore,the vibration measurement and visualization algorithm for power equipment constructed using this technology offers high measurement accuracy and efficiency.The results of this study provide a new noncontact and visual method for locating vibrations and performing amplitude-frequency analysis on power equipment.

Existence and numerical approximation of a solution to frictional contact problem for electro-elastic materials

In this paper,a frictional contact problem between an electro-elastic body and an electrically conductive foundation is studied.The contact is modeled by normal compliance with finite penetration and a version of Coulomb’s law of dry friction in which the coefficient of friction depends on the slip.In addition,the effects of the electrical conductivity of the foundation are taken into account.This model leads to a coupled system of the quasi-variational inequality of the elliptic type for the displacement and the nonlinear variational equation for the electric potential.The existence of a weak solution is proved by using an abstract result for elliptic variational inequalities and a fixed point argument.Then,a finite element approximation of the problem is presented.Under some regularity conditions,an optimal order error estimate of the approximate solution is derived.Finally,a successive iteration technique is used to solve the problem numerically and a convergence result is established.

Contact Stress Reliability Analysis Model for Cylindrical Gear with Circular Arc Tooth Trace Based on an Improved Metamodel

Although there is currently no unified standard theoretical formula for calculating the contact stress of cylindrical gears with a circular arc tooth trace(referred to as CATT gear),a mathematical model for determining the contact stress of CATT gear is essential for studying how parameters affect its contact stress and building the contact stress limit state equation for contact stress reliability analysis.In this study,a mathematical relationship between design parameters and contact stress is formulated using the KrigingMetamodel.To enhance the model’s accuracy,we propose a new hybrid algorithm that merges the genetic algorithm with the Quantum Particle Swarm optimization algorithm,leveraging the strengths of each.Additionally,the“parental inheritance+self-learning”optimization model is used to fine-tune the KrigingMetamodel’s parameters.Following this,amathematicalmodel for calculating the contact stress of Variable Hyperbolic Circular-Arc-Tooth-Trace(VH-CATT)gears using the optimized Kriging model was developed.We then examined how different gear parameters affect the VH-CATT gears’contact stress.Our simulation results show:(1)Improvements in R2,RMSE,and RMAE.R2 rose from0.9852 to 0.9974(a 1.22%increase),nearing 1,suggesting the optimized Kriging Metamodel’s global error is minimized.Meanwhile,RMSE dropped from3.9210 to 1.6492,a decline of 57.94%.The global error of the GA-IQPSO-Kriging algorithm was also reduced,with RMAE decreasing by 58.69%from 0.1823 to 0.0753,showing the algorithm’s enhanced precision.In a comparison of ten experimental groups selected randomly,the GA-IQPSO-Kriging and FEM-based contact analysis methods were used to measure contact stress.Results revealed a maximum error of 12.11667 MPA,which represents 2.85%of the real value.(2)Several factors,including the pressure angle,tooth width,modulus,and tooth line radius,are inversely related to contact stress.The descending order of their impact on the contact stress is:tooth line radius>modulus>pressure angle>tooth width.(3)Complex interactions are noted among various parameters.Specifically,when the tooth line radius interacts with parameters such as pressure angle,tooth width,and modulus,the resulting stress contour is nonlinear,showcasing amultifaceted contour plane.However,when tooth width,modulus,and pressure angle interact,the stress contour is nearly linear,and the contour plane is simpler,indicating a weaker coupling among these factors.

Calculating method of contact stress for non-circular gears

According to Hertz theory, the difference of contact stress for non-circular gears and equivalent gears is compared in the paper, a calculating method of contact stress for non-circular gears by using equivalent gears is researched, and computing formulas of power and rotation speed for equivalent gears are deduced. A numerical simulation of contact stress for non-circular gears has also been conducted based on the finite element method. By the comparison of fitting curves, the feasibility of using equivalent gears instead of non-circular gears to calculate the contact stress is testified.

