Corotational Model Research Articles

Development of three-dimensional co-rotational beam model for nonlinear dynamic analysis of highly flexible slender composite blades

The main purpose of this work is to introduce a novel method analyzing the dynamic response of a highly flexible slender composite beam having anisotropic property and variable cross-section. A three-dimensional co-rotational model is developed. The beam deformation in dynamic conditions is obtained by applying HHT-α method as dynamic analysis tool. Validation studies with various boundary conditions, multiple external loads and pre-curved structures are performed. Furthermore, dynamic analysis with a large, flexible, and slender composite blade is performed with and without structural couplings. It is shown the developed beam model accurately predicts nonlinear three-dimensional response and anisotropic structural coupling effects.

A nonlinear model for multilayered rubber isolators based on a co-rotational formulation

This article proposes a geometrically nonlinear co-rotational model aimed to characterize the mechanical behavior of elastomeric seismic isolators. The model is able to capture the axial and lateral coupling in both axial directions, i.e. compression and tension of the isolator. Also reproduces the instability the loads in tension as well as in compression, and provides theoretical evidence of the non-symmetric behavior of the isolator in these two directions. To validate model results, a quasistatic analysis was performed on a typical isolator with many different shape factors. From the parametric analysis performed, it is observed that buckling loads are higher in tension than in compression. However, as the shape factor of the isolator increases, the behavior in compression and tension becomes symmetric. It becomes apparent that significant differences in normal stresses and strains under tensile and compressives loads are observed for axial loads smaller than 10% of the nominal buckling load. The example presented shows that lateral displacements of about ±25% of isolator radius and tension forces up to 10% of the buckling load are possible without inducing cavitation in the rubber. Accuracy of the model was also tested against finite element model results and experimental data showing satisfactory results. Furthermore, a response-history analysis of an isolated structure is presented and compared for two isolator models: the two-spring model and the model proposed herein. Finally, material nonlinearity was introduced in the dynamic analysis using a Bouc-Wen type element in parallel with the isolator. The responses are similar between models; however, significant differences occur locally in the isolator for high axial loads and/or large lateral displacements.

Normal stress differences in large-amplitude oscillatory shear flow for the corotational “ANSR” model

Using the integral form of a nonlinear corotational model, we derive explicit analytical expressions for the zeroth, second, and fourth harmonics of the second normal stress difference in large-amplitude oscillatory shear (LAOS). This model yields an arbitrary normal stress ratio (ANSR) in any simple shearing deformation, including LAOS. This corotational ANSR model adds one parameter to the corotational Maxwell model, a time constant λ 0 controlling the ratio Ψ2/Ψ1 for both the real and imaginary parts of each harmonic of the normal stress difference. The explicit analytical expressions for all harmonics of the alternating shear stress and first normal stress difference responses in LAOS match those obtained previously for the corotational Maxwell model. We evaluate the corotational ANSR model for the case of a single Maxwell relaxation time fluid.

Well‐posedness for the FENE dumbbell model of polymeric flows

AbstractWe prove local and global well‐posedness for the FENE dumbbell model for a very general class of potentials. Indeed, in prior local or global well‐posedness results, conditions on the strength of the singularity (or on the parameter b) were made. Here we give a proof in the general case. We also prove global existence results if the data is small or if we restrict to the co‐rotational model in dimension 2. © 2008 Wiley Periodicals, Inc.

Analysis of Solar Wind Events Using Interplanetary Scintillation Remote Sensing 3D Reconstructions and Their Comparison at Mars

Interplanetary Scintillation (IPS) allows observation of the inner heliospheric response to corotating solar structures and coronal mass ejections (CMEs) in scintillation level and velocity. With colleagues at STELab, Nagoya University, Japan, we have developed near-real-time access of STELab IPS data for use in space-weather forecasting. We use a 3D reconstruction technique that produces perspective views from solar corotating plasma and outward-flowing solar wind as observed from Earth by iteratively fitting a kinematic solar wind model to IPS observations. This 3D modeling technique permits reconstruction of the density and velocity structure of CMEs and other interplanetary transients at a relatively coarse resolution: a solar rotational cadence and 10° latitudinal and longitudinal resolution for the corotational model and a one-day cadence and 20° latitudinal and longitudinal heliographic resolution for the time-dependent model. This technique is used to determine solar-wind pressure (“ram” pressure) at Mars. Results are compared with ram-pressure observations derived from Mars Global Surveyor magnetometer data (Crider et al.2003, J. Geophys. Res.108(A12), 1461) for the years 1999 through 2004. We identified 47 independent in situ pressure-pulse events above 3.5 nPa in the Mars Global Surveyor data in this time period where sufficient IPS data were available. We detail the large pressure pulse observed at Mars in association with a CME that erupted from the Sun on 27 May 2003, which was a halo CME as viewed from Earth. We also detail the response of a series of West-limb CME events and compare their response observed at Mars about 160° west of the Sun – Earth line by the Mars Global Surveyor with the response derived from the IPS 3D reconstructions.

