Concept Of Stiffness Research Articles

Pulmonary vascular stiffness: measurement, modeling, and implications in normal and hypertensive pulmonary circulations.

This article introduces the concept of pulmonary vascular stiffness, discusses its increasingly recognized importance as a diagnostic marker in the evaluation of pulmonary vascular disease, and describes methods to measure and model it clinically, experimentally, and computationally. It begins with a description of systems-level methods to evaluate pulmonary vascular compliance and recent clinical efforts in applying such techniques to better predict patient outcomes in pulmonary arterial hypertension. It then progresses from the systems-level to the local level, discusses proposed methods by which upstream pulmonary vessels increase in stiffness, introduces concepts around vascular mechanics, and concludes by describing recent work incorporating advanced numerical methods to more thoroughly evaluate changes in local mechanical properties of pulmonary arteries.

Study on the Stiffness, Carrying Efficiency and Fatigue Character of the End Anchor Cable

Effects of stiffness, carrying efficiency and fatigue of the end anchor cable on the mechanical behavior of long span cable-stayed bridge, were discussed respectively. Firstly, the concept of the effective stiffness and the stress ratio were introduced to discuss the effects of the dead load stress level and the stress ratio on the effective stiffness of the end anchor cable. Secondly, the effect of the cable material on the vertical carrying efficiency of the structure was analyzed. Finally, the main influential factors on the fatigue performance of the end anchor cable were analyzed in detail. It is shown that improving the dead load stress level and keeping the low stress ratio would increase the effective stiffness of the end anchor cable. The section of the end anchor cable effects on stiffness of the structure under high stress level. It can be drawn that as a novel material, The CFRP end anchor cable will increase the load carrying level of the long span cable-stayed bridges. It can also be concluded that the length of side span and main span, the height of pylon, the area of the cable section and the live load collection degree are all the main effective factors to the stress amplitude of the end anchor cable. It is suggested that in the practical design of large span cable-stayed bridge, all the effective factors together with the global state of the structure should be taken into account comprehensively.

Modal Stiffness Contributions of Components to Full Truck

In recent years, three optimal methods, size, shape and topological optimization, have been widely applied to the automotive component design and significant success have been achieved. However, most of the optimizations are limited to deal with the individual component of the truck. Because there exists the complex coupling relations between components under the assembly environment of the truck, it is difficult to deal with the component design by using the above three optimal method and it is necessary to develop a more effective method for solving the complex optimal problem under the assembly environment of full truck. To this end, the paper introduces the modal stiffness concept and develops the modal stiffness contributions of components to full truck which can identify which components are the key ones for controlling the modal frequencies. The present method is applied to a full truck analysis. The results obtained show that the proposed method is effective and the computation process is straightforward. The results can be directly used to improve the component design of full truck as a valuable guide.

Lateral-torsional buckling of discretely-braced i-girder

This paper presents an analytical solution for lateral-torsional buckling strength and stiffness requirements of I-girders with discrete torsional bracings subjected to non-uniform bending. The critical moment and torsional stiffness requirement are derived by using an energy method for an arbitrary number of bracing points. An equivalent moment factor is introduced to evaluate buckling moments of fully braced I-girders. From the results, it is found that proposed solutions agree well with results of finite element analyses regardless of the number of bracing points, while results for the equivalent continuous brace stiffness concept are not suitable for multiple discrete torsionally-braced beams.

Curvilinear fiber optimization tools for design thin walled beams

An investigation of the possible performance improvements of thin walled composite beams through the use of the variable stiffness concept with curvilinear fiber is presented. The beams are constructed from a single-cell closed cross section and a number of non-classical effects such as material anisotropy, transverse shear, warping inhibition and nonuniform torsional model are considered in the beam model. The governing equations were derived by means of the extended Hamilton's principle. Also the extended Galerkin's method is used to solve governing equations. Composite beams subjected to different loading with given geometry and material properties are optimized for maximum failure load. Improvements of variable-stiffness beams over conventional, constant-stiffness beams are also demonstrated.

