scholarly journals Energetics of collapsible channel flow with a nonlinear fluid-beam model

2021 ◽  
Vol 926 ◽  
Author(s):  
D.Y. Wang ◽  
X.Y. Luo ◽  
P.S. Stewart
Keyword(s):  
Limit Point ◽  
Elastic Beam ◽  
Static Solution ◽  
External Pressure ◽  
Constitutive Law ◽  
Beam Model ◽  
Lower Branch ◽  
Narrow Region ◽  
New Formulation ◽  
Approach Zero

We consider flow along a finite-length collapsible channel driven by a fixed upstream flux, where a section of one wall of a planar rigid channel is replaced by a plane-strain elastic beam subject to uniform external pressure. A modified constitutive law is used to ensure that the elastic beam is energetically conservative. We apply the finite element method to solve the fully nonlinear steady and unsteady systems. In line with previous studies, we show that the system always has at least one static solution and that there is a narrow region of the parameter space where the system simultaneously exhibits two stable static configurations: an (inflated) upper branch and a (collapsed) lower branch, connected by a pair of limit point bifurcations to an unstable intermediate branch. Both upper and lower static configurations can each become unstable to self-excited oscillations, initiating either side of the region with multiple static states. As the Reynolds number increases along the upper branch the oscillatory limit cycle persists into the region with multiple steady states, where interaction with the intermediate static branch suggests a nearby homoclinic orbit. These oscillations approach zero amplitude at the upper branch limit point, resulting in a stable tongue between the upper and lower branch oscillations. Furthermore, this new formulation allows us to calculate a detailed energy budget over a period of oscillation, where we show that both upper and lower branch instabilities require an increase in the work done by the upstream pressure to overcome the increased dissipation.

scholarly journals Application of the Generalized Nonlinear Constitutive Law in 2D Shear Flexible Beam Structures

2021 ◽  
Author(s):  
Damian Mrówczyński ◽  
Tomasz Gajewski ◽  
Tomasz Garbowski
Keyword(s):  
Finite Element ◽  
Cross Sections ◽  
Reference Model ◽  
Constitutive Models ◽  
Constitutive Law ◽  
Flexible Beam ◽  
Beam Model ◽  
Beam Structures ◽  
Nodal Displacements ◽  
Nonlinear Constitutive Law

The paper presents a modified finite element method for nonlinear analysis of 2D beam structures. To take into account the influence of the shear flexibility, a Timoshenko beam element was adopted. The algorithm proposed enables using complex material laws without the need of implementing advanced constitutive models in finite element routines. The method is easy to implement in commonly available CAE software for linear analysis of beam structures. It allows to extend the functionality of these programs with material nonlinearities. By using the structure deformations, computed from the nodal displacements, and the presented here generalized nonlinear constitutive law, it is possible to iteratively reduce the bending, tensile and shear stiffnesses of the structures. By applying a beam model with a multi layered cross-section and generalized stresses and strains to obtain a representative constitutive law, it is easy to model not only the complex multi-material cross-sections, but also the advanced nonlinear constitutive laws (e.g. material softening in tension). The proposed method was implemented in the MATLAB environment, its performance was shown on the several numerical examples. The cross-sections such us a steel I-beam and a steel I-beam with a concrete encasement for different slenderness ratios were considered here. To verify the accuracy of the computations, all results are compared with the ones received from a commercial CAE software. The comparison reveals a good correlation between the reference model and the method proposed.

scholarly journals The location of the grounding zone of Evans Ice Stream, Antarctica, investigated using SAR interferometry and modelling

2009 ◽  
Vol 50 (52) ◽  
pp. 35-40 ◽  
Author(s):  
Helena J. Sykes ◽  
Tavi Murray ◽  
Adrian Luckman
Keyword(s):  
Stream Flow ◽  
Elastic Beam ◽  
Tidal Height ◽  
Sar Interferometry ◽  
Beam Model ◽  
West Antarctica ◽  
Tidal Model ◽  
Tidal Forcing ◽  
Ice Stream ◽  
Grounding Line

AbstractEvans Ice Stream, West Antarctica, has five tributaries and a complex grounding zone. The grounding zone of Evans Ice Stream, between the landward and seaward limits of tidal flexing, was mapped using SAR interferometry. The width of the mapped grounding zone was compared with that derived from an elastic beam model, and the tidal height changes derived from interferometry were compared with the results of a tidal model. Results show that in 1994 and 1996 the Evans grounding zone was located up to 100 km upstream of its location in the BEDMAP dataset. The grounding line of Evans Ice Stream is subjected to 5 m vertical tidal forcing, which would clearly affect ice-stream flow.