Non-Contact Method of Heart Rate Measurement Based on Facial Tracking

Image photoplethysmography can realize low-cost and easy-to-operate non-contact heart rate detection from the facial video, and effectively overcome the limitations of traditional contact method in daily vital sign monitoring. However, it is hard to obtain more accurate heart rate detection values under the conditions of subject’s facial movement, weak ambient light intensity and long detection distance, etc. In this article, a non-contact heart rate detection method based on face tracking is proposed, which can effectively improve the accuracy of non-contact heart rate detection method in practical application. The corner tracker algorithm is used to track the human face to reduce the motion artifact caused by the movement of the subject’s face and enhance the use value of the signal. And the maximum ratio combining algorithm is used to weight the pixel space pulse wave signal in the facial region of interest to improve the pulse wave extraction accuracy. We analyzed the facial images collected under different experimental distances and action states. This proposed method significantly reduces the error rate compared with the independent component analysis method. After theoretical analysis and experimental verification, this method effectively reduces the error rate under different experimental variables and has good consistency with the heart rate value collected by the medical physiological vest. This method will help to improve the accuracy of non-contact heart rate detection in complex environments.

Numerical Exploration of Asymmetrical Impact Dynamics: Unveiling Nonlinearities in Collision Problems and Resilience of Reinforced Concrete Structures

This study provides a comprehensive analysis of collision and impact problems’ numerical solutions, focusing ongeometric, contact, and material nonlinearities, all essential in solving large deformation problems during a collision.The initial discussion revolves around the stress and strain of large deformation during a collision, followedby explanations of the fundamental finite element solution method for addressing such issues. The hourglassmode’s control methods, such as single-point reduced integration and contact-collision algorithms are detailedand implemented within the finite element framework. The paper further investigates the dynamic responseand failure modes of Reinforced Concrete (RC) members under asymmetrical impact using a 3D discrete modelin ABAQUS that treats steel bars and concrete connections as bond slips. The model’s validity was confirmedthrough comparisons with the node-sharing algorithm and system energy relations. Experimental parameterswere varied, including the rigid hammer’s mass and initial velocity, concrete strength, and longitudinal and stirrupreinforcement ratios. Findings indicated that increased hammer mass and velocity escalated RC member damage,while increased reinforcement ratios improved impact resistance. Contrarily, increased concrete strength did notsignificantly reduce lateral displacement when considering strain rate effects. The study also explores materialnonlinearity, examining different materials’ responses to collision-induced forces and stresses, demonstratedthrough an elastic rod impact case study. The paper proposes a damage criterion based on the residual axialload-bearing capacity for assessing damage under the asymmetrical impact, showing a correlation betweendamage degree hammer mass and initial velocity. The results, validated through comparison with theoreticaland analytical solutions, verify the ABAQUS program’s accuracy and reliability in analyzing impact problems,offering valuable insights into collision and impact problems’ nonlinearities and practical strategies for enhancingRC structures’ resilience under dynamic stress.

Non-Contact System for Global Reporting Format (GRF) Automation: Contaminant Body Detection and Depth Estimation in the Case of Rainy Weather

The paper designed a non-contact system in order to perform the application (on a runway) of the Global Reporting Format (GRF) developed by International Civil Aviation Organization (ICAO). The system involves devices that film the surface (a runway in our case) from the air and displays the contaminant (water) body and measures the depth of the water automatically during the inspection. While measuring, data are sent to a computer used as a receiver. The developed devices are automatic devices implemented specially to use during rainy weather or even for some other cases. The aerial system uses a raspberry pi 4 model B, a camera, a laser sensor, an ultrasonic module, a Virtual Network Computing (VNC) and python codes developed by the authors. Results obtained show that using these devices to retrieve the Runway Condition Report (RCR) is very fast and human presence on the runway is not needed. The results obtained using these devices show that the method used herein is a proper solution to the GRF issues in the rainy areas, where the contaminant body detection and the accurate depth measurement were not well estimated because of the lack of a suitable method.

