Calculation Of Forces Research Articles

Enhancing wet surface adhesion in walking robots: finite element-based analysis and morphology-changeable soft pads

In recent studies concerning walking robots, there has been a notable emphasis on investigating tribological phenomena and elucidating the role of capillary forces in tangential resistance. However, majority of these investigations have been restricted to specific geometric shapes, primarily spherical domes. In this research, we propose a novel approach based on the finite element method to address broader challenge of wet adhesion applicable to objects of various shapes. Additionally, we investigate the role of distributed domes on a soft foot in quantifying the tangential capillary force, which plays a crucial role in enhancing the performance of walking robots on wet surfaces. Through the optimization application, we identify that our designed foot (measuring 20 mm × 14 mm, comprising 78 domes with a radius of 0.5 mm and a distance of 1.5 mm between the two nearest domes) maximizes the value of the tangential capillary force. Moreover, we develop a finite element method using the Simulation Open Framework Architecture (SOFA) to model the interaction between wet liquid on a solid object's curved surface, enabling the calculation of wet adhesion force and capillary forces. Finally, to demonstrate the effectiveness of our proposed morphology-changeable soft pads foot, we conduct a presented a demonstration of a hexapod robot walking on different dry/wet condition of the surface. The obtained results are expected to pave a way to morphological design of soft pads for facilitating locomotion in various conditions. Supplementary video URL: https://youtu.be/yVteC95eqbo

Stress Analysis of Semi-covered Excavation Foundation Pit in Metro Stations based on Incremental Method

The station foundation pit of Ningbo Metro Line 2 is taken as engineering background, the support structure form of the semi covered excavation foundation pit is introduced. The standard section of the foundation pit is considered as a plane strain problem, a force calculation and analysis model for the half cover system structure is established based on the incremental method, concentrated load of a waste truck is applied within 5.0 m cover plate range outside the middle column and an impact coefficient of 0.4 is considered, overload with value of 20kPa is applied to the rest parts of the cover plate and 5.0 m outside the diaphragm wall. The excavation of the foundation pit is divided into 5 stages, the surface overload, structural self weight, soil pressure and elastic resistance increment, and support axial force are applied respectively, and the bending moment increment of the connecting wall and cover plate system at each excavation stage are calculated. The bearing capacities of the diaphragm wall and cover plate reinforcement are respectively calculated based on the rectangular bending normal section components, and they both meet the strength requirements.

Assessment of purlins with paired torsion bracing in sloped roof systems: Direct strength method approach

A Direct Strength Method based methodology has been developed by the authors for the prediction of local buckling and distortional buckling strength of purlins with paired torsion bracing. In a previous study, the methodology was presented and discussed for zero slope roof systems in by the authors. In this paper, the authors reformulated the developed methodology to include the effect of slope in the structural behavior of the roof systems. Equations have been developed for the strength prediction of sloped roof systems for simple span and multi-span interior conditions (fixed support conditions at both ends). As downslope forces are introduced to the sloped roof systems, the lateral displacement of the diaphragm is affected, and the stress distributions are impacted along the purlin cross sections. Typically, with the increase in the roof slope, the lateral diaphragm deflection decreases during which the stress distributions approach the constrained bending distribution increasing the strength. When the roof slope is increased further and the lateral deflection of the purlins moves downslope, there is a considerable decrease in the predicted strength. Therefore, for steep roof slopes, a considerable inelastic reserve capacity is observed which when accounted for will improve the predicted strength. The component stiffness method is utilized in the process, considering displacement compatibility for the calculation of the anchorage forces within the purlin system. Partial restraint of the diaphragm that is provided by the sheathing is considered in the procedure. The developed methodology herein this paper incorporates the effects of first-order and approximate second-order torsion for the prediction of the actual stress distributions along purlin cross sections. This stress distribution may significantly differ from the conventionally assumed constrained bending distributions which may result in substantial differences in the predicted local buckling and distortional buckling strengths for purlin systems.

