Showing papers on "Direct stiffness method published in 2005"
TL;DR: It has been found that although the component of the stiffness matrix differentiating the enhanced stiffness model from the conventional one is not always positive definite, the resulting stiffness matrix can still be positive definite.
Abstract: This paper presents the enhanced stiffness modeling and analysis of robot manipulators, and a methodology for their stiffness identification and characterization. Assuming that the manipulator links are infinitely stiff, the enhanced stiffness model contains: 1) the passive and active stiffness of the joints and 2) the active stiffness created by the change in the manipulator configuration, and by external force vector acting upon the manipulator end point. The stiffness formulation not accounting for the latter is known as conventional stiffness formulation, which is obviously not complete and is valid only when: 1) the manipulator is in an unloaded quasistatic configuration and 2) the manipulator Jacobian matrix is constant throughout the workspace. The experimental system considered in this study is a Motoman SK 120 robot manipulator with a closed-chain mechanism. While the deflection of the manipulator end point under a range of external forces is provided by a high precision laser measurement system, a wrist force/torque sensor measures the external forces. Based on the experimental data and the enhanced stiffness model, the joint stiffness values are first identified. These stiffness values are then used to prove that conventional stiffness modeling is incomplete. Finally, they are employed to characterize stiffness properties of the robot manipulator. It has been found that although the component of the stiffness matrix differentiating the enhanced stiffness model from the conventional one is not always positive definite, the resulting stiffness matrix can still be positive definite. This follows that stability of the stiffness matrix is not influenced by this stiffness component. This study contributes to the previously reported work from the point of view of using the enhanced stiffness model for stiffness identification, verification and characterization, and of new experimental results proving that the conventional stiffness matrix is not complete and is valid under certain assumptions.
307 citations
29 Jul 2005
TL;DR: A novel quasistatic algorithm is presented that alleviates geometric and material indefiniteness allowing one to use fast conjugate gradient solvers during Newton-Raphson iteration and a novel strategy for treating both collision and self-collision in this context is proposed.
Abstract: Quasistatic and implicit time integration schemes are typically employed to alleviate the stringent time step restrictions imposed by their explicit counterparts. However, both quasistatic and implicit methods are subject to hidden time step restrictions associated with both the prevention of element inversion and the effects of discontinuous contact forces. Furthermore, although fast iterative solvers typically require a symmetric positive definite global stiffness matrix, a number of factors can lead to indefiniteness such as large jumps in boundary conditions, heavy compression, etc. We present a novel quasistatic algorithm that alleviates geometric and material indefiniteness allowing one to use fast conjugate gradient solvers during Newton-Raphson iteration. Additionally, we robustly compute smooth elastic forces in the presence of highly deformed, inverted elements alleviating artificial time step restrictions typically required to prevent such states. Finally, we propose a novel strategy for treating both collision and self-collision in this context.
240 citations
01 Oct 2005-Precision Engineering-journal of The International Societies for Precision Engineering and Nanotechnology
TL;DR: In this article, a stiffness model based on the way the flexure members are connected together in serial or parallel combinations is proposed to formulate the functional relationship between stiffness and dimensions as well as the free shape of the FPM.
Abstract: Stiffness plays an important role in the precise performance of flexure-based ultra-precision manipulation systems. The finite element method (FEM) is currently used to determine the stiffness of the flexure parallel mechanism (FPM) with specified dimensions and free shape. This paper presents the stiffness model based on the way the flexure members are connected together in serial or parallel combinations. The modeling allows one to formulate the functional relationship between stiffness and dimensions as well as the free shape of the FPM in the design process. For illustration, stiffness matrices of a double linear spring and a three degree-of-freedom (DOF) translational flexure parallel mechanism are established. The proposed analytical model is validated by FEM model and experiments.
156 citations
TL;DR: In this article, a numerical approach to evaluate the stiffness parameters for corrugated board is presented, which is based on a detailed micromechanical representation of a region of Corrugated Board modelled by means of finite elements.