Non-Contact Electromagnetic Exciter Design with Linear Control Method

A non-contact type force actuator is necessary for studying the dynamic performance of a high-speed spindle system owing to its high-speed operating conditions. A non-contact electromagnetic exciter is designed for identifying the dynamic coefficients of journal bearings in high-speed grinding spindles. A linear force control method is developed based on PID controller. The influence of amplitude and frequency of current, misalignment and rotational speed on magnetic field and excitation force is investigated based on two-dimensional finite element analysis. The electromagnetic excitation force is measured with the auxiliary coils and calibrated by load cells. The design is validated by the experimental results. Theoretical and experimental investigations show that the proposed design can accurately generate linear excitation force with sufficiently large amplitude and higher signal to noise ratio. Moreover, the fluctuations in force amplitude are reduced to a greater extent with the designed linear control method even when the air gap changes due to the rotor vibration at high-speed conditions. Besides, it is possible to apply various types of excitations： constant, synchronous, and non-synchronous excitation forces based on the proposed linear control method. This exciter can be used as linear-force exciting and controlling system for dynamic performance study of different high-speed rotor-bearing systems.

Almost Sure Convergence of Proximal Stochastic Accelerated Gradient Methods

Proximal gradient descent and its accelerated version are resultful methods for solving the sum of smooth and non-smooth problems. When the smooth function can be represented as a sum of multiple functions, the stochastic proximal gradient method performs well. However, research on its accelerated version remains unclear. This paper proposes a proximal stochastic accelerated gradient (PSAG) method to address problems involving a combination of smooth and non-smooth components, where the smooth part corresponds to the average of multiple block sums. Simultaneously, most of convergence analyses hold in expectation. To this end, under some mind conditions, we present an almost sure convergence of unbiased gradient estimation in the non-smooth setting. Moreover, we establish that the minimum of the squared gradient mapping norm arbitrarily converges to zero with probability one.

Partition method for impact dynamics of flexible multibody systems based on contact constraint

The impact dynamics of a flexible multibody system is investigated. By using a partition method, the system is divided into two parts, the local impact region and the region away from the impact. The two parts are connected by specific boundary conditions, and the system after partition is equivalent to the original system. According to the rigid-flexible coupling dynamic theory of multibody system, system＇s rigid-flexible coupling dynamic equations without impact are derived. A local impulse method for establishing the initial impact conditions is proposed. It satisfies the compatibility con- ditions for contact constraints and the actual physical situation of the impact process of flexible bodies. Based on the contact constraint method, system＇s impact dynamic equa- tions are derived in a differential-algebraic form. The contact/separation criterion and the algorithm are given. An impact dynamic simulation is given. The results show that system＇s dynamic behaviors including the energy, the deformations, the displacements, and the impact force during the impact process change dramatically. The impact makes great effects on the global dynamics of the system during and after impact.

BOUNDARY ELEMENT METHOD FOR MOVING AND ROLLING CONTACT OF 2D ELASTIC BODIES WITH DEFECTS

A scheme of boundary element method for moving contact of two-dimensional elastic bodies using conforming discretization is presented. Both the displacement and the traction boundary conditions are satisfied on the contacting region in the sense of discretization. An algorithm to deal with the moving of the contact boundary on a larger possible contact region is presented. The algorithm is generalized to rolling contact problem as well. Some numerical examples of moving and rolling contact of 2D elastic bodies with or without friction, including the bodies with a hole-type defect, are given to show the effectiveness and the accuracy of the presented schemes.