Fast Force Estimation of Cable Structures Using Smartphone-Captured Video and Template Matching Algorithm

Cables are important components of long-span bridge structures, whose operation is significantly affected by cable force changes. Nowadays, cable force testing is performed by physical methods; that is, sensors are installed on the cable structure to monitor its force changes. Obviously, this strategy requires an extensive amount of time to achieve cable force calculation, which makes it impossible to monitor the force of the cable structure in real time. Meanwhile, smartphones have attracted extensive attention in the field of structural health monitoring (SHM) because of their higher cost-effectiveness than accelerometers, which include price and lifespan. Besides, many people own a smartphone, which leads to the possibility of a wider range of applications. Therefore, this paper presents a framework for the rapid estimation of the cable force of long-span bridges based on smartphones-captured video and a template matching algorithm. First, the empirical mode decomposition (EMD) method with wavelet decomposition (WD) method, that is, the EMDWD model, is constructed to extract the vibration signal of the bridge cable by eliminating the effects of smartphone vibration and environmental noise on the measured dynamic displacement, thus effectively improving the accuracy of data processing. In addition, the vibration identification model of bridge cable based on a template matching algorithm is established, and the deformation curve of cable is obtained. Finally, the frequency of bridge suspender is calculated by the Fourier transform method (FFT), and the cable force is estimated based on the smartphone-captured video.

A MPM Lagrangian‐Eulerian hydrocode for simulating buried explosions in transversely isotropic geomaterials

AbstractShock waves in geological materials are characterized by a sudden release of rapidly expanding gas, liquid, and solid particles. These shock waves may occur due to explosive volcanic eruptions or be artificially triggered. In fact, underground explosions have often been used as an engineering solution for large‐scale excavation, stimulating oil and gas recovery, creating cavities for underground waste storage, and even extinguishing gas field fires. As such, hydrocodes capable of simulating the rapid and significant deformation under extreme conditions can be a valuable tool for ensuring the safety of the explosions. Nevertheless, as most of the hydrocodes are often formulated in an Eulerian grid, this setting makes it non‐trivial to track the deformation configuration of the materials without a level set. The objective of this paper is to propose the use of the material point method equipped with appropriate equation of state (EOS) models as a hydrocode suitable to simulate underground explosions of transverse isotropic geomaterials. To capture the anisotropic effect of the common layered soil deposits, we introduce a new MPM hydrocode where an anisotropic version of the Mie‐Gruneisen EOS is coupled with a frictional Drucker‐Prager plasticity model to replicate the high‐strain‐rate constitutive responses of soil. By leveraging the Lagrangian nature of material points to capture the historical dependence and the Eulerian calculation of internal force, the resultant model is capable of simulating the rapid evolution of geometry of the soil as well as the high‐strain‐rate soil mechanics of anisotropic materials.

Configurational force method enables fracture assessment in soft materials

Configurational mechanics offers a framework for quantifying the tendency of defects to alter the material configuration. When applied to fracture mechanics, configurational forces can be used to quantify the propensity of cracks to propagate. An alternative, well-established approach involves analytical solutions for crack tip displacement fields. However, these solutions typically apply to a limited range of constitutive behaviors and oftentimes to the linear small strain regime. The ease of calculating configurational forces in a numerical Finite Element implementation, along with their applicability to soft fracture at large strains, motivates the study of their performance as a standalone fracture framework. In contrast to the majority of works that remain theoretical and numerical, our study includes a robust experimental approach to configurational forces at finite strains. We report tensile experiments on a soft elastomer with pre-cuts ante fracture initiation. In a first attempt to approach the J-integral via configurational forces, we explore the performance of the linear elastic fracture mechanics solutions on Pacman-shaped domains that reproduce the crack tip vicinity. Then, we implement the entire boundary value problem with three-dimensional simulations that replicate the empirical tensile deformation of the soft elastomer samples. Subsequently, the results are benchmarked against estimations of the J-integral obtained through a bespoke finite strain analytical crack tip solution. With the successful validation of the configurational force method at finite strains, we aim to establish a pipeline for the calculation of configurational forces in a standalone manner and circumventing the need for close-form analytical solutions.

Evaluation of the use of polylactic acid in 3d printing for the construction of an unmanned aerial vehicle in the department of cordoba

The use of polylactic acid (PLA) in the technology of fused deposition modeling (FDM), better known as 3D printing, to create all kinds of parts, from prototypes and simple pieces to highly technical end products, is a significant contender due to its wide range of properties compared to other petrochemical-based composite materials. The aim of this study was to evaluate the use of polylactic acid (PLA) for the construction of unmanned aerial vehicles (UAVs) through 3D printing. Power and force calculations for the UAV were performed, and a structural analysis using SolidWorks software was conducted to calculate maximum and minimum stresses and determine optimal manufacturing parameters. Additionally, an aerodynamic analysis using ANSYS software was carried out to determine the drag coefficient and the forces acting on the UAV. It was found that the force exerted by the motors on the arms is 13,63 N, and the power is 536 N. In the structural analysis, it was determined that the minimum stresses are located in the chassis arms, while the maximum stresses are found where the chassis is attached, with a value of 6,604 MPa and a safety factor of 3,23. In the aerodynamic analysis, a drag force of 1 N and a flight power of 108,44 N were calculated. The UAV achieved a flight height of 48 m and a flight autonomy of 17 minutes, concluding that 3D printing technology is a viable and cost-effective alternative.