138 citations
TL;DR: In this article, a damage diagnosis technique based on changes in dynamically measured flexibility and stiffness of structures is presented, where the objective is not only to detect the existence of damage, but also to locate it.
91 citations
TL;DR: In this paper, a higher-order theory for periodic multiphase materials is proposed, which employs an approximate, and standard, elasticity approach to the solution of the unit cell problem of periodic multi-phase materials.
Abstract: In this communication, we present a reformulation, based on the local/global stiffness matrix approach, of the recently developed higher-order theory for periodic multiphase materials, Aboudi et al. [Linear Thermoelastic Higher-Order Theory for Periodic Multiphase Materials, J. Appl. Mech., 68(5), pp. 697-707]. This reformulation reveals that the higher-order theory employs an approximate, and standard, elasticity approach to the solution of the unit cell problem of periodic multiphase materials based on direct volumeaveraging of the local field equations and satisfaction of the local continuity conditions in a surface-averge sense. This contrasts with the original formulation in which different moments of the local equilibrium equations were employed, suggesting that the theory is a variant of a micropolar, continuum-based model. The reformulation simplifies the derivation of the global system of equations governing the unit cell response, whose size is substantially reduced through elimination of redundant continuity equations employed in the original formulation, allowing one to test the theory's predictive capability in most demanding situations. Herein, we do so by estimating the elastic moduli of periodic composites characterized by repeating unit cells obtained by rotation of an infinite square fiber array through an angle about the fiber axis. Such unit cells possess no planes of material symmetry in the rotated coordinate system, and may contain a few or many fibers, depending on the rotation angle, which the reformulated theory can easily accommodate. The excellent agreement with the corresponding results obtained from the standard transformation equations confirms the new model's previously untested predictive capability for a class of periodic composites characterized by nonstandard, multi-inclusion repeating unit cells lacking planes of material symmetry. Comparison of the effective moduli and local stress fields with the corresponding results obtained from the original Generalized Method of Cells, which the higher-order theory supersedes, confirms the need for this new model, and dramatically highlights the original model's shortcomings for a certain class of unidirectional composites.
78 citations
TL;DR: In this article, a simple experimental method is presented to evaluate the frequency dependent rubber mount stiffness and damping characteristics by utilizing the measured complex frequency response function from impact test and by least-squares polynomial curve fitting the data obtained from the test.
76 citations
TL;DR: In this article, a procedure for building the dynamic stiffness matrix of two-dimensional elements with free edge boundary conditions is described, and a Kirchhoff rectangular plate element is constructed from this solution.
50 citations
TL;DR: In this paper, a scaled boundary finite element method combined with shell elements is used to represent the stiffness of a caisson foundation embedded in soil, and the accuracy of the method is tested against previous solutions for particular cases.
Abstract: Solutions are presented for stiffness coefficients to represent the elastic behavior of a caisson foundation embedded in soil. The solutions use a novel numerical technique, the scaled boundary finite element method, combined with shell elements to represent the foundation itself. The stiffness coefficients take into account the possibility of nonhomogeneity in the soil (stiffness varying with depth), the geometry of the foundation, and the contribution to the stiffness of the skirt of the caisson foundation. Tabulated values allow a simple curve fit to the stiffness values to be employed for particular cases. The accuracy of the method is tested against previous solutions for particular cases. Example calculations are given to illustrate the method.
46 citations
TL;DR: In this article, a method for selecting and understanding the performance of variable stiffness devices was developed to select a variable stiffness device for vibration control of a structure can be difficult due to the wide variety of types and capabilities of variable stiffeners.
45 citations
TL;DR: In this article, the authors presented a recursive algorithm of stiffness matrix method with improved efficiency for computing the total and surface stiffness matrices for a general multilayered anisotropic media.
