Efficient Contact Search Research Articles

An Efficient Contact Search Algorithm for Three-Dimensional Sphere Discontinuous Deformation Analysis

The efficiency of contact search is one of the key factors related to the computational efficiency of three-dimensional sphere discontinuous deformation analysis (3D SDDA). This paper proposes an efficient contact search algorithm, called box search algorithm (BSA), for 3D SDDA. The implementation steps and data structure for BSA are designed, with a case study being conducted to verify its efficiency. The data structure also has been improved for parallelizing the computation in contact search. For the demonstration of the proposed algorithm (BSA), six cases with various sphere numbers are simulated. Simulation results show that the time consumed in contact search using BSA (CTofBSA) is much less than that by the direct search algorithm (DSA) (CTofDSA). For the case with 12,000 spheres, CTofBSA is 1.1[Formula: see text]h, which is only 1.3% of CTofDSA (84.62[Formula: see text]h). In addition, the proportion of the computation quantity of contact search in the entire computation (Pcs) is 91.3% by using DSA, while this value by BSA is only 12.4%, which demonstrates the contribution of BSA. The efficiency brought about by BSA (time consumed and computation quantity) may enable 3D SDDA to simulate large-scale problems.

The interactions between an off-road tire and granular terrain: GPU-based DEM-FEM simulation and experimental validation

Numerical methods have become useful tools for predicting vehicle mobility performance on granular terrain. However, due to the large number of soil particles and complex contact search in tire-granular terrain simulation, time-consuming calculation has become the most critical problem restricting the application of these methods. In this study, an efficient GPU-based DEM-FEM for simulation of the interactions between an off-road tire and granular terrain is implemented to improve computational efficiency. In this method, the main body of calculation is executed on GPU and programmed into an in-house developed code CDFP. The new GPU-based computing framework consists of 14 kernels, including efficient contact calculation between large-scale particles, novel contact calculation between particles and complex tread, contact calculation between particles and boundary wall, internal force calculation of finite elements, and information update. As a result, the efficient contact search and the complex interactions between an off-road tire and granular terrain are accomplished. Based on the self-developed single-wheel test device, an accurate simulation model consistent with the experiment is established. The validity of the proposed method is verified by comparing the simulation results with the experimental results. Finally, the discussion of computational efficiency shows that the proposed GPU-based DEM-FEM can be a powerful tool to simulate the interactions between an off-road tire and granular terrain.

Simulation model of a gear synchronisation unit for application in a real-time HiL environment

ABSTRACTGear shifting simulations using the multibody system approach and the finite-element method are standard in the development of transmissions. However, the corresponding models are typically large due to the complex geometries and numerous contacts, which causes long calculation times. The present work sets itself apart from these detailed shifting simulations by proposing a much simpler but powerful synchronisation model which can be computed in real-time while it is still more realistic than a pure rigid multibody model. Therefore, the model is even used as part of a Hardware-in-the-Loop (HiL) test rig. The proposed real-time capable synchronization model combines the rigid multibody system approach with a multiscale simulation approach. The multibody system approach is suitable for the description of the large motions. The multiscale simulation approach is using also the finite-element method suitable for the analysis of the contact processes. An efficient contact search for the claws of a car transmission synchronisation unit is described in detail which shortens the required calculation time of the model considerably. To further shorten the calculation time, the use of a complex pre-synchronisation model with a nonlinear contour is presented. The model has to provide realistic results with the time-step size of the HiL test rig. To reach this specification, a particularly adapted multirate method for the synchronisation model is shown. Measured results of test rigs of the real-time capable synchronisation model are verified on plausibility. The simulation model is then also used in the HiL test rig for a transmission control unit.

LC-Grid: a linear global contact search algorithm for finite element analysis

The contact searching is computationally intensive and its memory requirement is highly demanding; therefore, it is significant to develop an efficient contact search algorithm with less memory required. In this paper, we propose an efficient global contact search algorithm with linear complexity in terms of computational cost and memory requirement for the finite element analysis of contact problems. This algorithm is named LC-Grid (Lei devised the algorithm and Chen implemented it). The contact space is decomposed; thereafter, all contact nodes and segments are firstly mapped onto layers, then onto rows and lastly onto cells. In each mapping level, the linked-list technique is used for the efficient storing and retrieval of contact nodes and segments. The contact detection is performed in each non-empty cell along non-empty rows in each non-empty layer, and moves to the next non-empty layer once a layer is completed. The use of migration strategy makes the algorithm insensitive to mesh size. The properties of this algorithm are investigated and numerically verified to be linearly proportional to the number of contact segments. Besides, the ideal ranges of two significant scale factors of cell size and buffer zone which strongly affect computational efficiency are determined via an illustrative example.

