Showing papers on "Stiffness published in 1990"

Stiffness mapping for parallel manipulators

Abstract: Mechanical systems containing closed-loop kinematic chains can exhibit special types of singularities that result in a loss of controllability of the element of interest (output link or gripper link). Therefore, it is very important for the designer to be able to predict this type of behavior. The approach used by the author is to establish stiffness or conditioning maps of the workspace of the manipulator. A method for obtaining these maps for planar and spatial parallel manipulators is presented. The maps reveal the existence of zones where the stiffness is not acceptable and also help the designer by providing a more accurate representation of the properties of the manipulator. >

Static Response of Sands Reinforced with Randomly Distributed Fibers

Abstract: Laboratory triaxial compression tests are performed to determine the static stress‐strain response of sands reinforced with discrete, randomly distributed fibers, and to observe the influence of various fiber properties, soil properties, and test variables on soil behavior. In addition to the experimental program, a model is developed, based on a statistical theory of strength for composites, to predict the fiber contribution to strength under static loads. Randomly distributed fiber inclusions significantly increase the ultimate strength and stiffness of sands. The increase in strength and stiffness is a function of sand granulometry (i.e., gradation and particle size and shape) and fiber properties (i.e., weight fraction, aspect ratio, and modulus). The sand‐fiber composites have either a curved linear or a bilinear failure envelope, with the break occurring at a threshold confining stress called the “critical confining stress.” The magnitude of the critical confining stress decreases with an increase i...

A perceptual analysis of stiffness.

Abstract: The perception of stiffness was studied in ten human subjects using two servo-controlled electromagnetic linear motors with computercontrolled stiffness, one motor coupled to each wrist of the subject. Using the contralateral limbmatching procedure in which subjects adjusted the stiffness of the motor connected to one (matching) arm until it was perceived to be the same as that connected to the other (reference) arm, a psychophysical function for stiffness was calculated. Eight different stiffness intensities were matched by subjects with five repetitions at each stimulus amplitude. The relation between the stiffness of the reference and matching motors was linear, and the accuracy with which subjects could match stiffness paralleled that reported previously for force and displacement. The Weber fraction for stiffness was 0.23 which is three times that reported for elbow flexion forces and forearm displacement. These findings were interpreted as indicating that subjects can perceive changes in the stiffness of mechanical devices used to effect action in the environment and that these perceptions are based on sensory signals conveying force and movement information.

A new method for analyzing data from continuous depth-sensing microindentation tests

Abstract: A new parameter, hardness/modulus2 (H/E2), has been derived from the equations used to calculate the hardness and elastic modulus from data taken during continuous depth-sensing microindentation tests. This paper discusses the use of this parameter to treat the data obtained from a sample whose surface roughness was of the same scale as the size of the indents. The resulting data were widely scattered. This scatter was reduced when the data were plotted in terms of H/E2 versus stiffness. The effect of surface roughness on the hardness and elastic modulus results is removed via stiffness measurements, provided single contacts are made between the indenter and the specimen. The function relating the cross-sectional area of the indenter versus the distance from its point is not required for calculation of H/E2, but the hardness and modulus cannot be determined separately. The parameter H/E2 indicates resistance to plastic penetration in this case.

Human arm stiffness characteristics during the maintenance of posture

Abstract: When the hand is displaced from an equilibrium position, the muscles generate elastic forces to restore the original posture. In a previous study, Mussa-Ivaldi et al. (1985) have measured and characterized the field of elastic forces associated with hand posture in the horizontal plane. Hand stiffness which describes the relation between force and displacement vectors in the vicinity of equilibrium position was measured and graphically represented by an ellipse, characterized by its size, shape and orientation. The results indicated that the shape and orientation of the stiffness ellipse are strongly dependent on arm configuration. At any given hand position, however, the values of these parameters were found to remain invariant among subjects and over time. In this study we investigate the underlying causes for the observed spatial pattern of variation of the hand stiffness ellipse. Mathematically analyzing the relation between hand and joint stiffness matrices, we found that in order to produce the observed spatial variations of the stiffness ellipse, the shoulder stiffness must covary in the workspace with the stiffness component provided by the two-joint muscles. This condition was found to be satisfied by the measured joint stiffness components. Using anatomical data and considering the effects that muscle cross-sections and changes in muscle moment arms have on the joint stiffness matrix, we found that these anatomical factors are not sufficient to account for the observed pattern of variation of joint stiffness in the workspace. To examine whether the coupling between shoulder and two-joint stiffnesses results from the coactivation of muscles contributing to these stiffnesses, EMG signals were recorded from shoulder, elbow and two-joint muscles. Our results indicated that, while some muscle coactivation may indeed exist, it can be found for only some of the muscles and in only part of the workspace.