Affinity-based engineering of carbon nanotube embedded polyamide membranes for simultaneous desalination and boron removal

Reverse osmosis (RO) is the leading technology for obtaining drinking and irrigation water from seawater. Although currently developed RO membranes achieve high salt rejection; several challenges exist, such as permselectivity trade-off, biological/chemical contamination, and insufficient retention of small and neutral molecules like boric acid. Due to its toxicity to living organisms and strictly monitored levels in potable water, removal of boron has gained considerable attention in RO industry. Thin film nanocomposite (TFN) membranes have emerged by incorporating nanomaterials with superior water/salt selectivity into polyamide (PA) layer of composite membranes. For the first time, our group investigated the potential of carboxylated carbon nanotube (CNT) embedding in the selective layer of TFN membranes for boron removal. Within this frame, we hypothesize that embedding fillers with low boron affinity accompanied by high water permeability in the selective layer of TFN membranes improves boron removal without suffering from the permselectivity trade-off. In this study, we investigated the boron removal performance of functionalized CNT (f-CNT) embedded TFN membranes. Initially, CNTs were functionalized with three different functional groups (namely, biotin (BIO), 8-amino caprylic acid (ACA), and zwitterion (ZWT)) to narrow down the tube entrance, provide repulsive electrostatic interactions with boron, and interfere with the hydrogen bonding between water and boric acid molecules. Then, TFN membranes incorporating f-CNTs were fabricated, characterized, and tested. Showing high compatibility with PA, ZWT functionalization has increased water/boron selectivity of TFN membranes by 66% and water permeability by 44%, while maintaining the salt rejection at 98%. Furthermore, we employed molecular dynamics simulations and potential of mean force calculations to elucidate the boron exclusion mechanism in f-CNTs. With its flexible structure and “gate-keeper” ability, ZWT functional group was found to show the highest energy barrier against boron transport. Hence, engineering CNT/PA TFN membranes to promote steric hindrance and decrease solute affinity is promising for efficient removal of detrimental small molecules from seawater.

Unraveling the molecular dynamics of sugammadex-rocuronium complexation: A blueprint for cyclodextrin drug design

Sugammadex, marketed as Bridion™, is an approved cyclodextrin (CD) based drug for the reversal of neuromuscular blockade in adults undergoing surgery. Sugammadex forms an inclusion complex with the neuromuscular blocking agent (NMBA) rocuronium, allowing rapid reversal of muscle paralysis. In silico methods have been developed for studying CD inclusion complexes, aimed at accurately predicting their structural, energetic, dynamic, and kinetic properties, as well as binding constants. Here, a computational study aimed at characterizing the sugammadex-rocuronium system from the perspective of docking calculations, free molecular dynamics (MD) simulations, and biased metadynamics simulations with potential of mean force (PMF) calculations is presented. The aim is to provide detailed information about this system, as well as to use it as a model system for validation of the methods. This method predicts results in line with experimental evidence for both the optimal structure and the quantitative value for the binding constant. Interestingly, there is a less profound preference for the orientation than might be assumed based on electrostatic interactions, suggesting that both orientations may exist in solution. These results show that this technology can efficiently analyze CD inclusion complexes and could be used to facilitate the development and optimization of novel applications for CDs.

Adaptive MPC-Based Lateral Path-Tracking Control for Automatic Vehicles

Adaptive MPC-Based Lateral Path-Tracking Control for Automatic Vehicles

Calculation of solvation force in molecular dynamics simulation by deep-learning method

Electrostatic calculations are generally used in studying the thermodynamics and kinetics of biomolecules in solvent. Generally, this is performed by solving the Poisson-Boltzmann equation on a large grid system, a process known to be time-consuming. In this study, we developed a deep neural network to predict the decomposed solvation free energies and forces of all atoms in a molecule. To train the network, the internal coordinates of the molecule were used as the input data, and the solvation free energies along with transformed atomic forces from the Poisson-Boltzmann equation were used as labels. Both the training and prediction tasks were accelerated on GPU. Formal tests demonstrated that our method can provide reasonable predictions for small molecules when the network is well-trained with its simulation data. This method is suitable for processing lots of snapshots of molecules in a long trajectory. Moreover, we applied this method in the molecular dynamics simulation with enhanced sampling. The calculated free energy landscape closely resembled that obtained from explicit solvent simulations.