A rheo-optical study of polydimethylsiloxane melt

Results from a rheo-optical study of polydimethylsiloxane (PDMS) melt flowing through a converging wedge cell at room temperature for pressure drops of 276, 483, and 689 kPa are described. Birefringence measurements in extensional flow confirmed that stress and polarizability tensors were linearly related over a range of strain rate that extended well into the non-Newtonian region. Local velocity measurements were made using Laser Doppler Anemometry (LDA) in order to compute the rate-of-strain tensor. Along the cell centerline, extensional flow behavior of the polymer was studied via birefringence measurements in the linear stress-optical region. Also, constitutive equations were tested in combined shear and extension flow by comparing their predicted orientation angles with experimental values. For this study, the two constitutive equations tested were the Power-law model and the Goddard-Miller model (a quasilinear corotational model). The orientation angles computed using a two-term version of the Goddard-Miller model with a single Maxwell-type relaxation time constant of 0.009 s and a zero-shear viscosity of 300 Pa s agreed quite well with experimental results.

Calculation of kinematic histories in two- and three-dimensional flows using streamline coordinate functions

In this paper, the theoretical elements of the stream-tube method are considered for the evaluation of strain-rate and strain histories required for the descriptions of memory-integral equations. One interest of the stream-tube analysis lies in the fact that the computation is performed in a transformed domain of the physical domain where the mapped streamlines are parallel and straight. Unknown mapping functions are used for analytic expressions of tensor components, for two- and three-dimensional flow situations. Calculations in three-dimensional flows for corotational models indicate that the relevant analytic expressions deduced from corotating frame determination are too complicated to be realistic for computation, but are exploitable for two-dimensional flow simulations. Strain histories are presented for two- and three-dimensional flows and may be applied to evaluation of stresses in both cases, when using codeformational constitutive equations.

Thermodynamic examination of the periodic shear strain of melts of linear polymers of narrow molecular-mass distribution

1. Maxwell's corotational model with one rekaxatuib time (Zaremba-Fromm-David [ZFD] model) can be used to describe the rheologic properties of melts of narrow MMD polymers subjected to periodic shear strain with finite amplitudes. 2. The onset of instability of melts of narrow-MMD polymers subjected to periodic shear strain is determined by their elastic, and not by their dissipative properties. 3. Using calculations performed in accordance with the ZFD model, three regions of the critical-amplitude/frequency relationship are established for periodic shear strain.

Components of the complex modulus during the periodic shear flow of a viscoelastic fluid

1. In the non-Newtonian region of steady shear flow, the relaxation properties of the flowing melt cannot be determined by a relaxation-time spectrum computed from measured frequency dependencies pf the complex shear modulus G*(ω, q) under conditions where periodic strain is superposed on steady flow. Measured values of G*(ω, q0) reflect both the relaxation characteristics of the flowing material (truncated spectrum) and the effect of a steady-flow disturbance. 2. Integral equations of state of a viscoelastic fluid predict: a) lim η′ '(ω,q0) =dσ12/dq=ηq; ω→0 for parallel superposition, irrespective of the type of equation; b) lim x′ (ω,q0) =d(Pw/2q)/dq ω→0 occurs only in the case of models with a nonlinear memory function, dependent on the straintensor invariants; with a nonlinear relaxation function dependent on strain-rate-tensor invariants for modulus nonlinearity; with a nonlinear memory function dependent or) strainrate invariants for relaxation nonlinearity. 3. When ω < qo, negative values of G′ (ω, qo) are observed, beginning at shear rates corresponding to values of d(Pw/2q)/dq ⩽ 0 only for elastic fluids described by models for which conclusion b) from item 2 is valid. For other models considered, the rates q*o are lower than those preducted by the relationship d(Pw/2q)/dq ⩽ 0 when G′(ω, qo) are negative where ω < qo. 4. Experimental results for a solution of polyisobutylene in cetane in the region of relatively low values of q0 are quantitatively satisfactorily described by a model with a nonlinear memory function, dependent on strain-rate invariants, and modulus nonlinearity. It is established experimentally that q**o > q*e. 5. Asymptotic values of and are obtained for corotational models of a viscoelastic fluid and for values of q*0 which satisfactorily reflect certain results of tests involving the steady flow of melts of linear polymers of narrow molecular-mass distribution. 6. For many polymer solutions, the shear rate q*o coincides with the appearance of a turbulent-flow condition, while in the case of polymer melts, the appearance of turbulent flow coincides with shear rates at which the specimen extrudes from the effective gap in the coneplane rheometer with small angles between the generatrix of the cone and plane.

Memory-function determination of viscoelastic fluids based on relaxation tests (normal and shear stresses)

We endeavour to check the co-rotational model of Le Roy-Pierrard based on Boltzmann's principle. An NBS polystyrene sample and a 50% by weight solution of polyisobutylene in mineral oil were used in a cone-and-plate experiment. A Weissenberg rheogoniometer was modified to perform relaxation tests. Flush mounted transducers were used to determine N 1( t) and N 2( t). The data satisfy Yamamoto's equation for the two samples. If the first and second normal stress difference decay at the same relative rate, the two memory functions of the model are not independent. Only the NBS sample (with narrow distribution in molecular weight) presents such a simplified behaviour. Moreover, in this case, the first memory function can be approximated by a single exponential.