NONLINEAR THIN-WALLED BEAMS WITH A RECTANGULAR CROSS-SECTION — PART II

2013 ◽  
Vol 23 (04) ◽  
pp. 743-775 ◽  
Author(s):  
LORENZO FREDDI ◽  
MARIA GIOVANNA MORA ◽  
ROBERTO PARONI
Keyword(s):  
Cross Section ◽  
Elastic Energy ◽  
Rectangular Cross Section ◽  
Limit Behavior ◽  
Rigorous Derivation ◽  
One Dimensional ◽  
Thin Walled ◽  
Dimensional Models ◽  
Nonlinear Elastic ◽  
Cross Section Part

In this paper we report the second part of our results concerning the rigorous derivation of a hierarchy of one-dimensional models for thin-walled beams with a rectangular cross-section. Denoting by h and δh ≪ h the length of the sides of the cross-section of the beam, we analyze the limit behavior of a nonlinear elastic energy which scales as [Formula: see text] when ϵh/δh → 0.

NONLINEAR THIN-WALLED BEAMS WITH A RECTANGULAR CROSS-SECTION — PART I

2012 ◽  
Vol 22 (03) ◽  
pp. 1150016 ◽  
Author(s):  
LORENZO FREDDI ◽  
MARIA GIOVANNA MORA ◽  
ROBERTO PARONI
Keyword(s):  
Cross Section ◽  
Elastic Energy ◽  
Rectangular Cross Section ◽  
Three Dimensional ◽  
Scaling Factor ◽  
One Dimensional ◽  
Thin Walled ◽  
The Cross ◽  
Limit Models ◽  
Cross Section Part

Our aim is to rigorously derive a hierarchy of one-dimensional models for thin-walled beams with rectangular cross-section, starting from three-dimensional nonlinear elasticity. The different limit models are distinguished by the different scaling of the elastic energy and of the ratio between the sides of the cross-section. In this paper we report the first part of our results. More precisely, denoting by h and δh the length of the sides of the cross-section, with δh ≪ h, and by [Formula: see text] the scaling factor of the bulk elastic energy, we analyze the cases in which δh/εh → 0 (subcritical) and δh/εh → 1 (critical).

The Exact One-Dimensional Theory for End-Loaded Fully Anisotropic Beams of Narrow Rectangular Cross Section

2001 ◽  
Vol 68 (6) ◽  
pp. 865-868 ◽  
Author(s):  
P. Ladeve`ze ◽  
J. G. Simmonds
Keyword(s):  
Cross Section ◽  
Plane Stress ◽  
Rectangular Cross Section ◽  
Dimensional Theory ◽  
Explicit Formulas ◽  
Cross Sectional ◽  
Rectangular Shape ◽  
One Dimensional ◽  
Anisotropic Elastic ◽  
Derivatives Of

The exact theory of linearly elastic beams developed by Ladeve`ze and Ladeve`ze and Simmonds is illustrated using the equations of plane stress for a fully anisotropic elastic body of rectangular shape. Explicit formulas are given for the cross-sectional material operators that appear in the special Saint-Venant solutions of Ladeve`ze and Simmonds and in the overall beamlike stress-strain relations between forces and a moment (the generalized stress) and derivatives of certain one-dimensional displacements and a rotation (the generalized displacement). A new definition is proposed for built-in boundary conditions in which the generalized displacement vanishes rather than pointwise displacements or geometric averages.

scholarly journals Analysis of high-rise constructions with the using of three-dimensional models of rods in the finite element program PRINS

2018 ◽  
Vol 33 ◽  
pp. 02033
Author(s):  
Vladimir Agapov
Keyword(s):  
Rectangular Cross Section ◽  
Three Dimensional ◽  
Free Vibrations ◽  
Finite Element Program ◽  
One Dimensional ◽  
Static And Dynamic Analysis ◽  
High Rise ◽  
Element Program ◽  
Dimensional Models ◽  
Three Dimensional Models

The necessity of new approaches to the modeling of rods in the analysis of high-rise constructions is justified. The possibility of the application of the three-dimensional superelements of rods with rectangular cross section for the static and dynamic calculation of the bar and combined structures is considered. The results of the eighteen-story spatial frame free vibrations analysis using both one-dimensional and three-dimensional models of rods are presented. A comparative analysis of the obtained results is carried out and the conclusions on the possibility of three-dimensional superelements application in static and dynamic analysis of high-rise constructions are given on its basis.