An Analytical Shape Memory Polymer Composite Beam Model for Space Applications

2016 ◽  
Vol 16 (02) ◽  
pp. 1450093 ◽  
Author(s):  
D. Bergman ◽  
B. Yang
Keyword(s):  
Shape Memory ◽  
Polymer Composite ◽  
Geometric Model ◽  
Shape Memory Polymer ◽  
Constitutive Law ◽  
Finite Difference Approximation ◽  
Dynamic Equations ◽  
Difference Approximation ◽  
Beam Model ◽  
Space Applications

Shape memory polymer composite (SMPC) structures, due to their ability to be formed into a small compact volume and then transform back to their original shape, are considered as a solution in the design of light-weight large deployable space structures. There is a wide array of constitutive and qualitative work being done on SMPC’s but little or no development of dynamic equations. This paper documents a macroscopic model for the shape fixation and shape recovery processes of a SMPC cantilever beam. In particular the focus is on the shape fixation process, whereby a quasi-static equilibrium model can be used instead of a full equation of motion. Numerical results are obtained in this regard by use of finite difference approximation with Newton’s method. This formulation combines a nonlinear geometric model with a temperature dependent constitutive law. Additionally, the dynamic equations of the SMPC cantilever are derived. Future work will include a dynamic numerical model, and a finite element model of the SMPC structure.

Scale Coefficient, Length, Mode and Radius Effect on Critical Axial Compressed Buckling Load of Carbon Nanotubes via Nonlocal Continuum Model

2012 ◽  
Vol 629 ◽  
pp. 296-301
Author(s):  
Hong Liang Tian
Keyword(s):  
Carbon Nanotubes ◽  
Continuum Model ◽  
Elastic Shell ◽  
Elastic Beam ◽  
Analytic Solutions ◽  
Buckling Load ◽  
Beam Model ◽  
Mechanical Behaviors ◽  
Nonlocal Beam ◽  
Scale Coefficient

Some exact concise analytic solutions of critical axial compressed buckling load for carbon nanotubes are derived via nonlocal beam. Scale coefficient, length, mode and radius effect on nonlocal critical axial compressed buckling load of CNTs is established and can be analyzed in terms of the general solutions. Radius effect on nonlocal critical axial compressed buckling load is only found through nonlocal elastic shell model but not derived via nonlocal elastic beam model. Numerical calculations of CNTs show that local critical axial compressed buckling load through local elastic theory is overestimated. Scale coefficient, length, mode and radius effect should be taken into account in predicting more accurate results for mechanical behaviors of CNTs via continuum model.

scholarly journals Tidal bending of glaciers: a linear viscoelastic approach

2003 ◽  
Vol 37 ◽  
pp. 83-89 ◽  
Author(s):  
Niels Reeh ◽  
Erik Lintz Christensen ◽  
Christoph Mayer ◽  
Ole B. Olesen
Keyword(s):  
Laboratory Experiments ◽  
Viscoelastic Model ◽  
Elastic Beam ◽  
Beam Theory ◽  
Model Parameters ◽  
Beam Model ◽  
Glacier Ice ◽  
Linear Viscoelastic ◽  
Reasonable Choice ◽  
Linear Viscoelastic Model

AbstractIn theoretical treatments of tidal bending of floating glaciers, the glacier is usually modelled as an elastic beam with uniform thickness, resting on an elastic foundation. With a few exceptions, values of the elastic (Young’s) modulus E of ice derived from tidal deflection records of floating glaciers are in the range 0.9–3 GPa. It has therefore been suggested that the elastic-beam model with a single value of E ≈ 1GPa adequately describes tidal bending of glaciers. In contrast, laboratory experiments with ice give E = 9.3 GPa, i.e. 3–10 times higher than the glacier-derived values. This suggests that ice creep may have a significant influence on tidal bending of glaciers. Moreover, detailed tidal-deflection and tilt data from Nioghalvfjerdsfjorden glacier, northeast Greenland, cannot be explained by elastic-beam theory. We present a theory of tidal bending of glaciers based on linear viscoelastic-beam theory. A four-element, linear viscoelastic model for glacier ice with a reasonable choice of model parameters can explain the observed tidal flexure data. Implications of the viscoelastic response of glaciers to tidal forcing are discussed briefly.

An Asymptotic Model of Viscous Flow Limitation in a Highly Collapsed Channel

1998 ◽  
Vol 120 (4) ◽  
pp. 544-546 ◽  
Author(s):  
O. E. Jensen
Keyword(s):  
Pressure Drop ◽  
Viscous Flow ◽  
External Pressure ◽  
Asymptotic Model ◽  
Flow Limitation ◽  
Two Dimensional ◽  
Inertial Effects ◽  
Channel One ◽  
Narrow Region ◽  
Flow Through

A viscous flow through a long two-dimensional channel, one wall of which is formed by a finite-length membrane, experiences flow limitation when the channel is highly collapsed over a narrow region under high external pressure. Simple approximate relations between flow rate and pressure drop are obtained for this configuration by the use of matched asymptotic expansions. Weak inertial effects are also considered.