Structural damage detection based on static and modal analysis

Abstract: The present paper describes an approach for structural damage assessment that has its basis in methods of system identification. Response of a damaged structure differs from predictions obtained from an analytical model of the original structure, where the analytical model is typically a finite-element representation. The out- put error approach of system identification is employed to determine changes in the analytical model necessary to minimize differences between the measured and predicted response. Structural damage is represented by changes in element stiffness matrices resulting from variations in geometry or material properties of the structure during damage. Measurements of static deflections and vibration modes are used in the identification procedure. The identification methodology is implemented for representative structural systems. Principal shortcomings in the proposed approach and methods to circumvent these problems are also discussed. of obtaining poor results. These difficulties are clearly evi- denced by the results obtained. Smith and Hendricks8 follow a similar approach using two different identification methods to identify the stiffness matrix based on the minimum deviation approach and using eigenmodes as experimental data. Similar difficulties are re- ported in their work. The entries of the stiffness matrix corre- sponding to the damaged members do show considerable vari- ations. However, entries corresponding to undamaged members are also affected, thereby making the damage detec- tion process more uncertain. The analysis of changes in the stiffness matrix is typically cumbersome, may not always yield correct answers, and does not permit the determination of the extent of damage. This paper presents an approach that is designed to circum- vent the problems just discussed. The output error method or structural identification9 is used, wherein the analytical model is refined to minimize the difference between the predicted and measured response of the structure. Iterative nonlinear pro- gramming methods are employed to determine a solution to the unconstrained optimization problem. Damage is repre- sented by reduction in the elastic extensional and shear moduli of the element, and those are designated as the design varia- bles of the problem. The use of static structural displacements as the measured response is a departure from the standard practice of using eigenmodes alone for the identification pro- blem. Numerical evidence clearly indicates that when eigen- modes alone are used for identification, the location and ex- tent of damage predicted by the optimization approach is dependent on the number of modes used to match the measured and the predicted response. Higher modes are diffi- cult to determine and measure, and the use of static displace- ments obtained by a loading that simulates higher modes is proposed as a solution to this problem. The paper also presents an implementation of the proposed damage assessment strategies, with special focus on problems of practical significance. In this context, the use of incomplete modal or static displacement information in the identification problem is discussed. Further, the approach of treating the modulus of each structural element as an independent design variable results in a large dimensionality problem. This results in significant computational costs when using a gradient-based nonlinear programming algorithm for function minimization. The use of a reduced set of dominant design variables and the construction of equivalent reduced-order models for damage assessment are explored with some success.

A Stiffness Degradation Model for Graphite/Epoxy Laminates

Abstract: Stiffness reduction in composite laminates is an important measure of fa tigue damage. The determination of fatigue damage and the prediction of fatigue life can be made through the development of a stiffness degradation model. This paper proposes a stiffness degradation model that can be used to predict the statistical distribution of the residual stiffness of composite laminates subjected to fatigue cycling. Based on the pro posed model, two analytical methods are presented, which are capable of predicting the stiffness degradation of a particular composite specimen under cyclic loading. One method is based on the linear regression analysis and the other on the Bayesian approach. Experi ments have been performed on graphite/epoxy [90, +45, —45,0], laminates to generate sta tistically significant data for evaluating the proposed analytical models and for verifying the predicted results. It is shown that theoretical predictions for the stiffness degradation of an individual specimen and for the statistica...

Estimation of subgrade resilient modulus from standard tests

Abstract: Mechanistic pavement design procedures based on elastic layer theory require the specification of elastic moduli for each material in the pavement section. Repeated load tests yielding a resilient modulus are frequently used to characterize the soil subgrade. Due to difficulties associated with cyclic testing, approximate methods are often used for design estimates of resilient modulus. These approximations are often based only on shear strength measures and do not account for the dependence on the magnitude of cyclic deviator stress. A procedure is described to relate the soil-index properties and the moduli obtained from unconfined compression tests, to resilient modulus. Two statistical models are described and demonstrated for 11 soils from throughout the state of Tennessee. One model provides an estimation of the breakpoint resilient modulus, or the modulus at a deviator stress of 6 psi (41 kPa). The second model provides a general nonlinear relationship for the modulus of fine-grained soils as a function of deviator stress. Both models are demonstrated for a range of soils and are shown to provide a good characterization of the response for the soils investigated. Similar relationships can be developed for other subgrade soils, and may prove useful to agencies that use deterministic pavement design procedures, but lack the capability for high-production repeated-load testing.

