Effect Of Bending Stiffness Research Articles

A coupled SPH-DEM model for micro-scale structural deformations of plant cells during drying

A single plant cell was modeled with smoothed particle hydrodynamics (SPH) and a discrete element method (DEM) to study the basic micromechanics that govern the cellular structural deformations during drying. This two-dimensional particle-based model consists of two components: a cell fluid model and a cell wall model. The cell fluid was approximated to a highly viscous Newtonian fluid and modeled with SPH. The cell wall was treated as a stiff semi-permeable solid membrane with visco-elastic properties and modeled as a neo-Hookean solid material using a DEM. Compared to existing meshfree particle-based plant cell models, we have specifically introduced cell wall–fluid attraction forces and cell wall bending stiffness effects to address the critical shrinkage characteristics of the plant cells during drying. Also, a moisture domain-based novel approach was used to simulate drying mechanisms within the particle scheme. The model performance was found to be mainly influenced by the particle resolution, initial gap between the outermost fluid particles and wall particles and number of particles in the SPH influence domain. A higher order smoothing kernel was used with adaptive smoothing length to improve the stability and accuracy of the model. Cell deformations at different states of cell dryness were qualitatively and quantitatively compared with microscopic experimental findings on apple cells and a fairly good agreement was observed with some exceptions. The wall–fluid attraction forces and cell wall bending stiffness were found to be significantly improving the model predictions. A detailed sensitivity analysis was also done to further investigate the influence of wall–fluid attraction forces, cell wall bending stiffness, cell wall stiffness and the particle resolution. This novel meshfree based modeling approach is highly applicable for cellular level deformation studies of plant food materials during drying, which characterize large deformations.

Linear and nonlinear dynamics of suspended cable considering bending stiffness

This paper reports a systematic investigation on the linear and nonlinear dynamics of a suspended cable, taking bending stiffness into account. Firstly, the linear dynamics features, for example, eigen frequencies and modes for in-plane and out-of-plane motions, are formulated. Secondly, parametrical studies are conducted to explore the effect of bending stiffness on the natural frequencies and mode shapes of the symmetrical/antisymmetrical in-plane and out-of-plane modes. Then, the three-to-one internal resonance between the first- and third-order in-plane symmetrical modes is analyzed by applying directly the method of multiple scales dealing with the nonlinear partial differential equation and boundary conditions. Finally, the frequency-response curves and force-response curves are obtained through solving the modulation equations using the Newton–Raphson method and the pseudo-arclength scheme. The results show that the bending stiffness plays a considerable role in changing the natural frequencies and mode shapes, shifting the conditions for the occurring of nonlinear interaction, saddle-node bifurcation and Hopf bifurcation of suspended cables.

Damage resistance and damage tolerance of dispersed CFRP laminates: The bending stiffness effect

The stiffness of a composite plate under low velocity impact loading is usually assessed by the equivalent bending stiffness. However, considering two different laminates with the same value of the equivalent bending stiffness, the bending stiffness coefficients along the major axis can be widely different. In the current communication, the effect of the bending stiffness coefficients along the major axis on the impact and compression after impact responses of laminated composites with the same value of the equivalent bending stiffness is investigated. The results show that the effect of the bending stiffness coefficients is insignificant when designing a laminate with the same equivalent bending stiffness.

Numerical Model of Journal Bearing Lubrication Considering a Bending Stiffness Effect

An analysis for operating characteristics of journal bearing lubrication system is performed based on the numerical model. Dynamic bearing lubrication characteristics such as oil film pressure and thickness distribution can be analyzed through a numerical model with an integration of elastohydrodynamics and multi-flexible-body dynamics (MFBD). In particular, the oil film thickness variation by elastic deformation is considered in the elastohydrodynamic analysis by applying the bending stiffness effect of journal. And the oil film thickness variation by the bending stiffness effect is applied to the fluid governing equations to calculate the oil film pressure in the elastohydrodynamic lubrication region. A series of process proposed in this study is available for the analysis of realistic elastohydrodynamic lubrication phenomenon. Also, a numerical example for the journal bearing lubrication system is demonstrated and compared with the experimental results. The numerical results considering the bending stiffness effect show a good agreement with the experimental results.

Vibration-based estimation of axial force for a beam member with uncertain boundary conditions

Focusing on the application for diagonal braces, tie-bars and short thick cables, this work proposes a new technique to identify the axial force of a two-dimensional Euler–Bernoulli beam member. Bending stiffness effects are taken into account. On the basis of the dynamic measurements from at least five sensors, the proposed method is capable of estimating the axial force as well as the translational and rotational stiffness at both beam ends. When fixing some end constraints, the required number of sensors can be reduced. Finite element simulations are performed for verification purpose, accounting for a wide range of bending stiffness. A laboratory experiment is conducted to investigate the feasibility and accuracy of the proposed method.

