Showing papers on "Stiffness published in 1998"
TL;DR: In this paper, a new plastic-damage model for concrete subjected to cyclic loading is developed using the concepts of fracture-energy-based damage and stiffness degradation in continuum damage mechanics.
Abstract: A new plastic-damage model for concrete subjected to cyclic loading is developed using the concepts of fracture-energy-based damage and stiffness degradation in continuum damage mechanics. Two damage variables, one for tensile damage and the other for compressive damage, and a yield function with multiple-hardening variables are introduced to account for different damage states. The uniaxial strength functions are factored into two parts, corresponding to the effective stress and the degradation of elastic stiffness. The constitutive relations for elastoplastic responses are decoupled from the degradation damage response, which provides advantages in the numerical implementation. In the present model, the strength function for the effective stress is used to control the evolution of the yield surface, so that calibration with experimental results is convenient. A simple and thermodynamically consistent scalar degradation model is introduced to simulate the effect of damage on elastic stiffness and its recovery during crack opening and closing. The performance of the plastic-damage model is demonstrated with several numerical examples of simulating monotonically and cyclically loaded concrete specimens.
2,825 citations
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01 Nov 1998TL;DR: In this paper, the design process of fiber reinforced composites has been studied in terms of stiffness and compliance in the context of failure and failure of first-ply failure, and failure failure.
Abstract: Introduction Basic Concepts The Design Process Composites Design Methods Design for Reliability Fracture Mechanics Materials Fiber Reinforcements Fiber-Matrix Compatibility Fiber Forms Matrix Materials Thermoset Matrices Thermoplastic Matrices Creep, Temperature, and Moisture Corrosion Resistance Flammability Manufacturing Processes Hand Lay-up Pre-preg Lay-up Bag Molding Autoclave Processing Compression Molding Resin Transfer Molding Vacuum Assisted Resin Transfer Molding Pultrusion Filament Winding Micro-mechanics Basic Concepts Stiffness Moisture and Thermal Expansion Strength Ply Mechanics Coordinate Systems Stress and Strain Stress-Strain Equations Off-axis Stiffness Macro-mechanics Plate Stiffness and Compliance Computation of Stresses Common Laminate Types Laminate Moduli Design Using Carpet Plots Hygro-thermal Stresses (*) Strength Lamina Failure Criteria Laminate First Ply Failure Laminate Strength Strength Design Using Carpet Plots Stress Concentrations (*) Damage Continuum Damage Mechanics Longitudinal Tensile Damage Longitudinal Compression Damage Transverse Tension and In-plane Shear Fabric-reinforced Composites Weave Pattern Description Analysis Tow Properties Element Stiffness and Constitutive Relationship Laminate Properties Failure Analysis Woven Fabrics with Gap Twill and Satin Randomly Oriented Reinforcement Beams Preliminary Design Thin Walled Beams Plates and Stiffened Panels Plate Bending Plate Buckling Stiffened Panels Shells Shells of Revolution Cylindrical Shells with General Loading Strengthening of Reinforced Concrete Strengthening Design Materials Flexural Strengthening of RC Beams Shear Strengthening Beam-column Appendices Bibliography
1,013 citations
TL;DR: It is found that human runners adjust their leg stiffness to accommodate changes in surface stiffness, allowing them to maintain similar running mechanics on different surfaces, and suggests that incorporating an adjustable leg stiffness in the design of hopping and running robots is important if they are to match the agility and speed of animals on varied terrain.
Abstract: A running animal coordinates the actions of many muscles, tendons, and ligaments in its leg so that the overall leg behaves like a single mechanical spring during ground contact. Experimental observations have revealed that an animal's leg stiffness is independent of both speed and gravity level, suggesting that it is dictated by inherent musculoskeletal properties. However, if leg stiffness was invariant, the biomechanics of running (e.g. peak ground reaction force and ground contact time) would change when an animal encountered different surfaces in the natural world. We found that human runners adjust their leg stiffness to accommodate changes in surface stiffness, allowing them to maintain similar running mechanics on different surfaces. These results provide important insight into mechanics and control of animal locomotion and suggest that incorporating an adjustable leg stiffness in the design of hopping and running robots is important if they are to match the agility and speed of animals on varied terrain.