A diagnosis-based approach for tire–road forces and maximum friction estimation

A new approach to estimate vehicle tire forces and road maximum adherence is presented. Contrarily to most of the previous works on this subject, it is not an asymptotic observer-based estimation, but a combination of elementary diagnosis tools and new algebraic techniques for filtering and estimating derivatives of noisy signals. In a first step, instantaneous friction and lateral forces will be computed within this framework. Then, extended braking stiffness concept is exploited to detect which braking efforts allow to distinguish a road type from another. A weighted Dugoff model is used during these ‘distinguishable’ intervals to estimate the maximum friction coefficient. Very promising results have been obtained in noisy simulations and real experimentations for most of the driving situations.

Research on the Definition of Armature Components Composite Stiffness

. The importance of the armature components and two kinds of whose definition have been illustrated. The concept of tandem and parallel stiffness has been proposed. The definition of armature components has been provided based on analyzing the working principle of the electro-hydraulic servo valve

Joint Stiffness and Deformation Behaviour of Discontinuous Rock

Summary Some rock masses are characterized by joints, fractures and other planes of weakness which reduce the strength and deformation properties of rock structure. Under different loading conditions, joints with weaker than normal and shear deformation strength undergo a relatively higher strain than intact rock. Because permeability of jointed rock masses in fractured reservoirs is a strong function of joint aperture size, one may expect a major change in the permeability when subjected to confining load variation. Therefore, it is important to establish the relation between the stress-strain of the jointed rock mass and the reservoir permeability. This relation is particularly important to model hydraulic fracturing and productivity decline in tight gas wells. In this paper, a new relation is proposed to model prepeak shear stiffness of the joint based on the conventional joint surface parameters and the confining load. Furthermore, constitutive matrices for evaluating deformation behaviour of a single-joint and regularly jointed rock are presented as the results of an analytical study. Based on the concept of joint stiffness, an equivalent stiffness for regularly jointed rock masses was derived, assuming that the deformation of the jointed rock mass equals the sum of the deformation of the rock matrix and the joints. Finite element technique is used to numerically model the deformation behaviour of the jointed rock under various loading conditions. The applicability of the constitutive model to represent jointed rock mass was confirmed from comparison of the numerical results with some of the existing experimental data. The model presented here will be the key element for integrated geomechanical modelling of tight gas wells, naturally fracture reservoirs and other fracturing processes in stress-sensitive reservoirs.

An algebraic approach for maximum friction estimation

A new approach to estimate the road maximum adherence is presented. It is based on a combination of new algebraic tools for estimation and diagnosis via numerical differentiation of noisy signals. Instantaneous friction is first computed within this framework. Then, extended braking stiffness concept is exploited to detect which braking efforts allow to distinguish a road type from another. A weighted Dugoff model is used during these “distinguishable” intervals to estimate the maximum friction coefficient. Promising results have been obtained in noisy simulations and real experimentations.

A novel approach to elasto-plastic finite element analysis of beam structures using the concept of incremental secant stiffness

This paper presents an incremental secant stiffness formulation for materially non-linear analysis of planar beam structures under monotonically increasing external loads. To describe the elasto-plastic behaviour of a typical beam member, a set of non-dimensional plasticity coefficients are introduced to progressively deteriorate the elastic stiffness properties over an incremental load history. The proposed method is developed to provide the accuracy of distributed plasticity approaches, while maintaining the computational effectiveness of plastic hinge methods. By enforcing individual members to maintain equilibrium during plastic deformation, the spread-of-plasticity effects are automatically taken into account. It should be noted that the element stiffness matrix in present study is explicitly formulated, which renders numerical integrations unnecessary. In order to improve the efficiency of solution process, a direct iteration scheme based on the incremental secant stiffness is proposed as an alternative to the commonly used Newton–Raphson methods. The solution procedure is found to converge rapidly when casting into an incremental-iterative analysis. The present method has been implemented into a finite element computer program using FORTRAN. Results of numerical examples have demonstrated that the present approach appears to be robust and efficient in predicting the inelastic response of planar beam structures.