Effect of Pipe Stiffness on Maxi-HDD Pull Loads

The ASTM standard F1962, Standard Guide for Use of Maxi-Horizontal Directional Drilling for Placement of Polyethylene Pipe or Conduit Under Obstacles, Including River Crossings, provides a procedure for estimating pull loads and stresses on polyethylene (PE) pipe as primarily a function of the drilled path and buoyant weight of the pipe in the borehole. Although the (capstan) effect of tension at route bends is reflected in the analysis, it is assumed that pipe bending stiffness effects may be ignored for the typically very flexible PE material. However, it is of interest to gain a quantitative understanding of the potential impact of such additional factors on the required pull force in somewhat stiffer pipe materials, such as polyvinyl chloride (PVC) or steel. The present investigation therefore focuses on an analytical means of estimating the associated frictional drag forces, allowing an appreciation of the possible importance of such effects and, as appropriate, an extension of the general ASTM F1962...

C 1 natural element method for strain gradient linear elasticity and its application to microstructures

C1 natural element method (C1 NEM) is applied to strain gradient linear elasticity, and size effects on microstructures are analyzed. The shape functions in C1 NEM are built upon the natural neighbor interpolation (NNI), with interpolation realized to nodal function and nodal gradient values, so that the essential boundary conditions (EBCs) can be imposed directly in a Galerkin scheme for partial differential equations (PDEs). In the present paper, C1 NEM for strain gradient linear elasticity is constructed, and several typical examples which have analytical solutions are presented to illustrate the effectiveness of the constructed method. In its application to microstructures, the size effects of bending stiffness and stress concentration factor (SCF) are studied for microspeciem and microgripper, respectively. It is observed that the size effects become rather strong when the width of spring for microgripper, the radius of circular perforation and the long axis of elliptical perforation for microspeciem come close to the material characteristic length scales. For the U-shaped notch, the size effects decline obviously with increasing notch radius, and decline mildly with increasing length of notch.

Finite element analysis of the effect of bending stiffness and contact condition of composite bone plates with simple rectangular cross-section on the bio-mechanical behaviour of fractured long bones

The relationship between mechanical stimuli and curing tissue generation and development should be quantitatively evaluated to better understand the effective healing of bone fractures. In this paper, finite element analyses were carried out to estimate the interfragmentary strain distribution at the fracture site of a tibia according to the bending stiffness and contact conditions of composite bone plates with simplified rectangular cross-section, and polymeric porous layers at the contact area. We found that a composite bone plate with polymeric porous layers provided positive effects on callus generation at the fracture site, and effectively reduced the contact stress at the contact area.

Effects Analysis of Bending Stiffness of Cables on Stress Distribution and Curve Shape in Super-Long Single Suspension Cable Structures

The design scheme of a suspension bridge with a super-long-span of 3300 m was taken as an example, and calculating results from 3 mechanics models are compared with each other to study the effects of bending stiffness of cables on stress distribution and curve shape in super-long single suspension cable structures on the basis of the Finite Element Method (FEM) algorithm of ANSYS and the analytical segmental catenary method for cables’ shape-finding. The study shows that the influence of bending stiffness on curve shape-finding of cables is negligible; Although its effects on stress distribution in cross sections of main cables due to dead loads is small, the error of horizontal forces probably results in great one for the calculation of bending moments at the bottom cross-sections of bridge pylons, which needs attention to ensure the structural safety.

Effect of bending stiffness on the deformation of liquid capsules enclosed by thin shells in shear flow

Shear-induced deformation of liquid capsule enclosed by thin shell causes the development of in-plane tensions and bending moments due to the shell thickness or to a preferred three-dimensional unstressed configuration. This paper considers the effect of bending stiffness due to a preferred three-dimensional structure on the deformation and motion of the liquid capsule. To perform the numerical simulations, an improved formulation for computing the forces generated on the capsule surface during deformation is proposed. This formulation takes full account of large deformation kinematics and the development of in-plane tensions and bending moments. The deformation and orientation dynamics of capsules with different reference shapes are studied under various shear rates, viscosity ratios, and bending modulus. The numerical results show that the bending stiffness not only restricts the deformation but also affects the motion mode of the capsules. In addition, raising bending stiffness amplifies the shape deformation oscillations in tank-treading mode but reduces the oscillations in tumbling mode.