Dynamics of an Arbitrary Flexible Body in Large Rotation and Translation

Abstract: Conventional theories underlying my multibody codes used for simulating the behavior of elastic structures undergoing large rotation and translation with small vibrations fail to predict dynamic stiffening of the structures. This can lead to significantly incorrect simulations in many practical situations. A theory that does not suffer from this defect and is valid for an arbifnary structure is given here. The formulation is based on Kane's equations and consists of two steps: First, generalized inertia forces are written for an arbitrary structure for which one is forced to linearize prematurely in the modal coordinates; next, this defect in linearization is compensated for by the introduction of contributions to the generalized active forces from the "motion stiffness" of the stnrctwe. The stress associated with the motion stiffness is identified as due to 12 sets of inertia forces and 9 sets of inertia couples distributed throughout the body during ihe most general motion of its flying reference frame. An algorithm is set for a reader wishing to implement the theory, and illustrative examples are given to demonstrate tbe validity and generality of the formulation.

Effect of spinal construct stiffness on early fusion mass incorporation: Experimental study

Abstract: The relationship between initial spinal construct stiffness and the stiffness of the resulting fusion mass was studied by performing standardized 10-segment posterior spinal fusions in goats. Animals were divided into 5 groups based on type of spinal construct, using rods of different diameters (3.2

Stiffness Characteristics of the Circular Ilizarov Device as Opposed to Conventional External Fixators

Abstract: Ilizarov proposes the use of a special circular fixation device for treatment of bone defects and nonunions or for limb lengthening. Supposition was that the success of this method has to do with the specific mechanical behavior of the device. This behavior is a result of the configuration of the fixation elements. Therefore, a mechanical study of the sensitivity of the circular compression and distraction device (CDD) to configuration parameters was performed. The CDD was found to exhibit a nonlinear stiffness behavior, in particular under axial load. This may be favorable for the induction and tolerance of bone formation. Among the different parameters tested the ring radius was the most important with respect to stiffness. In general, the stiffness of the CDD allows adjustment during postoperative management. In magnitude, it is equal or lower when compared to other fixator types.

Mass and stiffness interaction effects in analytical model modification

Abstract: The mass and stiffness matrices can be optimally corrected from incomplete modal test by using Lagrange multiplier method

Viscoelastic damping structures and related manufacturing method

Abstract: A composite structure of elastic and viscoelastic components in which dynamic loads are effectively damped by transmission through the viscoelastic components. The structure includes a continuous sandwich comprised either of a single elastic layer enclosed by two viscoelastic layers or of a single viscoelastic layer enclosed by two elastic layers such that the sandwich has little stiffness in any intended direction of loading, and two segmented elastic layers having stiffness in a desired loading direction. The segmented layers have alternating segments and gaps and are disposed one on each side of the viscoelastic layer in such a manner that the gaps of one segmented layer overlap the segments of the other segmented layer. Dynamic loads in the loading direction are transmitted back and forth from one segmented layer to the other, through the continuous sandwich layer containing the viscoelastic material, which thereby provides a high degree of damping. Static loads in the loading direction are transmitted through the elastic material in the continuous sandwich layer. By appropriate selection of elastic materials, the structure can be made suitable for the damping of loads in all directions while maintaining considerable strength and static stiffness. Appropriate selection of fiber orientations can increase the damping effect on either axial and bending loads, or on torsional loads.

Inelastic seismic response of one-storey, asymmetric-plan systems : effects of stiffness and strength distribution

Abstract: The effects of plan-wise distribution of stiffness and strength-as determined by the number, location, orientation and yield deformations of resisting elements-on the inelastic response of one-storey systems are evaluated. In particular, various systems are investigated for wide ranges of parameters involved, with the objective of establishing how the response is influenced by: (i) the presence of resisting elements perpendicular to the direction of ground motion; (ii) the number of resisting elements along the direction of ground motion; (iii) the overstrength typical of code-designed buildings; (iv) the relative values of strength and stiffness eccentricities; and (v) whether the asymmetry of the system is due to eccentricity in stiffness or in mass. The results presented for a simple excitation make it possible to explain the inconsistencies in conclusions from various earlier investigations, and to evaluate their applicability to actual buildings.

A microstructural model for the anisotropic drained stiffness of articular cartilage.

Abstract: A constitutive model for articular cartilage is developed to study directional load sharing within the soft biological tissue. Cartilage is idealized as a composite structure whose static mechanical response is dominated by distortion of a sparse fibrous network and by changes in fixed charge density. These histological features of living cartilage are represented in a microstructural analog of the tissue, linking the directionality of mechanical stiffness to the orientation of microstructure. The discretized 'model tissue' is used to define a stiffness tensor relating drained stress and strain over a regime of large deformation. The primary goal of this work was to develop a methodology permitting more complete treatment of anisotropy in the stiffness of cartilage. The results demonstrate that simple oriented microscopic behaviors can combine to produce complicated larger scale response. For the illustrative example of a homogeneous specimen subjected to confined compression, the model predicts a nonlinear anisotropic drained response, with inherent uncertainty at cellular size scales.