Abstract: This paper presents the recursive algorithm of stiffness matrix method with improved efficiency for computing the total and surface stiffness matrices for a general multilayered anisotropic media. Based on the eigensolutions commonly available for analysis of such media, the recursive algorithm deals with eigen-submatrices directly and bypasses all intermediate layer stiffness submatrices. The improved algorithm obviates the need to compute certain inverse of the original scheme and makes the stiffness matrix recursion more robust. In situation where transfer matrix is numerically stable and easily accessible, an improved recursive algorithm is also given directly in terms of transfer submatrices without involving their explicit inverse.
TL;DR: In this paper, the authors decompose a measured stiffness matrix into a stiffness matrix for a canonically oriented transversely isotropic medium (whose properties can be readily understood) plus a generally anisotropic perturbation (representing the medium's deviation from perfect symmetry), followed by a rotation.
Abstract: Mathematically, 21 stiffnesses arranged in a 6 × 6 symmetric matrix completely describe the elastic properties of any homogeneous anisotropic medium, regardless of symmetry system and orientation. However, it can be difficult in practice to characterize an anisotropic medium's properties merely from casual inspection of its (often experimentally measured) stiffness matrix. For characterization purposes, it is better to decompose a measured stiffness matrix into a stiffness matrix for a canonically oriented transversely isotropic (TI) medium (whose properties can be readily understood) plus a generally anisotropic perturbation (representing the medium's deviation from perfect symmetry), followed by a rotation (giving the relationship between the medium's natural coordinate system and the measurement coordinate system). To accomplish this decomposition, we must find the rotated symmetric medium that best approximates a given stiffness matrix. An analytical formula exists for calculating the distance between...
01 Jan 2005
TL;DR: A FEM-based method which rely on the decomposition of the deformation of each element into a rigid motion and a pure deformation, and a fast implicit dynamic integration without assembling a global stiffness matrix is presented.
Abstract: Many applications in biomedical engineering and surgical simulators require effective modeling methods for dynamic interactive simulations. Due to its high computation time, the standard Finite Element Method (FEM) cannot be used in such cases. A FEM-based method is first presented, which rely on the decomposition of the deformation of each element into a rigid motion and a pure deformation, and a fast implicit dynamic integration without assembling a global stiffness matrix. A second physically-based discrete method is also proposed, derived from computer graphics modeling. These methods are finally compared, in terms of accuracy and speed, to theoretical problems, FEMresults and experimental data.
18 Apr 2005
TL;DR: The purpose of this work is to evaluate the H4 stiffness, ie the displacement response of the tool controlled point when it is submitted to a given force using an analytical method.
Abstract: The H4 robot is a four-degree of freedom (dof) parallel machine. The purpose of this work is to evaluate the H4 stiffness, ie the displacement response of the tool controlled point when it is submitted to a given force using an analytical method. A stiffness analysis based on analytical calculations is performed. It has the advantage to be rather fast and easy to integrate into a design optimization. This method allows to compute stiffness matrix of parallel robots and takes into account particularity of parallel robots with articulated traveling plate. Some numerical results are presented at the end of this paper for the H4 first prototype.
01 Jan 2005
TL;DR: In this article, the harmonic balance method is used for the calculation of effective stiffness and damping coefficients of non-linear joints between linear substructures to characterize the properties of the nonlinear joints.