584 citations
TL;DR: Both joint stiffness and limb geometry adjustments are important in adjusting leg stiffness to allow similar hopping on different surfaces, and a computer simulation was used to examine the sensitivity ofLeg stiffness to the observed changes in ankle stiffness and touchdown knee angle.
Abstract: When humans hop in place or run forward, leg stiffness is increased to offset reductions in surface stiffness, allowing the global kinematics and mechanics to remain the same on all surfaces. The purpose of the present study was to determine the mechanism for adjusting leg stiffness. Seven subjects hopped in place on surfaces of different stiffnesses (23-35,000 kN/m) while force platform, kinematic, and electromyographic data were collected. Leg stiffness approximately doubled between the most stiff surface and the least stiff surface. Over the same range of surfaces, ankle torsional stiffness increased 1.75-fold, and the knee became more extended at the time of touchdown (2.81 vs. 2.65 rad). We used a computer simulation to examine the sensitivity of leg stiffness to the observed changes in ankle stiffness and touchdown knee angle. Our model consisted of four segments (foot, shank, thigh, head-arms-trunk) interconnected by three torsional springs (ankle, knee, hip). In the model, an increase in ankle stiffness 1.75-fold caused leg stiffness to increase 1.7-fold. A change in touchdown knee angle as observed in the subjects caused leg stiffness to increase 1.3-fold. Thus both joint stiffness and limb geometry adjustments are important in adjusting leg stiffness to allow similar hopping on different surfaces.
447 citations
TL;DR: In this article, the effect of the distribution of solid between the cell faces and edges on mechanical properties using finite element analysis of idealized 2D (hexagonal honeycomb) and 3D (closed-cell tetrakaidecahedral foam) cellular materials was investigated.
428 citations
TL;DR: In this paper, a new plastic-damage constitutive model for cyclic loading of concrete has been developed for the earthquake analysis of concrete dams, which consistently includes the effects of strain softening, represented by separate damage variables for tension and compression.
Abstract: A new plastic-damage constitutive model for cyclic loading of concrete has been developed for the earthquake analysis of concrete dams. The rate-independent model consistently includes the effects of strain softening, represented by separate damage variables for tension and compression. A simple scalar degradation model simulates the effects of damage on the elastic stiffness and the recovery of stiffness after cracks close. To simulate large crack opening displacements, the evolution of inelastic strain is stopped beyond a critical value for the tensile damage variable. Subsequent deformation can be recovered upon crack closing. The rate-independent plastic-damage model forms the backbone model for a rate-dependent viscoplastic extension. The rate-dependent regularization is necessary to obtain a unique and mesh objective numerical solution. Damping is represented as a linear viscoelastic behaviour proportional to the elastic stiffness including the degradation damage. The plastic-damage constitutive model is used to evaluate the response of Koyna dam in the 1967 Koyna earthquake. The analysis shows two localized cracks forming and then joining at the change in geometry of the upper part of the dam. The upper portion of the dam vibrates essentially as rigid-body rocking motion after the upper cracks form, but the dam remains stable. The vertical component of ground motion influences the post-cracking response. © 1998 John Wiley & Sons, Ltd.
410 citations
TL;DR: The present results suggest that humans control directional characteristics of hand stiffness by changing joint stiffness to achieve various interactions with objects.
Abstract: Human arm viscoelasticity is important in stabilizing posture, movement, and in interacting with objects. Viscoelastic spatial characteristics are usually indexed by the size, shape, and orientation of a hand stiffness ellipse. It is well known that arm posture is a dominant factor in determining the properties of the stiffness ellipse. However, it is still unclear how much joint stiffness can change under different conditions, and the effects of that change on the spatial characteristics of hand stiffness are poorly examined. To investigate the dexterous control mechanisms of the human arm, we studied the controllability and spatial characteristics of viscoelastic properties of human multijoint arm during different cocontractions and force interactions in various directions and amplitudes in a horizontal plane. We found that different cocontraction ratios between shoulder and elbow joints can produce changes in the shape and orientation of the stiffness ellipse, especially at proximal hand positions. During force regulation tasks we found that shoulder and elbow single-joint stiffness was each roughly proportional to the torque of its own joint, and cross-joint stiffness was correlated with elbow torque. Similar tendencies were also found in the viscosity–torque relationships. As a result of the joint stiffness changes, the orientation and shape of the stiffness ellipses varied during force regulation tasks as well. Based on these observations, we consider why we can change the ellipse characteristics especially in the proximal posture. The present results suggest that humans control directional characteristics of hand stiffness by changing joint stiffness to achieve various interactions with objects.