Determination of Contact Stiffness of Rod-Fastened Rotors Based on Modal Test and Finite Element Analysis

A series of simplified rod-fastened rotors, which have different surface contact roughness are manufactured and their modal parameters under different pretightening force, are measured in free-free state. The concept of surface contact stiffness is introduced to simulate the influence of pretightening force on modal parameters of these simplified rod-fastened rotors using finite element method. The experiment measured results are compared and fitted to the finite element analysis results and the relationship between contact stiffness and contact stress is established in which the contact stress is defined by the pretightening force. The relationship is then applied on the modal analysis of a real gas turbine rotor, and its modal test results and finite element analysis results are consistent with each other, proving that the relationship and the described determination method of contact stiffness based on modal test and finite element analysis are effective.

Theory of Metamaterial Beams for Broadband Vibration Absorption

This article presents methods for modeling, analysis, and design of metamaterial beams for broadband vibration absorption/isolation. The proposed metamaterial beam consists of a uniform isotropic beam with many small spring-mass-damper subsystems integrated at separated locations along the beam to act as vibration absorbers. For a unit cell of an infinite metamaterial beam, governing equations are derived using the extended Hamilton principle. The existence of stopband is demonstrated using a model based on averaging material properties over a cell length and a model based on finite element modeling and the Bloch-Floquet theory for periodic structures. However, these two idealized models cannot be used for finite beams and/or elastic waves having short wavelengths. For finite metamaterial beams, a linear finite element method is used for detailed modeling and analysis. Both translational and rotational absorbers are considered. Because results show that rotational absorbers are not efficient, only translational absorbers are recommended for practical designs. The concepts of negative effective mass and stiffness and how the spring-mass-damper subsystems create a stopband (i.e., no elastic waves in this frequency range can propagate forward) are explained in detail. Numerical simulations reveal that the actual working mechanism of the proposed metamaterial beam is based on the concept of conventional mechanical vibration absorbers. It uses the incoming elastic wave in the beam to resonate the integrated spring-mass-damper absorbers to vibrate in their optical mode at frequencies close to but above their local resonance frequencies to create shear forces and bending moments to straighten the beam and stop the wave propagation. This concept can be easily extended to design a broadband absorber that works for elastic waves of short and long wavelengths. Numerical examples validate the concept and show that, for high-frequency waves, the structure’s boundary conditions do not have significant influence on the absorbers’ function. However, for absorption of low-frequency waves, the boundary conditions and resonant modes of the structure need to be considered in the design. With appropriate design calculations, finite discrete spring-mass-damper absorbers can be used, and hence expensive micro- or nanomanufacturing techniques are not needed for design and manufacturing of such metamaterial beams for broadband vibration absorption/isolation.

Estimation of Optimal Fiducial Target Registration Error in the Presence of Heteroscedastic Noise

We study the effect of point dependent (heteroscedastic) and identically distributed anisotropic fiducial localization noise on fiducial target registration error (TRE). We derive an analytic expression, based on the concept of mechanism spatial stiffness, for predicting TRE. The accuracy of the predicted TRE is compared to simulated values where the optimal registration transformation is computed using the heteroscedastic errors in variables algorithm. The predicted values are shown to be contained by the 95% confidence intervals of the root mean square TRE obtained from the simulations.