Abstract: paper, a method is presented, which aims at the extension of the finite element method for the description of the dynamic behaviour of structures with non-linear joints. Such non-linear joints may either be structural connections, such as bolted or riveted joints between otherwise linear substructures, or may be non-linear interface conditions, such as friction, clearance, or bilinear stiffness between pre-loaded contacting surfaces. The approach to be presented is based on the harmonic balance method for the calculation of effective stiffness and damping coefficients, which shall characterise the properties of the non-linear joints between linear substructures. The representation of non-linear joints by their effective stiffness and damping properties allows for the calculation of non-linear frequency responses. The parameters describing the stiffness and damping properties of a joint generally suffer from a huge amount of uncertainty, even in the linear case. The calculation of the effective stiffness and damping properties of a simple bolted joint may be considered as an example. The determination of parameters describing the non-linear stiffness and damping properties is even more subject to uncertainty. Therefore, the application of a model updating procedure will be presented here, which allows for the adjustment of not only linear stiffness and damping parameters but also of such non-linear parameters by minimising the differences between experimental and analytical non-linear frequency response functions. Thus, the application of this model updating procedure yields a finite element model with an improved prediction capability in the non-linear regime. The procedure to be presented was developed within the European Research Project CERES and was applied there for non-linear frequency response analysis and non-linear joint parameter identification of a complex large order finite element model of an aero-engine structure. Examples will be presented.
TL;DR: In this paper, a design-oriented strength-allocation procedure to arrive at such strength and stiffness distributions is presented, and its effectiveness in minimizing torsional response is demonstrated through comparison of seismic performance of structures having strength allocated on the basis of the proposed procedure with those following current UBC and EC8 torsion provisions.
Abstract: Recent studies have pointed out that the stiffness and strength of many lateral force-resisting elements (LFRE) are dependent parameters. This paper examines the implication of this finding in the distribution of design strength among LFRE. It is shown here that in order to minimize torsional response, one should use a strength/stiffness distribution combination that leads to the location of the center of strength, CV, and the center of stiffness, CR, on opposite sides of the center of mass, CM. A design-oriented strength-allocation procedure to arrive at such strength and stiffness distributions is presented. Its effectiveness in minimizing torsional response is demonstrated through comparison of seismic performance of structures having strength allocated on the basis of the proposed procedure with those following current UBC and EC8 torsional provisions.
TL;DR: In this paper, a method for locating and estimating structural damage in two and three-dimensional analytical models of buildings is presented, where damage is defined in terms of changes in elements stiffness.
TL;DR: In this article, a ring model was used to predict the vertical stiffness of a single tire without regard to the physics of the tire, and a simple formula for tire vertical stiffness was developed from the master curve, correlated to a wide variety of tire stiffness measurements.
Abstract: Vertical stiffness is a fundamentally important property of tires. This property is often expressed by some empirical formula not directly tied to the physics of the tire. It would be useful to have a physics‐based formula that could reliably predict vertical stiffness from a minimum set of pertinent, easily obtained parameters. This paper extends the ring model used by Koutny in his thermodynamic studies of tire stiffness and applies it directly to the question of vertical stiffness without regard to thermodynamics. A master curve of tire vertical stiffness is obtained that includes all tires that meet the assumptions of the model, regardless of size. A simple formula for tire vertical stiffness is developed from the master curve. The formula is correlated to a wide variety of tire stiffness measurements. One use of such a formula could be to develop more reliable tire load capacity standards. In the course of the analysis, it is found that the vertical stiffness depends significantly on the str...
TL;DR: In this article, the authors present a variable bending stiffness model using the tangent stiffness method and its implementation in a classical finite-element formulation adapted for nonlinear analysis under arbitrary loading.
Abstract: Stranded conductors are widely used structural components. Owing to their construction in layers, their bending stiffness may vary according to their tension, curvature and deformation history. Recently, a sound and practical model of variable bending stiffness using the secant stiffness method became available. Based on the same physical assumptions, This work presents the development of a variable bending stiffness model using the tangent stiffness method and its implementation in a classical finite-element formulation adapted for nonlinear analysis under arbitrary loading. This extends its use to a general finite-element program. Comparisons with static and dynamic tests on short-span substation conductors show that the model computes a representative bending stiffness for such cases and yields adequate predictions of tractions generated at their ends, in both static and dynamic regimes.
TL;DR: In this article, the authors defined stiffness fields, stiffness lines, and stiffness decay vectors using newly introduced U* potential lines and showed that a load path can be expressed as a stiffness line that has a minimum stiffness decay vector.
