Analysis Of Multibody Systems Research Articles

A novel and efficient Hamiltonian dynamic analysis approach for constraint force determination in flexible multibody systems

In the dynamic analysis of flexible multibody systems, Hamiltonian formulations offer advantages in numerical stabilization and systematic handling of systems with varying mass. However, current approaches face challenges. Differential algebraic equations (DAEs) can directly express constraint forces but are computationally inefficient, while ordinary differential equations (ODEs) are more computationally efficient but cannot directly represent constraint forces due to the elimination of the Lagrange multiplier. This paper presents an innovative and efficient dynamic analysis approach based on the Hamiltonian formulation, incorporating velocity transformation and open-constraint coordinate methods. Compared to conventional DAE-based Hamiltonian formulations, our approach conducts analysis efficiently using only independent variables. Compared to conventional ODE-based Hamiltonian formulations, our approach effectively expresses constraint forces through Lagrange multiplier reformulation. Furthermore, when compared to the traditional ODE-based Lagrangian formulation, our approach exhibits superior computational efficiency. Numerical simulations assess our proposed formulation, showing agreement with conventional formulations, shorter calculation time, and alignment with analytical results, confirming the accuracy and usefulness of our approach.

Unified framework for geotechnical cross-contact problems with interfacial fluid flow

In the hydro-mechanical coupling analysis of multi-body contact systems, challenges arise from the fluid flow at the interface and the over-constraint at the cross line, necessitating special treatments. In this paper, a novel algorithm is developed to address these challenges comprehensively. The proposed method introduces an intermediate interface, serving as a bridge for contact stress transfer and fluid exchange between different subdomains. The intermediate interface concurrently carries the degrees of freedom related to the displacement, pore pressure, and Lagrange multiplier. As a result, the contact constraint and interfacial fluid flow can be integrated into a unified formulation, resulting in a simplified algorithm implementation; the elimination of over-constraint behaviour can also be achieved in a simple manner. Additionally, the storage capacity of interfaces is adequately considered in the current framework, enabling the accurate computation of water suction generated by the opening of contact interfaces. Finally, several numerical experiments are conducted to validate the performance of our proposed method. Results show that our method can provide a reliable computational tool for the two-phase contact problems with interfacial fluid flow.

Equivalent analytical formulation-based multibody elastic system analysis using one-dimensional finite elements

Equivalent analytical formulation-based multibody elastic system analysis using one-dimensional finite elements

A New Exoskeleton Prototype for Lower Limb Rehabilitation

This paper presents a new solution for an exoskeleton robotic system that is used for locomotor assistance in people with locomotor disabilities. As novel features of the present research, a novel structural solution of a plane-parallel kinematic chain, intended to be used as the leg of an exoskeleton robot, is proposed. A virtual prototype is made, on the basis of which kinematic and dynamic studies are carried out using ADAMS software for the dynamic analysis of multibody systems. The dynamic simulation of the exoskeleton is performed in two simulation situations: walking on a horizontal plane, as well as the simulation of motion assistance when climbing stairs. Following this analysis, it is noted that the robotic system achieves angular variations in the hip and knee joints similar to that of a human subject. As a result, the constructive solution is feasible, and the next stage of the study is to realize an experimental prototype by the rapid prototyping technique. The kinematic elements of the exoskeleton are designed to provide structural strength, to be easily manufactured by 3D printing and to be easy to assemble. For this purpose, the structural optimization is performed with the finite element method to eliminate stress concentrators. Finally, an experimental prototype of the exoskeleton robot is manufactured and assembled, whose motion is analyzed using ultrafast-camera-based video analysis.

Analytical mechanics methods in finite element analysis of multibody elastic system

The study of multibody systems with elastic elements involves at the moment the reevaluation of the classical methods of analysis offered by analytical mechanics. Modeling this system with the finite element method requires obtaining the motion equation for an element in the circumstances imposed by a multibody system. The paper aims to present the main analysis methods used by researchers, to make a comparative analysis, and to show the advantages or disadvantages offered by different methods. For the presentation of the main methods (namely Lagrange’s equations, Gibbs–Appell’s equations, Maggi’s formalism, Kane’s equations, and Hamilton’s equations) a unified notation is used. The paper provides a critical evaluation of the studied applications that involved some of these methods, highlighting the reason why it was decided to use them. Also, the paper identifies potential research areas to explore.