Effects of bending stiffness and rotatory inertia in a mass-rod piezoelectric vibratory gyroscope

Effects of bending stiffness and rotatory inertia in a mass-rod piezoelectric vibratory gyroscope

On the effect of the bending stiffness on the damping properties of a tensioned cable with an attached tuned-mass-damper

In this paper the vertical vibrations of a tensioned cable with bending stiffness and with an attached tuned-mass-damper (TMD) will be considered. The damping behavior of a cable with attached damper may be influenced by the bending stiffness of the cable. In this paper the bending stiffness is represented by the non-dimensional parameter a = E I / ( T L 2 ) , in which E I is the bending stiffness, T the constant cable tension, and L the length of the cable. The aim of this paper is to consider the effect of bending stiffness on the dynamics of a cable with an attached TMD. It will be discussed that the TMD is most effective to damp the n th mode of the undamped cable in the case where the frequency of the damper is tuned to be close to the frequency of this n th mode. The TMD parameters for which the TMD is most effective are the so-called optimum TMD parameters and result in the corresponding optimum damping rates. These optimum damping rates will be evaluated numerically for a cable without bending stiffness. Then, the influence of the bending stiffness on the damping rates will be studied. In the case where the frequency of the damper is tuned to the frequency of the first mode of the undamped cable, it will be found that a ≥ 1 0 − 3 can, depending on the TMD parameters, significantly reduce the damping rates. In the case where the frequency of the damper is tuned to the frequency of the second mode, a ≥ 1 0 − 4 can significantly reduce the damping rates.

Simulating the collapse transition of a two-dimensional semiflexible lattice polymer

It has been revealed by mean-field theories and computer simulations that the nature of the collapse transition of a polymer is influenced by its bending stiffness epsilon(b). In two dimensions, a recent analytical work demonstrated that the collapse transition of a partially directed lattice polymer is always first order as long as epsilon(b) is positive [H. Zhou et al., Phys. Rev. Lett. 97, 158302 (2006)]. Here we employ Monte Carlo simulation to investigate systematically the effect of bending stiffness on the static properties of a two-dimensional lattice polymer. The system's phase diagram at zero force is obtained. Depending on epsilon(b) and the temperature T, the polymer can be in one of the three phases: crystal, disordered globule, or swollen coil. The crystal-globule transition is discontinuous and the globule-coil transition is continuous. At moderate or high values of epsilon(b) the intermediate globular phase disappears and the polymer has only a discontinuous crystal-coil transition. When an external force is applied, the force-induced collapse transition will either be continuous or discontinuous, depending on whether the polymer is originally in the globular or the crystal phase at zero force. The simulation results also demonstrate an interesting scaling behavior of the polymer at the force-induced globule-coil transition.

Nonlinear dynamics of three-dimensional belt drives using the finite-element method

In this paper, new nonlinear dynamic formulations for belt drives based on the three-dimensional absolute nodal coordinate formulation are developed. Two large deformation three-dimensional finite elements are used to develop two different belt-drive models that have different numbers of degrees of freedom and different modes of deformation. Both three-dimensional finite elements are based on a nonlinear elasticity theory that accounts for geometric nonlinearities due to large deformation and rotations. The first element is a thin-plate element that is based on the Kirchhoff plate assumptions and captures both membrane and bending stiffness effects. The other three-dimensional element used in this investigation is a cable element obtained from a more general three-dimensional beam element by eliminating degrees of freedom which are not significant in some cable and belt applications. Both finite elements used in this investigation allow for systematic inclusion or exclusion of the bending stiffness, thereby enabling systematic examination of the effect of bending on the nonlinear dynamics of belt drives. The finite-element formulations developed in this paper are implemented in a general purpose three-dimensional flexible multibody algorithm that allows for developing more detailed models of mechanical systems that include belt drives subject to general loading conditions, nonlinear algebraic constraints, and arbitrary large displacements. The use of the formulations developed in this investigation is demonstrated using two-roller belt-drive system. The results obtained using the two finite-element formulations are compared and the convergence of the two finite-element solutions is examined.

An elastic rod model for anguilliform swimming

We develop a model for anguilliform (eel-like) swimming as an elastic rod actuated via time-dependent intrinsic curvature and subject to hydrodynamic drag forces, the latter as proposed by Taylor (in Proc Roy Proc Lond A 214:158-183, 1952). We employ a eometrically exact theory and discretize the resulting nonlinear partial differential evolution both to perform numerical simulations, and to compare with previous models consisting of chains of rigid links or masses connected by springs, dampers, and prescribed force generators representing muscles. We show that muscle activations driven by motoneuronal spike trains via calcium dynamics produce intrinsic curvatures corresponding to near-sinusoidal body shapes in longitudinally-uniform rods, but that passive elasticity causes Taylor's assumption of prescribed shape to fail, leading to time-periodic motions and lower speeds than those predicted Taylor (in Proc Roy Proc Lond A 214:158-183, 1952). We investigate the effects of bending stiffness, body geometry, and activation patterns on swimming speed, turning behavior, and acceleration to steady swimming. We show that laterally-uniform activation yields stable straight swimming and laterally differential activation levels lead to stable turns, and we argue that tapered bodies with reduced caudal (tail-end) activation (to produce uniform intrinsic curvature) swim faster than ones with uniform activation.