364 citations
TL;DR: Testing the hypothesis that cortical bone loss, trabecular bone density and the amount of bone ingrowth vary as a function of stem stiffness in a canine cementless hip replacement model found different patterns of functional adaptation are consistent with the idea that reduced stem stiffness enhances proximal load transfer.
223 citations
TL;DR: It is shown that assigning the same stiffness to all springs fails to simulate a uniform elastic membrane, for equilibrium calculations, and a formula for spring stiffness that provides a more accurate simulation is derived.
Abstract: Spring meshes have been used to model elastic material in computer graphics, with skin, textiles, and soft tissue being typical applications. A spring mesh is a system of vertices and edges, possibly with highly irregular geometry, in which each edge is a spring, and springs are connected by "pin-joints" ("gimbaljoints" in three dimensions) at the vertices. This method is computationally attractive, compared to some alternatives. Given a specified set of elastic material properties, however, the question of whether a particular spring mesh accurately simulates those properties has been largely ignored in the literature. Additionally, previous reports on the technique are silent on the subject of assigning stiffness to the various springs. This paper shows that assigning the same stiffness to all springs fails to simulate a uniform elastic membrane, for equilibrium calculations. A formula for spring stiffness that provides a more accurate simulation is then derived. In its simplest form, this formula specifies that stiffness varies as triangle area over edge length squared. Its accuracy is demonstrated on test and practical mesh examples. It is also shown that, in general, an exact simulation is not possible.
219 citations
TL;DR: Microstructurally accurate, large-scale finite element models were used to predict the experimental apparent stiffness of human vertebral cancellous bone and to estimate the trabecular hard tissue stiffness.
204 citations
TL;DR: In this paper, a finite difference formulation for vibration analysis of structural cables is introduced, which incorporates into a unified solution the effects of the bending stiffness of cable and its sag-extensibility characteristics and provides a tool for accurate determination of vibration mode shapes and frequencies.
Abstract: In this paper, a finite difference formulation for vibration analysis of structural cables is introduced. This formulation incorporates into a unified solution the effects of the bending stiffness of cable and its sag-extensibility characteristics and provides a tool for accurate determination of vibration mode shapes and frequencies. Various cable-end conditions, variable cross sections, and intermediate springs and/or dampers are taken into account. Using a nondimensional form of this formulation, a parametric study was conducted on the effects of sag-extensibility and bending stiffness. The formulation is verified with available theoretical solutions and compared with finite-element analyses. Capabilities of this formulation are demonstrated through examples. A simple relationship among nondimensional cable parameters is also introduced for the range of parameters applicable to stay cables in cable-stayed bridges. This simple relationship provides an accurate tool for measurement of tension forces in s...
TL;DR: Observations suggest that a combination of mechanical testing, three‐dimensional imaging, and finite‐element modeling might enable the physiological variations in tissue moduli to be determined as a function of age and gender.
TL;DR: In this paper, a torsionally constrained polymer is modeled as a fluctuating rod with bend stiffness AkBT and twist stiffness CkBT, and an experimental determination of the microscopic twist stiffness is obtained using C = 109 nm.