Assessing the dynamic behavior of multiconnected offshore floating photovoltaic systems under combined wave-wind loads: A comprehensive numerical analysis

Floating photovoltaic (FPV) systems have garnered considerable interest due to their numerous benefits. However, the mechanical design of these systems remains underexplored in existing literatures, necessitating further investigation before they can be commercially deployed in ocean environments. In this study, a novel modular offshore FPV solution was proposed, and numerical modeling and hydrodynamic coupling analysis of multi-body FPV systems were conducted to assess the relative behavior of multi-connected FPV modules under combined wave-wind conditions. Initially, the multi-connected system was modeled, taking into account fixed and hinged connection boundary conditions (BC). Utilizing frequency-domain analysis, the hydrodynamic coefficients essential for time-domain analysis were derived. Subsequently, the overall hydrodynamic performance and behavioral characteristics of various FPV platform types were evaluated. In addition, the strength of connectors under extreme conditions were assessed. Lastly, we compared the motion responses of the multi-body platform under different connection BCs and wave headings. It has been proven that the joint of the hinged connector will generate additional moments, which will affect the dynamic response of the platform as an excitation load. Moreover, the connector's structural responses were mainly dominated by the motion response of the FPV platforms. Furthermore, for the multi-body FPV systems, 0° wave heading should be avoided for installation to reduce the motion responses and structural responses. This study provides valuable insights into the mechanical design of FPV systems for ocean deployment.

Marine algae biomass energy source is increasing getting approval from policy maker and community. Beside production of seaweed for biomass energy, seaweed plantation has benefit for food, cosmetic, gelatin and pharmaceutical products. Large production of biomass will require deployment of very large multibody floating structure offshore. To ensure that the system is reliable, design needs to be built, a mooring

Marine algae biomass energy source is increasing getting approval from policy maker and community. Beside production of seaweed for biomass energy, seaweed plantation has benefit for food, cosmetic, gelatin and pharmaceutical products. Large production of biomass will require deployment of very large multibody floating structure offshore. To ensure that the system is reliable, design needs to be built, a mooring component for the mooring system, need to be properly sized to provide reliable strength for position keeping. This paper present, result of hydrodynamic test carried in UTM lab to determine coefficient required for the design and simulation of mooring system for very large floating structure for offshore aquaculture structure for ocean plantation, the paper also present safety and efficiency of the mooring system. Hydrodynamic test is traditionally used to secure coefficient require for design for environment for ship structure and offshore platform hydrodynamic interaction. The case of seaweed biomass is unique because the seaweed interacts directly and moves with the environment. The obtained the coefficient is used to model the static moorings system that assess the tension, tilt, safe mass and motion of the mooring components. Interpolated time dependent currents from the towing tank are used to estimate dynamic response of the mooring as well as the draft of the mooring components, the overall analysis is use to select required mooring components of the system. The outcome of the test presented in this paper will help for future development of offshore aquaculture system and multibody system deployment and analysis

Improved Craig–Bampton Method Implemented into Durability Analysis of Flexible Multibody Systems

The Craig–Bampton method is frequently applied in most commercial multibody dynamic software. Nevertheless, the Craig–Bampton modes only represent the free-free modes in flexible multibody systems. However, the free-free modes are incapable of all engineering applications. Hence, a rational set of reference conditions must be correctly chosen to define a unique displacement field. Firstly, a simple 2D beam with two revolute joints is taken as an example to prove that the free-free modes are not suitable for all engineering applications, and the results are validated by ANSYS and the analytical solution. Secondly, the Craig–Bampton method is improved by two different methods: (i) the reference conditions are added to the original Craig–Bampton matrix and (ii) the reference conditions are applied to the shape functions to redefine the mass and stiffness matrices before constructing the original Craig–Bampton matrix. This implementation illustrates that the improved Craig–Bampton matrix can not only generate the free-free modes but is also suitable for the non-free-free modes. Finally, two discrepant reference conditions are imposed to obtain the dynamic response of the flexible connecting rod based on the improved Craig–Bampton method, which is validated using the normal mode approach. Simulations show that the improved Craig–Bampton method can be used as a general-purpose method in durability analysis.

