A finite element formulation for dynamic parameter identification of robot manipulators

In this paper a finite element based approach is described for the automatic generation of models suitable for dynamic parameter identification. The method involves a nonlinear finite element formulation in which both links and joints are considered as specific finite elements [6, 7]. Since the identification procedure considers rigid-link robot models, the inertial properties of the link elements are described using a lumped mass formulation. The parameters to be identified are masses, first-order moments and inertial tensor components of the links. The equations of motion are written in a form which is linear in the dynamic parameters. This formulation is obtained by employing Jourdain’s principle of virtual power. The parameters are estimated using a linear least squares technique. Singular value decomposition of the regression matrix is used to find the minimum parameter set. Simulation results obtained from the 6 DOF PUMA 560 robot based on the estimated parameters show that the method yields accurate responses.     

Geometric stiffening of flexible link system with large overall motion

In the conventional hybrid-coordinate formulation, the Cartesian deformation variables are employed with a linear Cauchy strain measure. It has been found that such modeling method fails to capture the motion-induced stiffness terms and provides erroneous dynamic results in case of high rotating speed. In this paper, geometric stiffening of flexible link system is investigated. Using a non-Cartesian deformation variable, the equations of motion of each link, which include the stiffening terms, are obtained based on the virtual power principle, and forward recursive formulation is employed to derive the equations of flexible link system. Relative generalized coordinates are employed to derive the equations of motion of the link system. Numerical examples are presented to investigate the stiffening effect on large overall motion as well as deformation of the flexible link system and to testify the accuracy and efficiency of the formulation.     

Dynamics and elasto-dynamics optimization of a 2-DOF planar parallel pick-and-place robot with flexible links

Dynamic modeling and analysis of a 2-DOF translational parallel robot with flexible links for high-speed pick-and-place operation is presented in this paper. Optimization is implemented with the goal to improve the dynamic accuracy of the end-effector at high speed. The governing equations of flexible links within the robot are formulated in the floating reference frame using Euler–Lagrange method, leading to a global FEM model being generated using the KED (Kineto-Elasto-Dynamics) technique. The dynamic characteristics of the robot are then investigated by model analysis. A numerical dynamic index is proposed to identity the range of natural frequency when the robot reaches different configurations. The comparisons are made between the optimized and original designs in terms of dynamic stress and response.     

Feature based object decomposition for finite element meshing

Performing a finite element analysis requires overlaying an object with a mesh of varying density based on the expected stress levels within the part. Attempts have been made in the past to automat the finite element meshing procedure. The method presented here is intelligent in the sense that it examines the complete part for potential stress gradients and decomposes the part into hexahedral regions according to the geometry gradients in the part. High geometry gradients are regions of high curvature, especially edges. The algorithm segregates high gradient features into isolation volumes. It then continues to decompose each isolation volume dependent on the particular geometry contained in the feature. The result is a set of hexahedral bricks suitable for passing to an automatic meshing routine.     

Effect of the centrifugal forces on the finite element eigenvalue solution of a rotating blade: a comparative study

In this study, the effect of the centrifugal forces on the eigenvalue solution obtained using two different nonlinear finite element formulations is examined. Both formulations can correctly describe arbitrary rigid body displacements and can be used in the large deformation analysis. The first formulation is based on the geometrically exact beam theory, which assumes that the cross section does not deform in its own plane and remains plane after deformation. The second formulation, the absolute nodal coordinate formulation (ANCF), relaxes this assumption and introduces modes that couple the deformation of the cross section and the axial and bending deformations. In the absolute nodal coordinate formulation, four different models are developed; a beam model based on a general continuum mechanics approach, a beam model based on an elastic line approach, a beam model based on an elastic line approach combined with the Hellinger–Reissner principle, and a plate model based on a general continuum mechanics approach. The use of the general continuum mechanics approach leads to a model that includes the ANCF coupled deformation modes. Because of these modes, the continuum mechanics model differs from the models based on the elastic line approach. In both the geometrically exact beam and the absolute nodal coordinate formulations, the centrifugal forces are formulated in terms of the element nodal coordinates. The effect of the centrifugal forces on the flap and lag modes of the rotating beam is examined, and the results obtained using the two formulations are compared for different values of the beam angular velocity. The numerical comparative study presented in this investigation shows that when the effect of some ANCF coupled deformation modes is neglected, the eigenvalue solutions obtained using the geometrically exact beam and the absolute nodal coordinate formulations are in a good agreement. The results also show that as the effect of the centrifugal forces, which tend to increase the beam stiffness, increases, the effect of the ANCF coupled deformation modes on the computed eigenvalues becomes less significant. It is shown in this paper that when the effect of the Poisson ration is neglected, the eigenvalue solution obtained using the absolute nodal coordinate formulation based on a general continuum mechanics approach is in a good agreement with the solution obtained using the geometrically exact beam model.     