Abstract: We investigate the statistical mechanics of a torsionally constrained polymer. The polymer is modeled as a fluctuating rod with bend stiffness AkBT and twist stiffness CkBT. In such a model, thermal bend fluctuations couple geometrically to an applied torque through the relation Lk = Tw + Wr. We explore this coupling and find agreement between the predictions of our model and recent experimental results on single λ-DNA molecules. This analysis affords an experimental determination of the microscopic twist stiffness (averaged over a helix repeat). Quantitative agreement between theory and experiment is obtained using C = 109 nm (i.e., twist rigidity CkBT = 4.5 × 10-19 erg cm). The theory further predicts a thermal reduction of the effective twist rigidity induced by bend fluctuations. Finally, we find a small reflection of molecular chirality in the experimental data and interpret it in terms of a twist−stretch coupling of the DNA duplex.
TL;DR: In this paper, an extension to the available direct methods of model updating to estimate both the damping and stiffness matrices of a structure is presented, with the constraint that the measured modal data is reproduced.
Abstract: This note has outlined an extension to the available direct methods of model updating to estimate both the damping and stiffness matrices of a structure. The method minimizes the change in the damping and stiffness matrices, with the constraint that the measured modal data is reproduced
TL;DR: In this article, a two-dimensional finite element model is adopted to study the behavior of pontoon-type floating breakwaters in beam waves, and the stiffness coefficients of the slack mooring lines are idealized as the linear stiffness coefficients, which can be derived from the basic catenary equations of the cable.
TL;DR: In this paper, the transverse isotropy of small-strain stiffness of London clay and kaolin up to high stresses was investigated using the triaxial triaxials and the results showed that the inherent or structural anisotropy was a variable factor resulting from the plastic strain history and is not related to its natural structure.
Abstract: The paper presents the results of a program of research investigating the effectiveness of bender elements when used in conjunction with the triaxial apparatus for measuring the anisotropy of small strain stiffness of fine-grained soils. Tests were carried out on both intact and reconstituted samples of London clay and on kaolin up to high stresses. The paper shows that the transverse isotropy of small-strain stiffness that commonly occurs in many soils because of a one-dimensional loading history can be fully investigated in the conventional triaxial apparatus and that London clay is an example of such a soil. The stress-induced component of anisotropy was found to be very small for axi-symmetric loading conditions common to both the appartus and the in situ state of these soils. In contrast, the inherent or structural anisotropy was much more significant and is shown to be a variable factor resulting from the plastic strain history and is not related to its natural structure. Consequently, inherent anisotropy is reversible, but the rate of change is very slow when a new regime of stresses is imposed. Inherent anisotropy of the very small strain stiffness also persists long after the plastic strains of the soil have become oriented toward the new stresses.
TL;DR: In this paper, a shear connector stiffness based approach is developed to calculate the maximum beam deflection of steel-concrete composite beams with partial shear interaction, which is related to the strength of shear connectors in the composite beam.
Abstract: This paper is concerned with calculating the maximum deflection of steel-concrete composite beams with partial shear interaction. Under the guidance of various current design codes, this deflection is related to the strength of shear connectors in the composite beam. In this paper, a shear connector stiffness based approach is developed. This approach is obtained based on the solution for a simply supported beam under uniformly distributed load. To validate this approach, the predicted maximum beam deflection using the proposed method is compared against the results from a linear-elastic finite-element analysis and some tests on composite beams. In both the finite-element analysis and the proposed method, uniform distribution of shear connection stiffness along the beam length is assumed. In the absence of a reliable way to calculate the shear connector stiffness, this paper suggests a simple procedure to obtain this value so that the proposed method may be used in practice.
TL;DR: In this paper, the authors derived identical mathematical expressions for viscoelastic and viscous damper-brace components as the function of two fundamental non-dimensional parameters, which are used to investigate the properties of VE and VE systems by conducting parameter analysis.
Abstract: Identical mathematical expressions for viscoelastic and viscous damper-brace components are derived as the function of two fundamental nondimensional parameters. These two parameters are used to investigate the properties of viscoelastic (VE) and viscous (VS) systems by conducting parameter analysis. Usually both VS and VE damper-brace components provide added stiffness and damping to the whole system. The magnitude of the added stiffness and damping depends not only on the damper, but also on the interaction of the damper with other members of the frame. Under conditions of low frequency and stiff brace, the added stiffness provided by a VS damper-brace component is negligible. Based on harmonic theory, closed-form solutions for seismic response prediction are presented and are used to determine the optimal design. As an example, the seismic performance of a 10-story steel frame incorporated with VE and VS dampers is studied.