Transfer matrix method for linear vibration analysis of flexible multibody systems

Achieving high computational efficiency has been well recognized as a research challenge in the vibration analysis of flexible multibody systems. This paper presents a novel transfer matrix method to model and analyze the linear vibration of flexible multibody systems. The transfer equations, the transfer matrices, and the consistency equations of the general flexible body elements with multi-input ends are deduced for the first time. Subsequently, the automatic deduction theorem of the overall transfer equation is developed for flexible multibody systems. Based on the theorem, the overall transfer equation can be deducted automatically and the natural vibration characteristics can be obtained. The dynamic equations and augmented eigenvectors are formulated to solve the forced vibration response. Further, the proposed method is applied to study the dynamics of an ultra-precision machine tool with flexible body elements. The natural vibration characteristics and the forced vibration response are solved and validated with the data from the modal tests and the working conditions. The proposed method has the following advantages: easy deduction of the overall transfer equation, low order of system matrix, and high computational speed.

The testing of pneumatic tyres for the interpretation of tyre behaviour for road/rail vehicles when operating on rails

This paper describes a programme of tyre tests using a purpose built tyre test rig designed specifically to investigate the behaviour of tyres that are used with Road-Rail Vehicles (RRVs). These vehicles are used extensively by the rail industry to support the maintenance of existing rail lines and new construction works. In many cases, using a vehicle that can only operate on the road, or a rail engine that can only operate on tracks will not provide a suitable or effective solution for the task in hand. RRVs are able to operate on both roads and rail, and as such provide a very flexible solution to the rail industry. When operating on the road, RRVs use pneumatic tyres to control their motion and act to all intent and purpose as a normal road vehicle. When operating on rail lines RRVs use a combination of the pneumatic tyres and standard steel rail wheels to control their motion. The rail wheels maintain the directional stability on the track and the pneumatic tyres provide the tractive force to drive and brake the vehicle. Unlike standard road or rail vehicles, there is to date no predictive engineering practice that allows the use of computer simulation to design and optimise the performance of RRVs when they are operating on rails. Computer tools, such as multi-body systems (MBS) analysis are used extensively to design both road and rail vehicles. For road vehicles a tyre model is needed to represent the behaviour in the contact patch between the tyre and the road. For rail vehicles a model is needed to represent the contact force between the train wheel and the track. In both these applications the behaviour is well understood and over the last half century mathematical models have been developed that allow accurate and useful simulation to support the design of new vehicles and trains. In contrast, RRVs have evolved essentially as modifications to standard road vehicles. While the base vehicle may be very well designed to perform on the road, the performance on rail is based on experience and some testing. There is no up-front science involved in designing a RRV to perform effectively during this very important phase of its operation. In order to develop an accurate model to predict RRV performance on rails it is clear that a model of the behaviour of the tyre when in contact with the rail is needed. To date, no such model exists and additionally the testing needed to generate data that could be used to develop a model has never been carried out. The work described here addresses this with the design and build of a unique test rig that can be used to test tyres on rails for a range of operating conditions, and produce a set of initial results that provide a framework for a future tyre/rail model. The paper concludes with a review of the behaviour measured and provides new insights into how well tyres perform on rails and also where the behaviour differs from the well understood behaviour of tyres operating on roads. The important behaviours that would provide the main parameters for a new empirical tyre model are also identified and discussed.

Simulation of large-deformed discontinuity system with translation and rotation by discretized virtual internal bond

Discretized virtual internal bond (DVIB) is an effective mechanical modeling approach of solid material. It introduces no small deformation hypothesis in the constitutive model intrinsically, which leads to more convenience for the simulation of large deformation and large displacement problem, such as the multi deformable bodies system. However, DVIB is still underdeveloped for the simulation of multi discontinuities involved collision and interaction. To model the contact interaction happened among the discontinuous bodies, a key problem is to establish an effective contact characterization scheme in DVIB method. In this paper, the Munjiza’s penalty-based model with no binary search algorithm is introduced into DVIB to simulate the contact of discontinuities with large deformation and large displacement. Using this method, the large rotation and translation of deformable and contactable multi-body system can be straightly modeled without any mesh reconstruction or deformation decomposition. The results of numerical cases suggest the proposed method provides a simple and feasible alternative for the discontinuous deformation analysis of multi-body system.