Deadlock prevention for flexible manufacturing system

Deadlock must be prevented via the shop controller during the flexible manufacturing system （FMS） performing. Various models have been tried for the analysis and design of shop controller. Petri net is suitable to describe the dynamic behavior of the discrete event system, such as concurrency, conflict and deadlock, however, the verification of the .system behavior needs structure analysis with complex theoretical proof method. Temporal logic model checking has important advantages over traditional theorem prover. It is flatly automatic and can produce possible counter-example which is particularly important in finding subtle error in complex transition systems. In this paper, a new method for the deadlock prevention based on Petri net and Temporal Logic model checking is presented. The specification in the Temporal Logic is expressed according to some result of structure analysis of the Petri net. The model checking is employed to execute the formal verification, which will conduct an exhaustive exploration of all possible behaviors. Finally, an example is presented to demonstrate how the method works.     

Finite element methods for the time-dependent Ginzburg-Landau model of superconductivity

The initial-boundary value problem for the time-dependent Ginzburg-Landau equations that model the macroscopic behavior of superconductors is considered. The convergence of finite-dimensional, semidiscrete Galerkin approximations is studied as is a fully-discrete scheme. The results of some computational experiments are presented.     

Geometric nonlinear effects on the planar dynamics of a pivoted flexible beam encountering a point-surface impact

Flexible-body modeling with geometric nonlinearities remains a hot topic of research by applications in multibody system dynamics undergoing large overall motions. However, the geometric nonlinear effects on the impact dynamics of flexible multibody systems have attracted significantly less attention. In this paper, a point-surface impact problem between a rigid ball and a pivoted flexible beam is investigated. The Hertzian contact law is used to describe the impact process, and the dynamic equations are formulated in the floating frame of reference using the assumed mode method. The two important geometric nonlinear effects of the flexible beam are taken into account, i.e., the longitudinal foreshortening effect due to the transverse deformation, and the stress stiffness effect due to the axial force. The simulation results show that good consistency can be obtained with the nonlinear finite element program ABAQUS/Explicit if proper geometric nonlinearities are included in the floating frame formulation. Specifically, only the foreshortening effect should be considered in a pure transverse impact for efficiency, while the stress stiffness effect should be further considered in an oblique case with much more computational effort. It also implies that the geometric nonlinear effects should be considered properly in the impact dynamic analysis of more general flexible multibody systems.     

The development of a sliding joint for very flexible multibody dynamics using absolute nodal coordinate formulation

In this paper, a formulation for a spatial sliding joint is derived using absolute nodal coordinates and non-generalized coordinate and it allows a general multibody move along a very flexible cable. The large deformable motion of a spatial cable is presented using absolute nodal coordinate formulation, which is based on the finite element procedures and the general continuum mechanics theory to represent the elastic forces. And the nongeneralized coordinate, which is related to neither the inertia forces nor the external forces, is used to describe an arbitrary position along the centerline of a very flexible cable. Hereby, the non-generalized coordinate represents the arc-length parameter. The constraint equations for the sliding joint are expressed in terms of generalized coordinate and nongeneralized coordinate. In the constraint equations for the sliding joint, one constraint equation can be systematically eliminated. There are two independent Lagrange multipliers in the final system equations of motion associated with the sliding joint. The development of this sliding joint is important to analyze many mechanical systems such as pulley systems and pantograph-catenary systems for high speed-trains.     

A geometrically exact beam element based on the absolute nodal coordinate formulation

In this study, Reissner’s classical nonlinear rod formulation, as implemented by Simo and Vu-Quoc by means of the large rotation vector approach, is implemented into the framework of the absolute nodal coordinate formulation. The implementation is accomplished in the planar case accounting for coupled axial, bending, and shear deformation. By employing the virtual work of elastic forces similarly to Simo and Vu-Quoc in the absolute nodal coordinate formulation, the numerical results of the formulation are identical to those of the large rotation vector formulation. It is noteworthy, however, that the material definition in the absolute nodal coordinate formulation can differ from the material definition used in Reissner’s beam formulation. Based on an analytical eigenvalue analysis, it turns out that the high frequencies of cross section deformation modes in the absolute nodal coordinate formulation are only slightly higher than frequencies of common shear modes, which are present in the classical large rotation vector formulation of Simo and Vu-Quoc, as well. Thus, previous claims that the absolute nodal coordinate formulation is inefficient or would lead to ill-conditioned finite element matrices, as compared to classical approaches, could be refuted. In the introduced beam element, locking is prevented by means of reduced integration of certain parts of the elastic forces. Several classical large deformation static and dynamic examples as well as an eigenvalue analysis document the equivalence of classical nonlinear rod theories and the absolute nodal coordinate formulation for the case of appropriate material definitions. The results also agree highly with those computed in commercial finite element codes.     