АНАЛІТИЧНА МОДЕЛЬ І РОЗРАХУНКИ АЕРОДИНАМІЧНОГО ЗАХОВЛЮВАЧА ДЕТАЛЕЙ КРОЮ З ТЕКСТИЛЮ ЗІ СТОСУ МАНІПУЛЯТОРІВ ЗАВАНТАЖЕННЯ ШВЕЙНИХ МАШИН

The paper presents the results of the development and construction of a mathematical model for the design of an aerodynamic grabber of cut textile parts from a pile of loading manipulators of general-purpose sewing machines to create purpose-built robotic technological complexes based on them. Automatic one-by-one loading of cut parts from textile materials from a stack of sewing machines is one of the main stages of automation of the equipment and work process when using modern general-purpose computerized sewing machines. A numerical calculation of the stationary suction force F_st was performed during the piece-by-piece separation of cut textile parts from the stack by an aerodynamic gripper. It was established that the obtained results of the calculation of the stationary suction force of the gripper of the sewing manipulator can be used for other fairly close values of the geometric parameters of the aerodynamic plate. This allows us to assume that the equations used to calculate F_st reliably describe the studied work process under the accepted limitations and idealization of the work environment for piece-by-piece separation of cut textile parts from the foot. A mathematical model of an aerodynamic grabber of cut textile parts from a stack for automated loading of sewing machines has been developed. A method of calculating the stationary suction force of the aerodynamic grabber of the sewing manipulator based on the results of calculations based on the use of a mathematical model has been developed, which allows us to assume that the equations used to calculate F_st reliably describe the studied work process under the accepted limitations and idealization of the working environment for piece-by-piece separation of textile cut parts from the foot

Ensuring Safe Working Conditions under the Influence of Vibroacoustic Factors on Train Crew Workers

Introduction. The increased intensity of noise and vibration of railway traffic may become not only an urgent problem in the field of occupational safety, but also a serious environmental problem in the near future due to the constant need to increase the weight of freight trains, the speed of passenger trains and the capacity of railway lines. Recently, a lot has been done to minimize the negative effects of noise and vibration in railway transport. However, the problem of exceeding the indicators of vibration noise factors remains relevant. Reducing the harmful effects helps to improve the working conditions of train crew employees and improve the comfortable conditions of transport passengers. As a rule, the main focus of the analysis is on the external impact of vibroacoustic factors on residential areas and less attention is paid to the impact on rolling stock. However, these studies do not provide a complete picture of how noise and vibration actually affect the train in motion. The aim of the study was to obtain the result of an analysis of the impact of vibroacoustic factors on train crew workers and to propose a method of comprehensive protection based on the use of vibration damping materials.Materials and Methods. In the course of the work, regulatory documents were studied, a comprehensive analysis of relevant information on this topic was carried out, and methods for calculating vibration and vibration acceleration were used. The values of the sound pressure levels were obtained using a SPM-101 sound level meter. The object of the study was a carriage of the "reserved seat" type in the process of movement. As part of the research plan, sound pressure was measured at selected sites and a class of working conditions was determined.Results. The result of the analysis of the impact of vibroacoustic factors on train crew workers indicated the need to strengthen comprehensive measures to protect them. The obtained calculation of the vibration force became the basis of the method proposed by the authors to minimize the harmful effects of vibroacoustic factors, which was based on the use of vibration and sound insulation materials suitable for the necessary acoustic parameters in the construction of the car. In particular, it was proposed to cover the floor of the car with dense rubber and the ceiling of the car with an inorganic fiber material for sound insulation. The work also provides an economic assessment of the effectiveness of measures to minimize harmful vibration noise effects.Discussion and Conclusion. The proposed methods for minimizing noise and vibration impacts can help reduce the level of sound pressure and vibration indicators to standard values, which will significantly reduce the negative impact of vibroacoustic factors on train crew workers and railway passengers. The considered complex for minimizing vibration and noise includes a set of methods in which affordable materials based on recycled substances have found application.