Kinematics and dynamics of planar multibody systems with fully Cartesian coordinates and a generic rigid body

This work describes in detail the theoretical basis of the fully Cartesian coordinates formulation with a generic rigid body and evaluates its performance in the dynamic analysis of planar multibody systems. The topological features of the generic rigid body and the most relevant kinematic constraint equations are presented, aiming its application in the dynamic analysis of complex multibody systems and in advanced teaching.Contrarily to natural coordinates, in which the present formulation lays its foundation, planar rigid bodies are defined with a predetermined kinematic structure that resorts only to the Cartesian coordinates of one point and one unit vector. The introduction of the generic rigid body systematizes the discretization of the multibody system, simplifies the kinematic constraints required for its description, and renders higher physical meaning and sparsity to its mass matrix. However, it also slightly increases the number of generalized coordinates and kinematic constraints, required to model the multibody system, when compared to other global formulations.The present formulation was applied to the analysis of four planar models with different complexity levels, namely the slider-crank, double four-bar linkage, Jansen mechanism and a biomechanical model of the human body, presenting high agreement scores with benchmark and literature data.

Eigenvalue analysis of planar linear multibody system under conservative force based on the transfer matrix method

AbstractThe linear multibody system transfer matrix method (LMSTMM) provides a powerful tool for analyzing the vibration characteristics of a mechanical system. However, the original LMSTMM cannot resolve the eigenvalues of the systems with ideal hinges (i.e., revolute hinge, sliding hinge, spherical hinge, cylindrical hinge, etc.) or bodies under conservative forces due to the lack of the corresponding transfer matrices. This paper enables the LMSTMM to solve the eigenvalues of the planar multibody systems with ideal hinges or rigid bodies under conservative forces. For a rigid body, the transfer matrix can now consider coupling terms between forces and kinematic state perturbations. Also, conservative forces that contribute to the eigenvalues can be considered. Meanwhile, ideal hinges are introduced to LMSTMM, which enables the treatment of eigenvalues of general multibody systems using LMSTMM. Finally, the comparative analysis with ADAMS software and analytical solutions verifies the effectiveness of the proposed approach in this paper.

Computational structural analysis of spatial multibody systems based on mobility criteria

Computational efficiency is a critical aspect of multibody dynamics. Recent developments in linear algebra libraries and hardware architectures allow the multibody community to improve the performance of their kinematic and dynamic formulations. Kinematic substructuring of multibody systems may take great advantage of these resources by dividing the multibody system into modules that can be solved more efficiently than the whole set of equations of the multibody system at once. This work discusses some advantages of the kinematic substructuring based on mobility criteria over methods based on linear graph theory. It also introduces detailed information on the algorithms we have developed for the computational structural analysis of planar and spatial multibody systems. Structural transformations easily generate different kinematic substructures, ordered and classified under various criteria depending on the analyst’s needs, such as robustness and efficiency. A graphical user interface may guide the analyst while defining the topology of the multibody system and show detailed information about the obtained results. The algorithms are explained through an example, and the advantages of this method are reinforced as applied to several spatial multibody systems.

Inherent stability analysis for multibody systems with semi-active inerters

Inherent stability reflects the reliability performance of a semi-active control system, where for “active” semi-active inerter-based systems, the inherent stability problem has not been studied. The motivation of this paper is to present sufficient conditions that ensure inherent stability for such systems. The absolute stability theory is adopted, and the general multibody system with semi-active inerters is formulated in a Lurè form. Sufficient conditions are derived based on the circle criterion for three different cases including the case with only one semi-active inerter, the case with several semi-active inerters without common connection points, and the case with several semi-active inerters where the ground is the common connection point. Extensive numerical examples based on low-degree-of-freedom systems are provided to show the effectiveness of the derived conditions.