Dynamic relaxation approach with periodic boundary conditions in determining the 3-D woven textile micro-geometry

A dynamic digital element approach, utilizing a dynamic relaxation procedure, is developed to determine 3-D woven textile micro-geometries. Three yarn/tow structures, including plain yarn, twisted yarn, and twisted tow, are generated by the digital element mesh. An explicit algorithm with a periodic boundary condition is employed to calculate nodal forces, accelerations, velocities, and displacements within the unit cell. Because the majority of the computing time is consumed to detect contacts between fibers, an efficient contact search algorithm is proposed. In addition, a multi-level dynamic relaxation procedure is implemented to further reduce computer time. The yarn-level fabric micro-geometry is also generated in a format that can be read by commercial finite element software. The micro-geometries derived from numerical simulations are compared to the microscopic images of actual fabrics. Good agreement is found between numerical results and experimental results.

Numerical and experimental analysis for the skew phenomena on the flexible belt and roller contact systems

The thin, flexible, flat belt system is frequently employed for power transmission, conveyor systems, and various manufacturing process equipments, such as printers, elevators, and automated teller machines. In general, some critical problems can happen during operation, since a thin flexible belt on rollers can easily skew. This is especially serious for high-speed belt operations. In this skewed situation, due to possible relative roller misalignment, roller deflection, and/or belt non-uniformity itself, a thin flexible belt can move along the perpendicular direction to the travelling direction. In this investigation, an efficient analysis method for simulating skewing phenomena of thin flexible belt systems is presented using the complete integration of large deformable finite element methods and multibody dynamics. A 4-node shell element is used to describe a thin flexible belt and two rigid cylindrical bodies describe the roller. Each cylindrical body is fixed with a pin joint and the positions of the rollers are adjusted to impose a tension to thebelt. For the interactions between the belt and the rollers, an efficient contact search algorithm based on a compliant contact force model is presented in this study. The contact search algorithm is composed of a pre-search and a detailed search to identify points of contact between the belt and the rollers. In the pre-search, a simple algorithm is used to identify lines on the belt that are close enough to the rollers that there might potentially be contact between them. The detailed search is performed by making efficient two-dimensional (2D) comparisons of the cross-section of the roller with a 2D projection of the belt lines identified in the pre-search. Afterwards, the contact force is generated by a compliant force model that uses a stick–slip frictional algorithm. The simulation model is validated against experimental measurement systems for thin flexible belt and rollers. It shows a good agreement with the numerical results. Furthermore CPU time with commercial software ANSYS Workbench is compared to check the performance of the algorithm. The proposed method is more than 10 times faster compared with ANSYS Workbench.

수중세장체의 접촉응답해석 기법에 관한 연구

Dynamic analysis of a marine slender structure is often involved with contacts among bodies or between bodies and seafloor. This paper presents an efficient and general contact search algorithm for dynamics in the context of the compliance contact model. A global detecting method that a bounding box is divided into several pieces in global coordinate system is presented in this paper. The method has an advantage that the number of contacting searching am be smaller than other methods for a system. The developed an efficient contact search algorithm is applied to the simulation program of 3D nonlinear dynamics of slender structure. Some examples are presented to show the validity of the proposed method.

Dynamic Analysis of Contacting Spur Gear Pair for Fast System Simulation

The prime source of vibration and noise in a gear system is originated from transmission error between the meshing gears. In this paper, the dynamic modeling method and response of a spur gear pair for the efficient system simulation are investigated by using a detailed contact analysis at each time step. Input values such as time-varying mesh stiffness and static transmission error excitation are not required in this investigation because mesh forces are obtained by contact analysis directly. The efficient contact search kinematics and algorithms in the context of the compliant contact model are developed to detect the interactions between teeth surfaces. In this investigation the compliant force model based on the Herzian law is employed using Coulomb friction force model, and dynamic transmission error (DTE) and mesh frequency values of contacting gear system are also illustrated.

Development of a Multibody Dynamics Simulation Tool for Tracked Vehicles (Part I, Efficient Contact and Nonlinear Dynamic Modeling)

In this paper, the nonlinear dynamic modeling methods for the virtual design of tracked vehicle are investigated by using multibody dynamic simulation techniques. The results include high oscillatory signals resulting from the impulsive contact forces and the use of stiff compliant elements to represent the joints between the track links. Each track link is modeled as a body which has six degrees of freedom, and two compliant bushing elements is used to connect track links. The efficient contact search kinematics and algorithms in the context of the compliance contact model are developed to detect the interactions between track links, rollers, sprockets, and ground for the sake of speedy and robust solutions. In order to validate the developed nonlinear multibody dynamic model against the experimental measurements, several empirical techniques are suggested and applied to the physical proving ground tests of the high mobility tracked vehicle. In this empirical validations, positions, velocities, accelerations and forces of the chassis and the track sub-systems are correlated accordingly.

Finite‐element modeling of multibody contact and its application to active faults

AbstractEarthquakes have been recognized as resulting from a stick–slip frictional instability along the faults between deformable rocks. An arbitrarily‐shaped contact element strategy, named the node‐to‐point contact element strategy, is proposed, applied with the static‐explicit characters to handle the friction contact between deformable bodies with stick and finite frictional slip and extended here to simulate the active faults in the crust with a more general nonlinear friction law. An efficient contact search algorithm for contact problems among multiple small and finite deformation bodies is also introduced. Moreover, the efficiency of the parallel sparse solver for the nonlinear friction contact problem is investigated. Finally, a model for the plate movement in the north‐east zone of Japan under gravitation is taken as an example to be analyzed with different friction behaviors. Copyright © 2002 John Wiley & Sons, Ltd.