On the Dynamics of Fractional Visco-Elastic Beams

2012 ◽  
Author(s):  
Salvatore Di Lorenzo ◽  
Francesco P. Pinnola ◽  
Antonina Pirrotta
Keyword(s):  
Elastic Beam ◽  
Constitutive Law ◽  
Dynamic Loads ◽  
Elastic Behavior ◽  
Advanced Manufacturing ◽  
Suitable Model ◽  
Bernoulli Beam ◽  
Static Behavior ◽  
Creep Tests ◽  
Euler Bernoulli Beam

With increasing advanced manufacturing process, visco-elastic materials are very attractive for mitigation of vibrations, provided that you may have advanced studies for capturing the realistic behavior of such materials. Experimental verification of the visco-elastic behavior is limited to some well-known low order models as the Maxwell or Kelvin models. However, both models are not sufficient to model the visco-elastic behavior of real materials, since only the Maxwell type can capture the relaxation tests and the Kelvin the creep tests, respectively. Very recently, it has been stressed that the most suitable model for capturing the visco-elastic behavior is the spring-pot, characterized by a fractional constitutive law. Based on this assumption, the quasi-static behavior has been investigated very recently, however for noise control there is a need of exploiting the dynamic behavior of such a fractional visco-elastic beam. The present paper introduces the dynamic response of fractional visco-elastic Euler-Bernoulli beam under dynamic loads.

Analysis of Functional Scoliosis by Means of an Anisotropic Beam Model of the Human Spine

1985 ◽  
Vol 107 (3) ◽  
pp. 281-285 ◽  
Author(s):  
L. Lindbeck
Keyword(s):  
Reasonable Agreement ◽  
Small Difference ◽  
Frontal Plane ◽  
Elastic Beam ◽  
Beam Model ◽  
Leg Length ◽  
X Ray ◽  
Human Spine ◽  
Anisotropic Elastic ◽  
Experimental Findings

An upright, muscle-relaxed human spine, suffering from a mild functional scoliosis, caused by a small difference in leg length, is modeled as an anisotropic, elastic beam. The lower end of the beam is built-in in a fixed body, i.e., the laterally tilted pelvis. The upper end is rigidly attached to a rigid body, i.e., the supported upper part of the trunk, which is supposed to move freely in the frontal plane. It is shown that the characteristic scoliotic curvature of the spine, observed on an X-ray picture, can be reproduced by means of buckling analysis of the beam model, using realistic values of geometric and loading parameters and a properly chosen bending stiffness, which is found to be in reasonable agreement with earlier experimental findings. The analysis also shows that the muscle-relaxed upright equilibrium position of the spine is mechanically unstable.

scholarly journals The use of tiltmeters to study the dynamics of Antarctic ice-shelf grounding lines

1991 ◽  
Vol 37 (125) ◽  
pp. 51-58 ◽  
Author(s):  
A. M. Smith
Keyword(s):  
Elastic Beam ◽  
Ice Thickness ◽  
Elastic Model ◽  
Beam Model ◽  
Line Position ◽  
Stream Data ◽  
Ice Shelf ◽  
Ice Stream ◽  
Grounding Line ◽  
Data Coverage

Abstract New tiltmeter data are presented from Doake Ice Rumples on Ronne Ice Shelf, Antarctica. Five sites which showed a tidal ice-shelf flexure have been analysed using an elastic beam model to investigate the variation of flexure amplitude with distance from the grounding line. An earlier study on Rutford Ice Stream which also used an elastic model required an ice thickness much less than that observed. Reworking the Rutford Ice Stream data suggests that this greatly reduced ice thickness is not required, given the current sparse data coverage. The elastic model is used to improve the estimated grounding-line position on Rutford Ice Stream. Some of the difficulties in modelling ice-shelf flexure and locating grounding lines are discussed.

scholarly journals Stationary and axisymmetric configurations of compact stars with extremely strong and highly localized magnetic fields

2010 ◽  
Vol 6 (S274) ◽  
pp. 232-235
Author(s):  
Kotaro Fujisawa ◽  
Shin'ichiro Yoshida ◽  
Yoshiharu Eriguchi
Keyword(s):  
Magnetic Fields ◽  
Current Density ◽  
Compact Stars ◽  
Model Parameters ◽  
Flux Function ◽  
Narrow Region ◽  
Deep Interior ◽  
Equilibrium Configurations ◽  
Basic Equations ◽  
New Formulation

AbstractUsing a new formulation to compute structures of stationary and axisymmetric magnetized barotropic stars in Newtonian gravity, we have succeeded in obtaining numerically exact models of stars with extremely high interior magnetic fields. In this formulation, there appear four arbitrary functions of the magnetic flux function from the integrability conditions among the basic equations. Since in our new formulation these arbitrary functions appear in the expression of the current density, configurations with different current distributions can be specified by choosing the forms of the arbitrary functions.By choosing appropriate forms for the four arbitrary functions, we have solved many kinds of equilibrium configurations both with poloidal and toroidal magnetic fields. Among them, by choosing special form for the toroidal current density, we have been able to obtain magnetized stars which have extremely strong poloidal magnetic fields deep inside the core region near the symmetric axis. By adopting the appropriate model parameters for the neutron stars, the magnetic fields could be 1014 ~ 1015 G on the surfaces and be about 1017 G in the deep interior regions. For other model parameters appropriate for white dwarfs, the magnetic fields could be around 107 ~ 108 G (surface regions) and 109 ~ 1010 G (core regions). It is remarkable that the regions with very strong interior magnetic fields are confined to a very narrow region around the symmetric axis in the central part of the stars. The issues of stability of these configurations and of evolutionary paths to reach such configurations need to be investigated in the future work.

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