Damping phenomena in a wire rope vibration isolation system

Abstract: A study of the dynamic characteristics of a wire rope vibration isolation system constructed with helical isolators is presented. Emphasis is placed on the analytical modeling of damping mechanisms in the system. An experimental investigation is described in which the static stiffness curve, hysteresis curves, phase trajectories, and frequency response curves were obtained. A semi-empirical model having nonlinear stiffness, nth-power velocity damping, and variable Coulomb friction damping is developed and results are compared to experimental data. Conclusions about dynamic phenomena in the wire rope system are made based on the experimental and semi-empirical results.

Aggregate interlock: a pure-shear load transfer mechanism

Abstract: A finite element investigation was made of the behavior of jointed or cracked pavement systems equipped with a pure-shear load transfer mechanism, such as aggregate interlock. Dimensional analysis was used in the interpretation of the data, leading to a general definition of the relative joint stiffness of the pavement system in terms of its structural characteristics. Results obtained in this study were verified by comparisons with earlier published field, laboratory, and analytical information. The investigation demonstrated that deflection load transfer efficiency is related to stress load transfer efficiency and that this relationship is sensitive to the size of the applied loading (or to the gear configuration). A simple back calculation procedure is outlined to evaluate the in situ joint stiffness of such pavements. Pure-shear load transfer devices are shown to be particularly desirable under a combined externally applied and thermal loading condition, since they offer no additional restraint to longitudinal curling.

Measurement of stiffness during simulated spinal physiotherapy

Abstract: A new device was designed to simulate a physiotherapist's assessment of spinal stiffness. The device applies an oscillating postero-anterior force over a spinous process and the force-displacement relation is measured. From these data the stiffness of the movement can be computed. The accuracy and repeatability of stiffness values were found to be high when an elastic beam was tested. Test-retest reliability in 11 human subjects was investigated and found to be good.

Task-dependent changes in gain of the reflex response to imperceptible perturbations of joint position in man.

Abstract: 1. It has been demonstrated recently that, when suitably instructed, subjects could alter the stiffness at the elbow in response to a slowly and imperceptibly changing elastic load. Although evidence was provided in favour of this occurring via changes in gain of the reflex response to stretch, changes in the degree of co-contraction could not be entirely ruled out. The major objective of the present experiments was to determine if subjects could alter stiffness at the wrist in a similar task, and then to determine whether they retained this ability when co-contraction was made impossible by anaesthetizing the nerve to the wrist extensors. A second objective was to determine if changes in stiffness could be controlled independently at the wrist and elbow. 2. Subjects, with eyes closed, initially held position constant against a constant force that loaded the flexors. For the wrist, they were instructed: (i) to keep the hand as still as possible (keep position constant) or (ii) to let the hand be moved by the perturbation (keep force constant). The perturbation was an initially imperceptible elastic load whose direction (loading or unloading) could not be predicted. Subjects were also asked to indicate when the perturbation was first perceived. 3. When asked to hold position constant or force constant at the wrist, subjects demonstrated task-dependent changes in stiffness prior to perception of the perturbation. These changes in stiffness were still achieved when the nerve to the wrist extensors was anesthetized and thus co-contraction was prevented. 4. Five subjects demonstrated the ability to control stiffness independently at the wrist and the elbow although most subjects had difficulty with the task we employed to demonstrate this. 5. The results demonstrate: (i) that for the wrist, set-dependent changes in stiffness that occur prior to perception of a slowly developing perturbation can be mediated by changes in gain of reflex responses to those perturbations, and (ii) that stiffness can be controlled independently at the wrist and elbow, presumably in part by changes in gain of stretch reflexes.

Modulus and thickness of the pavement surface layer from sasw tests

Abstract: The spectral analysis of surface waves (SASW) test can be used rapidly in the field to determine the stiffness and thickness of the pavement surface layer. The test is equally applicable to asphalt concrete and portland cement concrete pavements. One of the most important features is that testing can be performed quickly (in approximately 5 min at each location). Values of Young's modulus and thickness of the surface layer are determined using a straightforward procedure. Analytical studies are presented to substantiate this procedure and to optimize its use. Several case studies from asphalt concrete pavements and one portland cement concrete pavement are presented. The results show that this adaptation of the SASW test provides values of Young's modulus that are sensitive to the elastic stiffness of the surface layer and also provides reasonable estimates of the thickness of the surface layer. In addition, changes in the stiffness of the surface layer with time and temperature are easily monitored in situ.

Submatrix approach to stiffness matrix correction using modal test data

Abstract: An efficient method six stiffness matrix correction to match modal testing data is presented. Significant reduction of unknown parameters is achieved by grouping the elements of the same stiffness characteristics and representing them as a multiplication of a scaling factor and a submatrix. A concise formulation to identify the scaling factors is found by utilizing a least squares solution. The formulation also incorporates a capability of reducing finite element mass and stiffness matrices to test degrees-of-freedom for a direct analysis/experiment correlation