01 Jun 1998
TL;DR: It is shown that the 20-dimensional subspace of "realizable" spatial stiffness matrices achieved with parallel simple springs is defined by a linear necessary and sufficient condition on the positive semidefinite stiffness matrix.
Abstract: We identify the space of spatial compliant behavior that can be achieved through the use of simple springs connected in parallel to a single rigid body. Here, the expression "simple spring" refers to the set of compliant relations associated with passive translational springs and rotational springs. The restriction on the stiffness matrices is derived using the screw theory by investigating the compliant behavior of individual simple springs. We show that the restriction results from the fact that simple springs can only provide either a pure force or a pure torque to the suspended body. We show that the 20-dimensional subspace of "realizable" spatial stiffness matrices achieved with parallel simple springs is defined by a linear necessary and sufficient condition on the positive semidefinite stiffness matrix. A procedure to synthesize an arbitrary full-rank stiffness matrix within this realizable subspace is provided. This procedure requires no more than seven simple springs.
TL;DR: In this article, the linear elastic response of a multicontact interface to a moderate shear force is investigated, i.e. below the threshold for incipient sliding, in the spirit of macroscopic friction laws, which should be of practical interest when evaluating the performances of a built-up system.
Abstract: The macroscopic multicontact between two rough nominally flat surfaces is a common object whose physics is only partially understood. This paper is aimed at giving experimental evidence for the linear elastic response of a multicontact interface to a moderate shear force, i.e. below the threshold for incipient sliding. Non–intuitive properties of the interfacial shear stiffness are exhibited, in the spirit of macroscopic friction laws, which should be of practical interest when evaluating the performances of a built–up system. These are explained qualitively within the random surface framework prevailing in multicontact mechanics, and a numerical treatement of the three–dimensional profile of a real rough surface is proposed, which enables a direct quantitative simulation of the elastic stiffness. This is found to be compatible with experimental data on a polymer glass and an aluminium alloy. The sensitivity of interfacial stiffness measurements is discussed, and illustrated by the experimental evidence of the plastic deformation of aluminium alloy asperities under light nominal pressure. This emphasizes the need for an elastoplastic description of asperity deformation within a multicontact.
TL;DR: In this article, failure envelopes for unidirectional composites and multi-layered composite laminates have been predicted by linear laminate theory using the ply-by-ply discount method with parallel spring stiffness reduction model.
TL;DR: In this paper, a sinusoidal displacement modulation (DM) and lock-in technique was used to characterize local viscoelastic properties of carbon-reinforced polymers.
Abstract: Scanning force microscopy (SFM) has been used to assess the local mechanical properties of fibre-reinforced polymers. Using a sinusoidal displacement modulation (DM) and lock-in technique the method allows to characterize local viscoelastic properties with a high lateral resolution. The simultaneous measurement of the local electrical conductivity is proposed which facilitates the interpretation of the mechanical data. The investigation of cross-sections perpendicular to the axis of carbon fibres embedded in PPS delivers some information about the change in local stiffness within the interfacial region. As a first approach, assuming a single-exponential decrease in local stiffness along a radial line from fibre to polymer we find characteristic decay lengths which are distributed in a range between 20 and 80 nm. Further, a modified DM-mode is proposed which is expected to provide a contrast enhancement of the signal which is related to local stiffness. This can be achieved by installing an additional feedback loop which keeps constant the amplitude of dynamic indentation (CDI-mode).
TL;DR: In this paper, a combination of electrostatic actuators is used to tune the linear and nonlinear stiffness coefficients of a uniaxial micromechanical device without affecting the resonant frequency or the linear stiffness.
Abstract: Using a combination of electrostatic actuators, we present a method to independently tune the linear and nonlinear stiffness coefficients of a uniaxial micromechanical device. To demonstrate the method's capability, we investigated the tuning of an oscillator with linear and cubic restoring forces. We successfully tuned the cubic stiffness from 0.31/spl times/10/sup 11/ to -5.1/spl times/10/sup 11/ N/m/sup 3/ without affecting the resonant frequency or the linear stiffness. Numerical results are presented which characterize the actuators and indicate important design parameters. Finally, issues such as actuator design, quadratic stiffness, and stability are discussed.