T-4-4-3 An Efficient Contact Search Algorithm using the Relative Coordinate System for Multibody System Dynamics

Dynamic analysis of many mechanical systems is often involved with contacts among bodies. This paper presents an efficient and general contact search algorithm for multibody dynamics in the context of the compliance contact model. Many conventional collision detection algorithms are based on the absolute coordinate system. This paper proposes to use the relative coordinate system in detecting a contact. A boundary box of a defense surface geometry is divided into many blocks. A contact reference frame is defined on the defense body of a contact pair. Since all geometric variables necessary to detect a contact are measured relative to the contact reference frame attached to the defense body, the variables belonging to the defense body are constant, which significantly reduces computation time associated with the contact search. Therefore, the contact reference frame plays a key role in developing an efficient contact search algorithm. Contour of the defense body is approximated by many piecewise triangular patches, while contour of the hitting body is represented by hitting nodes along its boundary. Bounding boxes inside which contain each body of a contact pair are defined at a preprocessing stage to eliminate an exhaustive contact inspection when two bodies are in a distance. If two bounding boxes are turned out to be in a contact during the pre-search, each node on the hitting boundary is inspected to find out to which block the node belongs in the post-search. Since each block dividing the boundary of the defense body has a list of patches, each node on the hitting boundary is tested for a contact only with the patches in the block that the node belongs. Actual contact calculation is then carried out to find the contact penetration used in calculating the compliant contact force. Since the searching algorithm is coupled with the stepping algorithm of the numerical integration, a strategy for deciding an integration stepsize is proposed. Dynamic analysis of a paper fed into a copying machine is performed to demonstrate the validity of the proposed method.

A relative contact formulation for multibody system dynamics

Dynamic analysis of many mechanical systems is often involved with contacts among bodies. This paper presents a relative contact formulation for multibody dynamics in the context of the compliance contact model. Many conventional collision detection algorithms are based on the absolute coordinate system. This paper proposes to use the relative coordinate system in detecting a contact. A contact reference frame is defined on the defense body of a contact pair. Since all geometric variables necessary to detect a contact are measured relative to the contact reference frame attached to the defense body, the variables for a defense body are constant, which significantly reduces computation time. Therefore, the contact frame plays a key role in developing an efficient contact search algorithm. Contour of a defense body is approximated by many piecewise straight lines, while contour of a hitting body is represented by hitting nodes along its boundary. Bounding boxes containing each body of a contact pair are defined at a pre-search stage to eliminate the exhaustive contact inspection process when two bodies are in a distance. Domain of the bounding box for a defense body is divided into many sectors each of which has a list of line segments lying inside or on the sector boundary. Post-search for a contact is processed in the sequence of broad and narrow phases. In the broad phase, the bounding boxes of a contact pair are inspected for a contact. If two boxes are in a contact, each node on the hitting boundary is inspected to find out to which sector the node belongs. Since each domain sector of the defense body has a list of line segments, each node on the hitting boundary is tested for a contact only with the line segments in the list. In the narrow phase, actual contact calculation is carried out to find the contact penetration used in calculating the contact force. Since the searching algorithm is coupled with the stepping algorithm of the numerical integration, a strategy for deciding an integration stepsize is proposed. One numerical example is presented to demonstrate the validity of the proposed method.

Investigation into tool surface description for finite element analysis of three-dimensional sheet metal forming processes

A general method for the mathematical description of arbitrarily-shaped tool surfaces is proposed by introducing the parametric and non-parametric patch approaches. The cubic Ferguson patch is employed to describe the tool surface in the parametric patch approach and an efficient contact search algorithm is suggested to make this parametric patch approach more realistic for the FE analysis. The non-parametric patch approach introduces a cubic blending function as in the case of the parametric patch approach to allow C 1 continuity. In the approach, an array of equi-spaced points is required to construct the whole tool surface. Computations are carried out for some complex sheet forming examples including actual auto-body panel to verify the validity and the robustness of the developed contact search algorithms.

Rigid-plastic finite element analysis of sheet metal forming processes using continuous contact treatment and membrane elements incorporating bending effects

An improved method of contact treatment is developed in which both the FEM (finite element method) mesh and the tool surfaces are described with parametric patches which have C 1 continuity or more. The FEM mesh at the current configuration is globally converted into smooth surface patches of net form. A continuous sheet surface normal scheme is devised by using the globally smoothed mesh surface. A robust and efficient contact search algorithm is also developed in connection with the proposed continuous contact treatment. As an improved version of conventional membrane element, the BEAM (abbreviated from Bending Energy Augmented Membrane) element is newly developed based on node spring. In order to verify the effectiveness of the proposed continuous contact treatment and BEAM element, deep drawing processes of complicated parts including actual auto-body panel are analysed. Comparisons with the available experiment and analysis show that the proposed continuous contact treatment in connection with BEAM elements can be effectively applied to the analysis of sheet metal forming processes for arbitrarily curved parts with deformation regions in which the bending effect must be taken into account.