A new steel structural system of a suspension pedestrian bridge

The paper deals with a new structural system of pedestrian steel bridge consisting of carrying suspension members made of stiff (in bending) rolled or welded sections and a flexible cylindrical deck. Structural behaviour of such a suspension member subjected to unsymmetrical live loading has been discussed on a basis of kinematic conditions. Ways of stabilization of kinematic displacements have been under consideration. Effects of bending stiffness and geometrical non-linearity of the suspension structure are taken into account. Analytical expressions for the analysis of the flexible cylindrical deck have been proposed. In an alternative concrete deck, a layered model has been applied for the stress and strain analysis.

Riser-Soil Interaction: Local Dynamics at TDP and a Discussion on the Eigenvalue and the VIV Problems

Abstract The eigenvalue problem of risers is of utmost importance, particularly if vortex-induced vibration (VIV) is concerned. Design procedures rely on the determination of eigenvalues and eigenmodes. Natural frequencies are not too sensitive to the proper consideration of boundary condition, within a certain extent where dynamics at the touchdown area (TDA) may be modeled as dominated by the dynamics of the suspended part. However, eigenmodes may be strongly affected in this region because, strictly speaking, this is a nonlinear one-side (contact-type) boundary condition. Actually, we shall consider a nonlinear eigenvalue problem. Locally, at TDA, riser flexural rigidity and soil interaction play important roles and may affect the dynamic curvature. Extending and merging former analytical solutions on touchdown point (TDP) dynamics and on the eigenvalue problem, obtained through asymptotic and perturbation methods, the present work critically address soil and bending stiffness effects a little further. As far as linear soil stiffness and planar dynamics hypotheses may be considered valid, it is shown that penetration in the soil is small and that its effect does not change significantly the bending loading that is mainly caused by the cyclic excursion of the TDP and corresponding dynamic tension. A comparison of the analytical results with a full nonlinear time-domain simulation shows a remarkable agreement for a typical steel catenary riser. The WKB approximation for the eigenvalue problem gives good estimates for TDP excursion. As the dynamic tension caused solely by VIV is very small, the merged analytical solution may be used as a first estimate of the curvature variation at TDP in the cases of current perpendicular to the “riser plane.”

Vibration of elevator cables with small bending stiffness

The effects of bending stiffness and boundary conditions on the lateral vibration of the stationary and moving hoist cables are investigated. The role of the trial functions in the approximate methods is examined. The optimal stiffness and damping coefficient of the suspension of the car against its guide rails are identified for the moving cable.Copyright © 2002 by ASME

Flutter Limits and Behaviors of Flexible Webs Having a Simplified Basic Configuration in High-Speed Flow

Fluttering conditions were analyzed for webs with a simplified basic configuration with both leading and trailing edges fixed in a uniform flow. The predicted flutter limits are expressed in terms of a ratio of fluid force to tension (σ*), a ratio of tension to bending stiffness (τ*), and a reduced frequency fR. Three characteristic zones of the behavior are seen to appear depending on the magnitude of τ*. For medium τ* of 1×103 to 1×106, flutter-limit values of σ* and fR remain nearly constant, respectively. For low τ*<1×103 effect of bending stiffness becomes significant and buckling-like instabilities tend to occur preceding the flutter. For high τ*>1×106 ripple-like modes tend to occur and σ* falls drastically and fR scatters much. Experimental flutter limits obtained in the wind tunnel were seen on the average to agree with the expected ones for the tested range of 9×102<τ*<4×104.

A revisit of spinning disk models. Part I: derivation of equations of motion

Previous models of spinning disks have focused on modelling the disk as a spinning membrane. The effect of bending stiffness was then incorporated by adding the appropriate term to the previously derived spinning membrane equation. A pure spinning plate model does not exist in the literature. Furthermore, in both existing linear and nonlinear models of spinning disks, the in-plane inertia and rotary inertia of the disk have been ignored. This paper revisits the derivation of the equations of motion of a spinning plate. The derivation focuses on the use of Hamilton's principle with linear Kirchhoff and nonlinear von Karman strain expressions. In-plane and rotary inertias of the plate are automatically taken into account. The use of Hamilton's principle guarantees the correct derivation of the corresponding boundary conditions. The resulting equations and boundary conditions are discussed.