TL;DR: In this article, the stiffness of a rail pad is measured as a function of the excitation frequency for known loading conditions, where the resilient element is placed between two large blocks, the vibrations of which are measured.
TL;DR: In this article, the results of a numerical study of the horizontal deformations of reinforced soil walls with a continuous panel facing are presented, and the most important material parameters are shown to be the rei...
Abstract: The results of a numerical study of the horizontal deformations of reinforced soil walls with a continuous panel facing are presented. The most important material parameters are shown to be the rei...
TL;DR: The Fast Support Layout Optimization (FSLO) model proposed in this paper uses a finite element analysis (FEA) model to characterize workpiece stiffness and then uses the FEA model to determine support locations that will minimize the maximum displacement to tolerance ratio of a set of workpiece features subject to a system of machining loads.
Abstract: Machining-fixture supports are used to increase workpiece rigidity. A critical problem of machining-fixture design is where to place a fixed number of supports in order to minimize workpiece deformation during machining. This paper presents the Fast Support Layout Optimization (FSLO) model. The objective of the FSLO model is to determine support locations that will minimize the maximum displacement-to-tolerance ratio of a set of workpiece features subject to a system of machining loads. The FSLO model utilizes a Finite Element Analysis (FEA) model to characterize workpiece stiffness. Solution of the FSLO model improves an existing support layout by systematically altering the boundary conditions applied to the FEA model. The FSLO model is unique in that its solution time is both very small and insensitive to the size of the FEA model, the sizes of machined features considered, and the sizes of the candidate regions of the supports. In addition to describing the formulation of the FSLO model, this paper describes a set of experiments that were used for its verification.
TL;DR: The stability of bone fragments within a circular external fixator is affected by manipulation of the parameters of fixation or individual components of the frame, and the contribution of each component to overall bone fragment stability is dependent upon the mode of loading.
TL;DR: In this paper, a perturbation of the healthy eigenvalue problem is performed to yield the relationship between the changes in eigenvalues and in the global stiffness matrix, where stiffness change is represented as a sum over every structural member by a product of a stiffness reduction factor and a stiffness submatrix.
Abstract: A method is presented to improve the robustness of current damage detection methodologies. Measured statistical changes in natural frequencies and mode shapes along with a correlated analytical stochastic finite element model are used to assess the integrity of a structure. The approach accounts for variations in the modal properties of a structure (due to experimental errors in the test procedure). A perturbation of the healthy eigenvalue problem is performed to yield the relationship between the changes in eigenvalues and in the global stiffness matrix. This stiffness change is represented as a sum over every structural member by a product of a stiffness reduction factor and a stiffness submatrix. The determination of damaged stiffness statistics permits the comparison of probability density functions between the healthy and estimated damaged stiffnesses. A set of graphical and statistical probability damage quotients are then found that indicate a confidence level on the existence of damage. The effectiveness of the proposed technique is illustrated using simulated data on a three-degree-of-freedom spring-mass system and on an Euler-Bernoulli cantilever aluminum beam.
TL;DR: In this paper, it was shown that effective beam yield curvature can be considered constant, when non-dimensionalized by beam depth and yield strain, indicating that beam stiffness is proportional to strength.
Abstract: It is shown, from analysis of typical reinforced concrete beam sections, that current design practice, which assumes beam stiffness is independent of reinforcement ratio but equal to a constant fraction of gross section stiffness is inappropriate. The analyses indicate that effective beam yield curvature can be considered constant, when non-dimensionalized by beam depth and yield strain, indicating that beam stiffness is proportional to strength. Based on this observation, a simple expression for yield drift of frames is proposed and is calibrated by comparing with results of a large number of beam/column subassemblage experiments. Good agreement is obtained. It is pointed out that current estimates of frame stiffness are generally too high. A consequence is that simple calculations show that the vast majority of frame buildings will be unable to achieve code design ductility levels before exceeding code drift limitations.