Artificial muscles with adjustable stiffness

This paper reports on a stiffness enhancement methodology based on using a suitablydesigned contact surface with which cantilevered-type conducting polymer bendingactuators are in contact during operation. The contact surface constrains the bendingbehaviour of the actuators. Depending on the topology of the contact surface, theresistance of the polymer actuators to deformation, i.e. stiffness, is varied. As opposed totheir predecessors, these polymer actuators operate in air. Finite element analysis andmodelling are used to quantify the effect of the contact surface on the effective stiffness of atrilayer cantilevered beam, which represents a one-end-free, the-other-end-fixed polypyrrole(PPy) conducting polymer actuator under a uniformly distributed load. Afterdemonstrating the feasibility of the adjustable stiffness concept, experiments wereconducted to determine the stiffness of bending-type conducting polymer actuators incontact with a range (20–40 mm in radius) of circular contact surfaces. The numerical andexperimental results presented demonstrate that the stiffness of the actuatorscan be varied using a suitably profiled contact surface. The larger the radius ofthe contact surface is, the higher is the stiffness of the polymer actuators. Theoutcomes of this study suggest that, although the stiffness of the artificial musclesconsidered in this study is constant for a given geometric size, and electrical andchemical operation conditions, it can be changed in a nonlinear fashion to suitthe stiffness requirement of a considered application. The stiffness enhancementmethodology can be extended to other ionic-type conducting polymer actuators.

An oil sand pseudo-elastic model for determining ground deformation under large mobile mining equipment

Strain softening of oil sand under dynamic loading from large mining equipment inhibits the ability of the equipment to function at optimal design performance. This paper looks at the findings of dynamic plate load tests, which effectively mimick the loading and unloading action of a shovel track pad. A pseudo-elastic model was proposed based on the results of the dynamic plate load testing to predict the deformation of oil sand under cyclic loading. Both field and laboratory cyclic plate load tests were performed on oil sand materials. The field tests were performed with different plate sizes, or footprints. The load was normalized based on the pressure stiffness concept in units of pressure per unit deformation. FLAC was used to model the field plate load test deformation with the elastic concept. The laboratory tests were performed at room temperature with more control on the load, loading rate, and cycles than possible during the field testing. Tests were conducted using a circular plate of 14.9 cm diameter, at stress magnitudes of 200, 400, 500 and 600 kPa. The plate load tests were conducted for varying loads, holding, and relaxation times of 0, 2, 5 and 10 min respectively for each magnitude of stress. The outcome of laboratory plate load tests show that after frequent cycles, the pressure stiffness (ratio of stress to deformation) converges on a plateau value of 8 kPa/mm. The proposed approach can be used to evaluate oil sands ground performance, enhancing the prediction process for ground deformation under the operation of ultra-class mining equipment.

Lateral–torsional buckling of I-girders with discrete torsional bracings

Discrete torsional bracing systems are widely used in practice to increase the lateral–torsional buckling (LTB) strength of I-girders. However, only limited studies are available on the LTB strength of I-girders with mid-span torsional bracing. In addition, equivalent continuous brace stiffness concept is adopted for general discrete torsional bracing problems. This article presents an analytical solution for LTB strength and stiffness requirements of I-girders with discrete torsional bracings under a uniform bending condition. Firstly, the critical moment and torsional stiffness requirement are derived by using an energy method for an arbitrary number of bracing points. The proposed equations are then compared with the results of finite element analyses and those obtained by previous researchers. From the results, it is found that the proposed solutions agree well with the results of finite element analyses regardless of the number of bracing points, while the results for the equivalent continuous brace stiffness concept are not suitable for multiple discrete torsionally braced beams. Finally, reduced formula for the total stiffness requirement is proposed for the purpose of design, and effects of linear moment gradient loading and geometric imperfections on critical moments and stiffness requirement are also observed.

Is there any Additional Prognostic Value of Central Blood Pressure Wave Forms Beyond Peripheral Blood Pressure?