Investigation on charge parameters of underwater contact explosion based on axisymmetric SPH method

This paper investigates the effects of charge parameters of the underwater contact explosion based on the axisymmetric smoothed particle hydrodynamics （SPH） method. The dynamic boundary particle is proposed to improve the pressure fluctuation and numerical accuracy near the symmetric axis. An in-depth study is carried out over the influence of charge shapes and detonation modes on the near-field loads in terms of the peak pressure and impulse of shock waves. For different charge shapes, the cylindrical charge with different length-diameter ratios may cause strong directivity of peak pressure and impulse in the near field. Compared with spherical charge, the peak pressure of cylindrical charge may be either weakened or enhanced in different directions. Within a certain range, the greater the length-diameter ratio is, the more obvious the effect will be. The weakened ratio near the detonation end may reach 25% approximately, while the enhanced ratio may reach around 20% in the opposite direction. However, the impulse in different directions seems to be uniform. For different detonation modes, compared with point-source explosion, the peak pressure of plane-source explosion is enhanced by about 5%. Besides, the impulse of plane-source explosion is enhanced by around 5% near the detonation end, but close to those of the point-source explosion in other directions. Based on the material constitutive relation in the axisymmetric coordinates, a simple case of underwater contact explosion is simulated to verify the above conclusions, showing that the charge parameters of underwater contact explosion should not be ignored.

Numerical modeling of large deformation and nonlinear frictional contact of excavation boundary of deep soft rock tunnel

Roadways excavated in soft rocks at great depth are difficult to be maintained due to large deformation of surrounding rocks, which greatly influences the safety and efficiency of deep resources exploitation. During the excavation process of a deep soft rock tunnel, the rock wall may be compacted due to large deformation. In this paper, the technique to address this problem by a two-dimensional (2D) finite element software, large deformation engineering analyses software (LDEAS 1.0), is provided. By using the Lagrange multiplier method, the kinematic constraint of non-penetrating condition and static constraint of Coulomb friction are introduced to the governing equations in the form of incremental displacement. The numerical example demonstrates the efficiency of this technology. Deformations of a transportation tunnel in inclined soft rock strata at the depth of 1 000 m in Qishan coal mine and a tunnel excavated to three different depths are analyzed by two models, i.e. the additive decomposition model and polar decomposition model. It can be found that the deformation of the transportation tunnel is asymmetrical due to the inclination of rock strata. For extremely soft rock, large deformation can converge only for the additive decomposition model. The deformation of surrounding rocks increases with the increase in the tunnel depth for both models. At the same depth, the deformation calculated by the additive decomposition model is smaller than that by the polar decomposition model.

A measurement method for distinguishing the real contact area of rough surfaces of transparent solids using improved Otsu technique

An experimental method of measuring the real contact area of transparent blocks based on the principle of total internal reflection is presented, intending to support the investigation of friction characteristics, heat conduction, and energy dissipation at the contact interface. A laser sheet illuminates the contact interface, and the transmitted laser sheet is projected onto a screen. Then the contact information is acquired from the screen by a camera. An improved Otsu method is proposed to process the data of experimental images. It can compute the threshold of the overall image and filter out all the pixels one by one. Through analyzing the experimental results, we describe the relationship between the real contact area and the positive pressure during a continuous loading process, at different loading rates, with the polymethyl methacrylate（PMMA）material. A hysteresis phenomenon in the relationship between the real contact area and the positive pressure is found and explained.

An experimental method for quantitative analysis of real contact area based on the total reflection optical principle

The simulation of real contact area between materials is foundationally important for the contact mechanics of mechanical structures. The Greenwood and Williamson(GW) model and the Majumdar(MB) model are the basic models in this field, which are widely accepted and proven to be valid in many experiments and engineering. Although the contact models have evolved considerably in recent years, the verifications of the models are most based on the indirect methods such as electrical conductivity and contact stiffness, because of the lack of effective methods to directly measure the variation of contact surface. In this paper, the total reflection(TR) method is introduced into the verification of contact models.An experiment system based on TR method is constructed to measure the real contact area of two PMMA specimens. The comparison analysis between the results of experiment and models suggests that the experiment result has the same trend with simulation, the MB model has better agreement with the experimental result because this method can take into account the variation of radius and the merging of asperities, while the GW model has a huge deviation because of the dependence on resolution and the lack of considering the variation of radius and asperity's merging process. Taking the interaction of asperities into account could give a better result that is closer to the experiment. Our results and analysis prove that the experimental methods in this paper could be used as a more direct and valid method to quantitatively measure the real contact area and to verify the contact models.