Comparison of the Casimir force between SiC plates with different permittivity models: Lorentz model and Palik data

Accurate calculation of Casimir forces is essential for the development of micro- and nanoelectromechanical systems. Silicon carbide (SiC) is an excellent material for fabricating microsensors due to its high durability, high stiffness, and low thermal expansion. The permittivity of the SiC could be characterized by the Lorentz model or the Palik data. However, the influence of the two models of calculating permittivity on the Casimir force has not been discussed. In this work, we calculate the Casimir force between SiC plates by the Lorentz model and the Palik data, respectively. The Casimir force calculated by the Lorentz model could be 4 times greater than the Palik data for SiC at a gap distance of 10 nm. The difference of the permittivity in the ultraviolet lead to different Casimir forces. This work demonstrates the difference between the two models of permittivity for calculating the SiC-based Casimir force, and provides a reliable base for more accurate Casimir force calculations.

The adsorption mechanism of 5-fluorouracil on MnO2-based nanostructures by DFT calculation and experimental analysis

It is of great significance to explore the mechanism of drug molecules hiking on nanomaterials for targeted delivery. In this study, we evaluated the interaction potential of three manganese dioxide (MnO2) nanostructures with 5-fluorouracil (5-FU) using a density function theory (DFT) framework and dispersion correction (D3BJ) and conducted experimental verification. All possible adsorption modes and locations were predicted by electrostatic surface potential (ESP) and van der Waals force calculations. The charge transfer between molecular groups was estimated by electron density difference (EDD). The energy-favorable model of 5-FU interaction with distinct MnO2 crystals was investigated by using partial density of states (PDOS). Further, the quantum theory of atoms in molecules (QTAIM) calculation and independent gradient model based on Hirshfeld partition (IGMH) analysis were applied to reveal the interaction details. Our results suggest that 5-FU can be absorbed at different positions on the surface of MnO2, in which the O-adsorption mode is mainly dominated by hydrogen bond, while the Mn-adsorption mode is dominated by coordination interaction. Besides, the dispersion-dominated interaction cannot be ignored. DFT calculations show that MnO2 nanostructures are promising drug carriers, and β-MnO2 exhibits better adsorption behavior than the other two crystals. Experimental study showed that the 5-FU drug loading of β-MnO2 (28.82 %) was higher than that of α-MnO2 (16.72 %) and δ-MnO2 (21.69 %).

High-efficient helium purification through a novel Si-PWN zeolite membrane: Insights from molecular simulations

Zeolites are recognized as a proper nanoporous material for gas separation. In this study, we employed molecular dynamics simulations to investigate the performance of the pure silica PWN-type (Si-PWN) zeolite membrane for helium recovery from natural gas, which consists mainly of methane. The molecular simulations were done under different temperatures and applied pressures. The results indicated that the Si-PWN membrane could satisfy both the necessity of high permeance and selectivity by presenting the best helium permeance of 1.22 × 106 GPU and ultrahigh selectivity of helium over methane molecules. The vdW interactions and potential of the mean force calculations were also carried out to evaluate the molecules’ permeation through this membrane. The results revealed that adsorption favors methane molecules on the surface of the membrane, whereas diffusion prefers helium over methane across the membrane. All the obtained results indicate the considerable performance of the Si-PWN membrane in helium purification, making it a promising membrane in industrial applications.

Magnetic Safety Equipment Development for Ship Cleaning Robot

This paper presents a comprehensive development process of magnetic adhesion modules designed for mobile robots working in shipyards, performing hull-cleaning duties. The main aim is to prepare a secure system that will allow robots to safely navigate on ferromagnetic hulls. Typical process involves sandblasting performed by human personnel, which creates highly dangerous working conditions and requires numerous safety precautions to prevent both human accidents and environmental contamination related to cleaning medium spreading. Delegating this task to robot allows the deployment of specially designed cleaning equipment, reducing accidents’ chance, medium spreading and its usage thanks to dedicated salvage system. Existing literature lacks precise information on magnetic force calculations due to the high complexity of the problem that can be accounted to magnet shape or used materials. This study could be used as a guideline for development of similar equipment. The Finite Element Method Magnetics (FEMM) software is utilized for modelling and simulating numerous solutions that align with the working conditions of the robot. To generate a high-density, low-range magnetic field, which would be highly compatible for working conditions, Halbach array was used and comparison with single magnet of equivalent size was provided. The paper also discusses material choice and geometric considerations for the chassis. Experimental measurements of physical system involved multiple magnets’ configurations. This study provides a thorough comparison of numerical predictions and an actual performance of developed magnetic adhesion modules, establishing a field-tested design that can serve as a valuable reference for future work.

Variable Time-Step Physics Engine with Continuous Compliance Contact Model for Optimal Robotic Grinding Trajectory Planning.