Abstract: A concept of a parameter U* has been introduced by the authors to express load transfer paths in a structure. In this paper, matrix formulation of internal stiffness shows that the value of U* expresses a degree of connection between a loading point and an internal arbitrary point. Stiffness fields, stiffness lines, and stiffness decay vectors are defined using newly introduced U* potential lines. A concept of a load path can be expressed as a stiffness line that has a minimum stiffness decay vector. A simple model structure is calculated using FEM for an application of U* analysis. The distribution of U* values shows that a diagonal member between a loading point and a support point Plays an important rold for the load transfer.
05 Dec 2005
TL;DR: This paper explores a novel six degree-of-freedom large workspace flexure parallel mechanism based on the concept of wide-range flexure hinge, which can attain sub-micron scale accuracy over cubic centimeter motion range.
Abstract: Parallel-structure flexure mechanisms are increasingly designed due to their superior characteristics. This paper explores a novel six degree-of-freedom large workspace flexure parallel mechanism based on the concept of wide-range flexure hinge, which can attain sub-micron scale accuracy over cubic centimeter motion range. The geometric dimensions of the flexure hinges utilized in this mechanism as passive joints will influence the system stiffness directly and other properties indirectly such as the workspace, load-carrying capacity, and driving-load capacity etc. In this paper, the stiffness model of individual flexure hinge is established firstly, and then the stiffness of the whole flexure mechanism is modeled via assembling stiffness matrices and formulating constraint equations. Based on the system stiffness model of the whole mechanism, the stiffness atlases' analysis is presented which provides theoretical principles for designing and developing this kind of flexure parallel mechanism in further. Finally, a 6-PSS large workspace flexure parallel mechanism prototype is proposed according to the analysis results, which will be utilized in the precision positioning.
TL;DR: In this article, an explicit finite element method for Biot dynamic formulation in fluid-saturated porous media is proposed, which does not need to assemble a global stiffness matrix and solve a set of linear equations in each time step, so the computational effort and memory requirement can be reduced considerably.
01 Jan 2005
TL;DR: In this article, the coupling between lateral and torsional vibrations has been investigated for a rotor dynamic system with breathing crack model, and the stiffness matrix has been developed for the shaft element which accounts for the effect of the crack and all six degrees of freedom per node.
Abstract: The coupling between lateral and torsional vibrations has been investigated for a rotor dynamic system with breathing crack model. The stiffness matrix has been developed for the shaft element which accounts for the effect of the crack and all six degrees of freedom per node. Since the off-diagonal terms of the stiffness matrix represent the coupling of the respective modes, the special attention has been paid on accurate determination of their values. Based on the concepts of fracture mechanics, the variation of the stiffness matrix over the full shaft revolution is represented by the truncated cosine series where the fitting coefficient matrices are extracted from the stiffness matrices of the cracked shaft for a number of its different angular positions. The variation of the system eigenfrequencies and dynamic response of the rotor with two cracks have been studied for various shaft geometries, crack axial locations, and relative phase of cracks.Copyright © 2005 by ASME
TL;DR: In this paper, a decomposition-based assembly synthesis for structural stiffness is presented, where the three-dimensional finite element model of a vehicle body-in-white (BIW) is optimally decomposed into a set of components considering stiffness of the assembled structure under given loading conditions, manufacturability, and assembleability of components.
Abstract: This paper presents an extension of our previous work on decomposition-based assembly synthesis for structural stiffness, where the three-dimensional finite element model of a vehicle body-in-white (BIW) is optimally decomposed into a set of components considering (1) stiffness of the assembled structure under given loading conditions, (2) manufacturability, and (3) assembleability of components. Two case studies, each focusing on the decomposition of a different portion of a BIW, are discussed. In the first case study, the side frame is decomposed for the minimum distortion of front door frame geometry under global bending. In the second case study, the side/floor frame and floor panels are decomposed for the minimum floor deflections under global bending. In each case study, multiobjective genetic algorithm with graph-based crossover, combined with finite element methods analyses, is used to obtain Pareto optimal solutions. Representative designs are selected from the Pareto front and trade-offs among stiffness, manufacturability, and assembleability are discussed.
