AN ASYMPTOTIC ANALYSIS ON THE FORM OF NAGHDI TYPE ARCH MODEL

2008 ◽  
Vol 18 (03) ◽  
pp. 417-442 ◽  
Author(s):  
SHENG ZHANG
Keyword(s):  
Correction Factor ◽  
Cross Sections ◽  
Full Range ◽  
Relative Energy ◽  
Beam Model ◽  
Arch Model ◽  
Dimensional Model ◽  
One Dimensional ◽  
Shear Correction Factor ◽  
Transverse Shearing

We consider a one-dimensional model of generally curved elastic arches whose cross-sections are rectangular. The model is of Naghdi's type which is a generalization of the Timoshenko beam model, which allows bending, membrane and transverse shearing deformations. Its form is basically determined in the literature, except for the value of a shear correction factor. With this factor being set to 1, we prove that the modelling error in the interior relative energy norm is proportional to the arch thickness. This result holds for the full range of arch shapes and very general loads. Lower modelling accuracy is proven to hold up to the arch ends. Any shear correction factor other than 1 makes the model diverge from the elasticity theory when a significant shear is involved in the deformation.

Properties of the transition superoperator

1994 ◽  
Vol 72 (3-4) ◽  
pp. 152-161
Author(s):  
R. F. Snider ◽  
J. G. Muga
Keyword(s):  
Boltzmann Equation ◽  
Cross Sections ◽  
Separable Potential ◽  
Line Broadening ◽  
Dimensional Model ◽  
One Dimensional ◽  
Mathematical Arguments ◽  
The Subject ◽  
Spectral Line Broadening ◽  
Transition Operators

Two different transition superoperators naturally arise in physical theories. First, there is the abstract transition superoperator that arises in the quantum Boltzmann equation and collision cross sections. Second, there is a transition superoperator that arises in the theory of spectral line broadening. The latter is parameterized by the frequency of the light being observed. At present the standard method of evaluating the effects of transition superoperators is through the use of transition operators. However, the connection between transition superoperators and operators has been the subject of controversy while the diversity of transition superoperators and operators can be confusing. This paper reviews the basic definitions and methods of relating these quantities, exemplifying these properties by using a separable potential with explicit calculations for a particular one-dimensional model. In this way the validity of previously presented abstract mathematical arguments is demonstrated explicitly.

A biodegradable elastic stent model

2018 ◽  
Vol 24 (8) ◽  
pp. 2591-2618
Author(s):  
Josip Tambača ◽  
Bojan Žugec
Keyword(s):  
Cross Sections ◽  
Applied Mathematics ◽  
Contact Forces ◽  
Dimensional Model ◽  
One Dimensional ◽  
Vascular Stents ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Curved Rods ◽  
The One

In this paper we derive and analyse a one-dimensional model of biodegradable elastic stents. The model is given as a nonlinear system of ordinary differential equations on a graph defined by the geometry of stent struts. The unknowns in the problem are the displacement of the middle curve of the struts, the infinitesimal rotation of the cross-sections of the stent struts, the contact couples and contact forces at struts and a function describing the degradation of the stent. The model is based on the one-dimensional model of a biodegradable elastic curved rod model by Tambača and Žugec (‘One-dimensional quasistatic model of biodegradable elastic curved rods’, Zeitschrift für Angewandte Mathematik und Physik 2015; 66(5): 2759–2785) and the ideas from the one-dimensional elastic stent modelling by Tambača et al. (‘Mathematical modeling of vascular stents’, SIAM Journal on Applied Mathematics 2010; 70(6): 1922–1952) used to formulate contact conditions at vertices. We prove the existence and uniqueness results for the model.

Development of One-Dimensional Models for Elastic Waves in Heterogeneous Beams

2000 ◽  
Vol 67 (4) ◽  
pp. 671-684 ◽  
Author(s):  
H. Murakami ◽  
J. Yamakawa
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Numerical Solutions ◽  
Constitutive Relations ◽  
Small Diameter ◽  
Reinforced Concrete Beams ◽  
Stress Fields ◽  
Beam Model ◽  
Transverse Stress ◽  
One Dimensional