An efficient facet shell element for corotational nonlinear analysis of thin and moderately thick laminated composite structures

In the present work, an efficient facet shell element for the geometrically nonlinear analysis of laminated composite structures using the corotational approach is developed. The facet element is developed by combining the discrete Kirchhoff-Mindlin triangular bending element (DKMT), and the optimal membrane triangular element (OPT). The membrane-bending coupling effect of composite laminates is incorporated in the formulation, and inconsistent stress stiffness matrix is formulated. Using corotational formulation and the proposed facet element, some example laminated composite structures with geometric nonlinearity are analyzed, and the results are compared with those found using other facet elements.     

Finite element computation of absorbing boundary conditions for time-harmonic wave problems

This paper proposes a new method, in the frequency domain, to define absorbing boundary conditions for general two-dimensional problems. The main feature of the method is that it can obtain boundary conditions from the discretized equations without much knowledge of the analytical behavior of the solutions and is thus very general. It is based on the computation of waves in periodic structures and needs the dynamic stiffness matrix of only one period in the medium which can be obtained by standard finite element software. Boundary conditions at various orders of accuracy can be obtained in a simple way. This is then applied to study some examples for which analytical or numerical results are available. Good agreements between the present results and analytical solutions allow to check the efficiency and the accuracy of the proposed method.     

Web-based post-processing visualization system for finite element analysis

In this paper, we propose and implement a website of post-processing system for finite element analysis (WebDFEA). Finite element analysis is a computer-aided engineering tool and is popular for static/dynamic structure analysis. It includes three processing systems where post-processing system is to graphically demonstrate the analysis result of a structure model analyzed by finite element method. WebDFEA performs as a website. It is cross-platform because it can auto-detect a client computer platform and auto-download proper OpenGL API for drawing computer graphics. It can draw precise graphics on webpage which can be free controlled by the mouse as a manner in professional software. A database server is involved to store finite element model data and its analysis result. The graphic user interface (GUI) of WebDFEA is a flexible GUI comprising three parts: the switch buttons designed by HTML, the display board and the color bar both developed in Java. The three components are independent and cooperative with each other. They can be recombined without running errors for different purposes. A ship hull section with half a hatch is chosen as the study case to test WebDFEA website. Its finite element model comprises 11,442 triangle elements (shapes). The timeframe starting when WebDFEA is connected to the end when the model is demonstrated is acceptable.     

Computer modelling of wire strands and ropes part II: Finite element-based applications

In the comparison with the theoretical analyses of wire strands reported in the literature where obviously single-layered strands with a construction of the 1 + 6 wires were modelled and analysed, this paper is focused on a multi-layered strand with a construction of the 1 + 6 + 12 + 18 wires. The geometric parametric equations developed in the first part of this paper [1] are implemented in CATIA V5 software code for geometric modelling of the multi-layered strand. The methodology of their implementation and the approach for the generation of the strand geometric model are demonstrated. To predict the behaviour of the multi-layered strand under tensile loads, the mathematical geometric model is further implemented in a finite element program. For this purpose ABAQUS/Explicit software is used. The derived 3D geometric models of the multi-layered strands and the results of the finite element elastic behaviour analyses of the strand under tension loads are validated through comparisons with experimental and theoretical data available. The results obtained confirm the correctness of the derived parametric equations and mathematical and physical importance of the finite element model developed.     

A splitting-based finite element method for the Biot poroelasticity system

In this work, we propose a finite element method for solving the linear poroelasticity equations. Both displacement and pressure are approximated by continuous piecewise polynomials. The proposed method is sequential, leading to decoupled smaller linear systems compared to the systems resulting from a fully implicit finite element approach. A priori error estimates are derived. Numerical results validate the theoretical convergence rates.     