For a long time the consideration of blood pressure was based exclusively on measurements of peripheral (brachial) blood pressure. However, there is now a growing interest in the investigation of central (aortic) pressure. There is increasing awareness that the central hemodynamics, reflected by central pressure wave forms and arterial stiffness, can provide new and better insight into the pathophysiology of cardiovascular disorders associated with ageing, hypertension, diabetes, as well as end-stage renal disease. Understanding the concept of arterial stiffness, elevated central blood pressure and pulse pressure has given a new view on the mechanisms of target organ damage and their prevention and treatment. Hence, the measurements of arterial stiffness and central blood pressure, and not only peripheral pressure, have been performed in a few recent interventional trials. Not surprisingly, it was found that observed disparity in cardiovascular events obtained by different antihypertensive drugs might be attributed to their diverse effect on central pressure wave forms, despite similar control of peripheral blood pressure. Putting all currently available data together it appears certainly that there is an additional prognostic value of central pressure wave forms beyond peripheral blood pressure. The aim of this article is to provide the pathophysiology and predictive role for cardiovascular events of central pressure wave forms that are beyond peripheral blood pressure. Crucially, we will review data supporting the view that improvement of central blood pressure can result in reduction of cardiovascular events. Lastly, the future perspectives in this exciting and promising field will be presented.

Long-term slow slip events are not necessarily caused by high pore fluid pressure at the plate interface: an implication from two-dimensional model calculations

A recent tomographic study proposed that high-pore pressure in the deeper portion of the locked zone of a subduction thrust resulting from metamorphic dehydration reactions may cause long-term slow slip events. The study used the concept of ‘critical fault stiffness’, which derives from laboratory-derived rate- and state-dependent friction laws. To test the proposition, we execute 2-D model calculations using laboratory-derived rate- and state-dependent friction laws. Our numerical result is against the proposition, but it can also be explained by the concept of the critical fault stiffness. We agree that metamorphic dehydration reactions definitely produce a bulk property of high fluid saturation, but we caution that they do not necessarily lead to high-pore pressure in the fault zone.

Critical contact stiffness concept and simulation of crack generation in particle models of large length-scales

When the particle simulation method is used to simulate large length-scale problems, such as crustal length-scale problems in the field of geology, it is necessary to include gravity effect into the particle model. To consider gravity effect appropriately, there is a minimum value requirement for the contact stiffness of a particle so that unexpected particle overlap can be avoided. This minimum value is called the critical contact stiffness of a particle due to gravity effect. Using the vertical force equilibrium condition of a particle at the bottom of a two-dimensional particle model, a theoretical formula has been successfully derived for determining the critical contact stiffness of the particle in this paper. For the two-dimensional particle model consisting of circular particles of unit thickness, there is a relationship between the critical contact stiffness of a particle and the critical elastic modulus of the particle material when a linear-elastic-contact model between any two particles is used. Since the elastic moduli of most crustal rocks are greater than the corresponding critical elastic modulus of the particle material, it has been theoretically demonstrated that the particle simulation method, which is based on the linear-elastic-contact model between any two particles, is suitable for simulating gravity effect within the particle model of a large length-scale. The related simulation results have demonstrated the usefulness of the particle simulation method for simulating spontaneous crack generation patterns within brittle crustal rocks.

Negative stiffness and enhanced damping of individual multiwalled carbon nanotubes

The mechanical instabilities and viscoelastic response of individual multiwalled carbon nanotubes and nanofibers (MWCNTs/Fs) under uniaxial compression are studied with atomic force microscopy. Specific buckling events are evident by regimes of negative stiffness, i.e., marked drops in force with increasing compression. Uniaxial cyclic loading can be repeatedly executed even in initially postbuckled regimes, where the CNTs/Fs display incremental negative stiffness. Increases in mechanical damping of $145\text{--}600\phantom{\rule{0.2em}{0ex}}%$ in these initially postbuckled regimes, as compared to the linear prebuckled regimes, are observed. Increased damping is attributed to frictional energy dissipation of walls in buckled configurations of the MWCNTs/Fs. This represents the extension of the concept of negative stiffness to the scale of nanostructures and opens up possibilities for designing nanocomposites with high stiffness and high damping simultaneously.