Recent Advances in the Absolute Nodal Coordinate Formulation: Literature Review From 2012 to 2020

Abstract Absolute nodal coordinate formulation (ANCF) is a nonincremental nonlinear finite element procedure that has been successfully applied to the large deformation analysis of multibody systems for more than two decades. Although a comprehensive review on ANCF was conducted by Gerstmayr et al. (2013, “Review on the Absolute Nodal Coordinate Formulation for Large Deformation Analysis of Multibody Systems,” J. Comput. Nonlinear Dyn., 8(3), p. 031016), significant theoretical developments have been made since then at a much faster pace to improve the element accuracy and computational efficiency. In order to overview recent advances in ANCF simulation capabilities that are not covered in the first review paper, this paper aims to conduct a comprehensive review of 259 papers concerning ANCF published from 2012 to 2020. It is shown that the ANCF element library has grown substantially for beam, plate/shell, solid elements, eliminating drawbacks of ANCF elements developed earlier. The application areas have extended, especially in the aerospace field, and the enhanced ANCF simulation capabilities have been demonstrated in solving challenging engineering problems. Research efforts have been made continually to integrate computer-aided design (CAD) and analysis with ANCF elements. Furthermore, computational improvements and multiphysics simulations have become major research topics for ANCF. It is also demonstrated that the accurate ANCF geometry description can be exploited to facilitate structural optimization of multibody systems.

L1-norm based dynamic analysis of flexible multibody system modeled with trimmed isogeometry

Isogeometric analysis is an efficient method to accurately represent geometry and obtain accurate solutions, and can be utilized for dynamic analysis of flexible multibody systems. In this paper, l1 norm based dynamic analysis of flexible multibody system modeled with trimmed isogeometry is presented, in which, (1) the exact shape deformation of regular NURBS element after trimming is characterized by geometric transformation, (2) the l1 norm optimization is employed to select the predominant modal shapes for accurate dynamic analysis under rapidly changed loads, and (3) motion equations are sampled by considering the acceleration of control variables influence on control variables variation to obtain stable dynamic results. Finally, the presented approach is validated with three examples. The dynamic response results show that the trimmed isogeometric analysis can be employed to achieve considerable accuracy. As the continuity between NURBS elements increases from C0 to C1, the degree of freedom is reduced by 75%, and the computational time of l1 norm based dynamic analysis is about 35% of the full order modal shapes method. Furthermore, the proposed sampling method can be utilized to reduce the 33% sampling number compared with the Latin Hypercube sampling method.

Selecting Main Parts of a Four-Axis Palletizing Robot Through Dynamic Analysis of Rigid-Flexible Multibody Systems

Selecting Main Parts of a Four-Axis Palletizing Robot Through Dynamic Analysis of Rigid-Flexible Multibody Systems

Finite Element Method-Based Elastic Analysis of Multibody Systems: A Review

This paper presents the main analytical methods, in the context of current developments in the study of complex multibody systems, to obtain evolution equations for a multibody system with deformable elements. The method used for analysis is the finite element method. To write the equations of motion, the most used methods are presented, namely the Lagrange equations method, the Gibbs–Appell equations, Maggi’s formalism and Hamilton’s equations. While the method of Lagrange’s equations is well documented, other methods have only begun to show their potential in recent times, when complex technical applications have revealed some of their advantages. This paper aims to present, in parallel, all these methods, which are more often used together with some of their engineering applications. The main advantages and disadvantages are comparatively presented. For a mechanical system that has certain peculiarities, it is possible that the alternative methods offered by analytical mechanics such as Lagrange’s equations have some advantages. These advantages can lead to computer time savings for concrete engineering applications. All these methods are alternative ways to obtain the equations of motion and response time of the studied systems. The difference between them consists only in the way of describing the systems and the application of the fundamental theorems of mechanics. However, this difference can be used to save time in modeling and analyzing systems, which is important in designing current engineering complex systems. The specifics of the analyzed mechanical system can guide us to use one of the methods presented in order to benefit from the advantages offered.

The Motion Formalism for Flexible Multibody Systems

Abstract This paper describes a finite element approach to the analysis of flexible multibody systems. It is based on the motion formalism that (1) uses configuration and motion to describe the kinematics of flexible multibody systems, (2) recognizes that these are members of the special Euclidean group thereby coupling their displacement and rotation components, and (3) resolves all tensors components in local frames. The goal of this review paper is not to provide an in-depth derivation of all the elements found in typical multibody codes but rather to demonstrate how the motion formalism (1) provides a theoretical framework that unifies the formulation of all structural elements, (2) leads to governing equations of motion that are objective, intrinsic, and present a reduced order of nonlinearity, (3) improves the efficiency of the solution process, and (4) prevents the occurrence of singularities.