TL;DR: This paper presents a computer-based method for nonlinear analysis of planar steel frameworks under monotonic loading that is directly based on the matrix displacement method of analysis and is shown to give results comparable to both experimental and analytical results previously published in the literature.
TL;DR: In this paper, an exact dynamic stiffness matrix for a two-part beam-mass system is developed from the free vibration theory of a Bernoulli-Euler beam, which allows an exact free vibration analysis of structures such as a plane or a space frame.
Abstract: Using two different, but related approaches, an exact dynamic stiffness matrix for a two-part beam-mass system is developed from the free vibration theory of a Bernoulli-Euler beam. The first approach is based on matrix transformation while the second one is a direct approach in which the kinematical conditions at the interfaces of the two-part beam-mass system are satisfied. Both procedures allow an exact free vibration analysis of structures such as a plane or a space frame, consisting of one or more two-part beam-mass systems. The two-part beam-mass system described in this paper is essentially a structural member consisting of two different beam segments between which there is a rigid mass element that may have rotatory inertia. Numerical checks to show that the two methods generate identical dynamic stiffness matrices were performed for a wide range of frequency values. Once the dynamic stiffness matrix is obtained using any of the two methods, the Wittrick-Williams algorithm is applied to compute the natural frequencies of some frameworks consisting of two-part beam-mass systems. Numerical results are discussed and the paper concludes with some remarks.
TL;DR: In this paper, a geometric stiffness matrix is derived from load perturbation of the discrete equilibrium equations of a given linear finite element formulation, and an out-of-plane geometric stiffness matrices is then introduced to account for the effect of rigid body rotations on member forces.
TL;DR: In this paper, a stiffness matrix evaluation method based on the boundary curve approximation by piecewise oblique curves which can cross several elements was proposed for the discretized system by the fixed-grid method.
TL;DR: In this article, the actuation stiffness of a set of steel Kagome Double-Layer Grid (KDLG) structures with brazed joints is measured experimentally and compared with predictions by the finite element method.
Abstract: The actuation stiffness of a set of steel Kagome Double-Layer Grid (KDLG) structures with brazed joints is measured experimentally and compared with predictions by the finite element method. The predicted actuation stiffnesses for the perfect KDLGs much exceed the measured values, and it is argued that the low values of observed actuation stiffness are due to the presence of geometric imperfections introduced during manufacture. In order to assess the significance of geometric defects upon actuation stiffness, finite element calculations are performed on structures with a stochastic dispersion in nodal position from the perfectly periodic arrangement, and on structures with wavy bars. It is found that bar waviness has the dominant effect upon the actuation stiffness. The predicted actuation stiffness for the imperfect structures are in satisfactory agreement with the measured values assuming the same level of imperfection between theory and experiment.
TL;DR: All parameters for the RFMB generalized stiffness matrix can be directly derived from component test, resulting in a more rigorous definition of test/analysis correlation, and is implemented in the latest release of the general purpose finite element program, MSC.Nastran.
Abstract: An improved method of mixed-boundary component representation is presented. This residual flexibility mixed-boundary (RFMB) method presents two compelling features over the existing mixed-boundary methods. First, RFMB is accurate for the entire range of component boundary representations, that is, from all-fixed to mixed to all-free boundaries; therefore, resorting to other methods to cover the all-fixed- or all-free-boundary cases is not necessary. Second, all parameters for the RFMB generalized stiffness matrix can be directly derived from component test, resulting in a more rigorous definition of test/analysis correlation. Two example problems are presented, demonstrating the benefits of the subject method. This new RFMB method has been implemented in the latest release of the general purpose finite element program, MSC.Nastran, as the default.