In the transition from virtual environments to real-world applications, the role of physics engines is crucial for accurately emulating and representing systems. To address the prevalent issue of inaccurate simulations, this paper introduces a novel physics engine uniquely designed with a compliant contact model designed for robotic grinding. It features continuous and variable time-step simulations, emphasizing accurate contact force calculations during object collision. Firstly, the engine derives dynamic equations considering spring stiffness, damping coefficients, coefficients of restitution, and external forces. This facilitates the effective determination of dynamic parameters such as contact force, acceleration, velocity, and position throughout penetration processes continuously. Secondly, the approach utilizes effective inertia in developing the contact model, which is designed for multi-jointed robots through pose transformation. The proposed physics engine effectively captures energy conversion in scenarios with convex contact surface shapes through the application of spring dampers during collisions. Finally, the reliability of the contact solver in the simulation was verified through bouncing ball experiments and robotic grinding experiments under different coefficients of restitution. These experiments effectively recorded the continuous variations in parameters, such as contact force, verifying the integral stability of the system. In summary, this article advances physics engine technology beyond current geometrically constrained contact solutions, enhancing the accuracy of simulations and modeling in virtual environments. This is particularly significant in scenarios wherein there are constant changes in the outside world, such as robotic grinding tasks.

Cyclodextrins: Establishing building blocks for AI-driven drug design by determining affinity constants in silico

Cyclodextrins (CDs) are cyclic carbohydrate polymers that hold significant promise for drug delivery and industrial applications. Their effectiveness depends on their ability to encapsulate target molecules with strong affinity and specificity, but quantifying affinities in these systems accurately is challenging for a variety of reasons. Computational methods represent an exceptional complement to in vitro assays because they can be employed for existing and hypothetical molecules, providing high resolution structures in addition to a mechanistic, dynamic, kinetic, and thermodynamic characterization. Here, we employ potential of mean force (PMF) calculations obtained from guided metadynamics simulations to characterize the 1:1 inclusion complexes between four different modified βCDs, with different type, number, and location of substitutions, and two sterol molecules (cholesterol and 7-ketocholesterol). Our methods, validated for reproducibility through four independent repeated simulations per system and different post processing techniques, offer new insights into the formation and stability of CD-sterol inclusion complexes. A systematic distinct orientation preference where the sterol tail projects from the CD's larger face and significant impacts of CD substitutions on binding are observed. Notably, sampling only the CD cavity's wide face during simulations yielded comparable binding energies to full-cavity sampling, but in less time and with reduced statistical uncertainty, suggesting a more efficient approach. Bridging computational methods with complex molecular interactions, our research enables predictive CD designs for diverse applications. Moreover, the high reproducibility, sensitivity, and cost-effectiveness of the studied methods pave the way for extensive studies of massive CD-ligand combinations, enabling AI algorithm training and automated molecular design.

Development of a GPU-based multisphere DE–FE coupling method for interaction simulations between an off-road tire and a gravel terrain

For decades, growing interest has been devoted to simulating the tire–soil interaction phenomena using discrete element/finite element (DE–FE) coupling methods. In contrast to the widely used approach that idealizes soils as spherical DEs, a newly developed multisphere DE–FE method has been demonstrated to be more accurate in reproducing such phenomena; however, it requires considerable computational cost for large-scale tire–soil interaction simulations. Therefore, this study aims to develop an efficient graphics processing unit (GPU)-based multisphere DE–FE method based on a CUDA FORTRAN programming environment. To this end, two-level grids are introduced for the parallelization of contact detection for targeted multisphere DEs and subspheres, which helps to find contact pairs for the targeted subspheres of a multisphere DE in an efficient manner. In contrast to existing GPU-based parallelization techniques, which typically use atomic operations to avoid memory access conflicts, this study presents a parallelization strategy to process a contact pair between bounding spheres using one GPU thread to efficiently handle with owner-member relationships between multisphere DEs and their subspheres. In the parallelization for force calculation, our method introduces an efficient technique that utilizes one GPU thread to process a contact pair between subspheres, or between subspheres and FE segments, to reduce the number of repeated calculations. Finally, the developed GPU-based method is applied to analyze the travelling behaviors of a complex-patterned off-road tire on a gravel terrain, and the effectiveness and computational efficiency of this method are validated via indoor soil-bin experimental outcomes as well as serial and parallel simulation results. It is found that a speedup of approximately 38 has been achieved with the aid of the developed method.