The elastic problem for fractal media: basic theory and finite element formulation

In a previous paper [Comput. Methods Appl. Mech. Eng. 190 (2001) 6053], the framework for the mechanics of solids, deformable over fractal subsets, was outlined. Anomalous mechanical quantities with fractal dimensions were introduced, i.e., the fractal stress [σ∗], the fractal strain [ε∗] and the fractal work of deformation W∗. By means of the local fractional operators, the static and kinematic equations were obtained, and the Principle of Virtual Work for fractal media was demonstrated. In this paper, the constitutive equations of fractal elasticity are put forward. From the definition of the fractal elastic potential φ∗, the linear elastic constitutive relation is derived. The physical dimensions of the second derivatives of the elastic potential depend on the fractal dimensions of both stress and strain. Thereby, the elastic constants undergo positive or negative scaling, depending on the topological character of deformation patterns and stress flux. The direct formulation of elastic equilibrium is derived in terms of the fractional Lamé operators and of the equivalence equations at the boundary. The variational form of the elastic problem is also obtained, through minimization of the total potential energy. Finally, discretization of the fractal medium is proposed, in the spirit of the Ritz-Galerkin approach, and a finite element formulation is obtained by means of devil’s staircase interpolating splines.     

Intelligent fault-tolerant system of vibration control for flexible structures

This paper describes an intelligent fault-tolerant control method for vibration control of flexible structures. We consider a case where the fault phenomena of the control system for flexible structures can be treated as a change of system parameters. Therefore, the adaptive control method can be applied to a vibration control system for flexible structures with a fault. In this paper, a neural network (NN) adaptive control system is used to compensate for the change in the parameters of a plant with a fault. When the characteristics of the plant and of a nominal model have been agreed by a NN adaptive control system, the control method designed for the nominal model, such as decoupling feedback control or linearizing feedback control, can be used even if the change in the system parameters has been caused by a fault. To confirm the effectiveness of the proposed fault-tolerant control method, the simulational results from a 5-link robotic arm are shown at the end of the paper. This work was presented, in part, at the Fourth International Symposium on Artificial Life and Robotics, Oita, Japan, January 19–22, 1999     

A posteriori error analysis of an augmented fully-mixed formulation for the stationary Boussinesq model

In this paper we undertake an a posteriori error analysis along with its adaptive computation of a new augmented fully-mixed finite element method that we have recently proposed to numerically simulate heat driven flows in the Boussinesq approximation setting. Our approach incorporates as additional unknowns a modified pseudostress tensor field and an auxiliary vector field in the fluid and heat equations, respectively, which possibilitates the elimination of the pressure. This unknown, however, can be easily recovered by a postprocessing formula. In turn, redundant Galerkin terms are included into the weak formulation to ensure well-posedness. In this way, the resulting variational formulation is a four-field augmented scheme, whose Galerkin discretization allows a Raviart–Thomas approximation for the auxiliary unknowns and a Lagrange approximation for the velocity and the temperature. In the present work, we propose a reliable and efficient, fully-local and computable, residual-based a posteriori error estimator in two and three dimensions for the aforementioned method. Standard arguments based on duality techniques, stable Helmholtz decompositions, and well-known results from previous works, are the main underlying tools used in our methodology. Several numerical experiments illustrate the properties of the estimator and further validate the expected behavior of the associated adaptive algorithm.     

Modal synthesis method of lateral vibration analysis for rotor-bearing system

Rigid coupling and flexible connection made up of elastic coupling units are widely applied to rotor-bearing system with multi-branched shafting system. This paper proposes a modal synthesis method of lateral vibration analysis for such kind of rotor-bearing system. When the proposed approach is developed, the elastic coupling unit is defined as “flexible substructure” which is treated individually and the other parts are partitioned into some substructures which are analyzed by finite element method. The lower-frequency normal modes of the substructures are retained; whereas the higher-frequency normal modes are neglected by a frequency truncation criterion and the residual flexibility of those omitted modes is considered. The lower-frequency normal modes and residual flexibility are considered to be the assumed modes of Rayleigh–Ritz analysis of whole structure. The approach to the treatment of higher-frequency modes leads to a great reduction in the calculation time and a significant improvement in the efficiency of modal synthesis. Examples show that the proposed approach is very effective for the vibration analysis of rotor-bearing system with multi-branched shafting system and the results derived from this approach are in a good agreement with those from transfer matrix method.     

高速公路护栏的冲击动力学分析有限元模型

为了对高速公路护栏系统开展全面的冲击动力学分析及其优化设计,建立了高速公路波形梁护栏系统受冲击荷载作用的有限元模型,并对建立的护栏系统模型进行了合理性的检验.采用FEMB软件作为前处理软件,首先根据行业规范建立起包含波形护栏梁、防阻块以及立柱的护栏系统有限元模型,将建立好的三跨缩比护栏系统的有限元模型在冲击条件下与相应的冲击试验进行对比分析,检验了模型的有效性.由于真实护栏系统是多跨连续的,通过对比不同跨数的模型在冲击条件下的结果,确定了足够反映真实多跨连续护栏的合理跨数.结果表明,建立的有限元模型可准确有效地反映真实护栏系统的特性,可用于护栏系统的冲击动力学分析及其优化设计.