In order to develop an accurate one-dimensional model for wave propagation in heterogeneous beams with uniform cross sections, a Hamilton-type principle is developed by incorporating Reissner’s semi-complimentary energy function. Trial displacement and transverse stress fields are constructed from the solutions of micro-boundary value problems (MBVP’s) defined over the cross section. The MBVP’s are developed from asymptotic expansions that assume a small diameter cross section compared to the axial length and a typical signal wavelength. Saint Venant’s semi-inverse torsion and flexure problems are included in the system of MBVP’s. By utilizing the displacement and transverse stress fields constructed from the numerical solutions of the MBVP’s, the constitutive relations are developed. The model generalizes the Mindlin-Hermann rod model and the Timoshenko beam model for anisotropic heterogeneous beams. The accuracy of the model is assessed by comparing the predicted phase velocity spectra to those computed by using a semi-analytical finite element method. Numerical results are shown for reinforced concrete beams with exterior composite layers. [S0021-8936(01)00601-8]

scholarly journals On the Choice of Shear Correction Factor in Sandwich Structures

2000 ◽  
Author(s):  
Victor Birman ◽  
Charles W. Bert
Keyword(s):  
Correction Factor ◽  
Cross Sections ◽  
Transverse Shear ◽  
Sandwich Structures ◽  
Shear Deformation Theory ◽  
Shear Correction Factor ◽  
Stress Resultant ◽  
Local Problems ◽  
Key Factor ◽  
Non Local

Abstract The first-order shear deformation theory (FSDT) is a relatively simple tool that has been found to yield accurate results in the non-local problems of sandwich structures, such as buckling and free vibration. However, a key factor in practical application of the theory is determination of the transverse shear correction factor (K), which appears as a coefficient in the expression for the transverse shear stress resultant. The physical basis for this factor is that it is supposed to compensate for the FSDT assumption that the shear strain is uniform through the depth of the cross section. In the present paper, the philosophies and results of K determination for homogeneous rectangular cross sections are first reviewed, followed by a review and discussion for the case of sandwich structures.

Timoshenko Beam Model for Exploration and Sensing With a Continuum Centipede Inspired Robot

2013 ◽  
Author(s):  
Javad S. Fattahi ◽  
Davide Spinello
Keyword(s):  
Cross Sections ◽  
Timoshenko Beam ◽  
Continuum Model ◽  
Beam Model ◽  
Timoshenko Beam Model ◽  
One Dimensional ◽  
Surrounding Environment ◽  
Continuum Description ◽  
Robotic Application ◽  
The Continuum

We present the continuum model of a robot inspired by organisms like centipedes and polychaete worms. The continuum model is obtained as the limit of a rigid body chain with pinned elements, which leads to a Timoshenko beam model that is described by a one dimensional continuum with local Euclideian structure. The local Euclideian structure models the cross sections that are kinematically described by their position and orientation. The leg structures in the biological systems are modeled in the continuum limit as a distribution of compliant elements. Modal properties of the system are investigated. The compliance of the legs can be exploited for sensing purposes with specific application to the reconstruction of the surrounding environment and to the estimation of physical properties. The class of models in this papers applies to the continuum description of several emerging robotic application that range from tools for exploration in hazardous or generally not accessible environments (to humans) to novel healthcare systems as for example endoscopic tools for diagnostic in the gastrointestinal tract.

Modelling Techniques in Applied Glaciology: Numerical Modelling of Avalanches

1983 ◽  
Vol 4 ◽  
pp. 297-297
Author(s):  
G. Brugnot
Keyword(s):  
Finite Difference Method ◽  
Transverse Velocity ◽  
Longitudinal Velocity ◽  
Momentum Conservation ◽  
Dimensional Model ◽  
One Dimensional ◽  
Modelling Techniques ◽  
Reference Grid ◽  
The One ◽  
Near Future

We consider the paper by Brugnot and Pochat (1981), which describes a one-dimensional model applied to a snow avalanche. The main advance made here is the introduction of the second dimension in the runout zone. Indeed, in the channelled course, we still use the one-dimensional model, but, when the avalanche spreads before stopping, we apply a (x, y) grid on the ground and six equations have to be solved: (1) for the avalanche body, one equation for continuity and two equations for momentum conservation, and (2) at the front, one equation for continuity and two equations for momentum conservation. We suppose the front to be a mobile jump, with longitudinal velocity varying more rapidly than transverse velocity.We solve these equations by a finite difference method. This involves many topological problems, due to the actual position of the front, which is defined by its intersection with the reference grid (SI, YJ). In the near future our two directions of research will be testing the code on actual avalanches and improving it by trying to make it cheaper without impairing its accuracy.

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