Thin-Walled Beams: the Case of the Rectangular Cross-Section

2004 ◽  
Vol 76 (1) ◽  
pp. 45-66 ◽  
Author(s):  
Lorenzo Freddi ◽  
Antonino Morassi ◽  
Roberto Paroni
Keyword(s):  
Cross Section ◽  
Rectangular Cross Section ◽  
Thin Walled

Simulation on Composite Backscattering from Rough Surface with Target above it

2012 ◽  
Vol 490-495 ◽  
pp. 603-607
Author(s):  
Wei Tian ◽  
Xin Cheng Ren
Keyword(s):  
Rough Surface ◽  
Root Mean Square ◽  
Cross Section ◽  
Correlation Length ◽  
Rectangular Cross Section ◽  
Mean Square ◽  
Method Of Moment ◽  
Backscattering Coefficient ◽  
One Dimensional ◽  
Surface Fluctuation

One-dimensional Gaussion rough surface is simulated and employed by Monte Carlo Method, the composite backscattering from one-dimensional Gaussion rough surface with rectangular cross-section column above it is studied using Method of Moment. The curves of composite backscattering coefficient with scattering angle and frequency of incident wave are simulated by numerical calculation, the influence of the root mean square and the correlation length of rough surface fluctuation, the height between the center of the rectangular cross-section column and the rough surface, the length and the width of the rectangular cross-section column is discussed. The characteristic of the composite back-scatting from one-dimensional Gaussion rough surface with a rectangular cross-section column above it is obtained. The results show that the influences of the root mean square and the correlation length of rough surface fluctuation, the height between the center of the rectangular cross-section column and the rough surface, the width of the rectangular cross-section column on the composite backscattering coefficients are obvious while the influences of the length of the rectangular cross-section column on the complex backscattering coefficient is less.

Experimental and Numerical Study of the Energy Absorbed with Various Thickness of Thin Rectangular and Square Sections

2012 ◽  
Vol 229-231 ◽  
pp. 1120-1124
Author(s):  
Sajjad Dehghanpour ◽  
Sobhan Dehghanpour
Keyword(s):  
Numerical Analysis ◽  
Energy Absorption ◽  
Cross Section ◽  
Numerical Study ◽  
Rectangular Cross Section ◽  
Lateral Loading ◽  
Thin Walled

Impact is one of very important subjects which always have been considered in mechanical science. Nature of impact is such that which makes its control a hard task. Therefore it is required to present the transfer of impact to other vulnerable part of a structure, when it is necessary, one of the best method of absorbing energy of impact , is by using Thin-walled tubes these tubes collapses under impact and with absorption of energy, it prevents the damage to other parts. Purpose of recent study is to survey the deformation and energy absorption of tubes with different type of cross section (rectangular or square) and with similar volumes, height, mean cross section, and material under loading. Lateral loading of tubes are quasi-static type and beside as numerical analysis, also experimental experiences has been performed to evaluate the accuracy of the results. Results from the surveys is indicates that in a same conditions which mentioned above, samples with square cross section ,absorb more energy compare to rectangular cross section, and also by increscent in thickness, energy absorption would be more.

One-dimensional model of fourth order for rods with loading on lateral boundary: The case of rectangular cross section

2016 ◽  
Vol 22 (12) ◽  
pp. 2269-2287 ◽  
Author(s):  
Erick Pruchnicki
Keyword(s):  
Cross Section ◽  
Fourth Order ◽  
Displacement Field ◽  
Rectangular Cross Section ◽  
Transverse Dimension ◽  
Lateral Boundary ◽  
Dimensional Model ◽  
Equilibrium Equations ◽  
Lagrange Equations ◽  
One Dimensional

We propose deducing from three-dimensional elasticity a one dimensional model of a beam when the lateral boundary is not free of traction. Thus the simplification induced by the order of magnitude of transverse shearing and transverse normal stress must be removed. For the sake of simplicity we consider a beam with rectangular cross section. The displacement field in rods can be approximated by using a Taylor–Young expansion in transverse dimension of the rod and we truncate the potential energy at the fourth order. By considering exact equilibrium equations, the highest-order displacement field can be removed and the Euler–Lagrange equations are simplified.

Flexural Vibrations of a Thin-Walled Cylinder of Rectangular Cross Section

1958 ◽  
Vol 9 (4) ◽  
pp. 331-345
Author(s):  
E. H. Mansfield
Keyword(s):  
Cross Section ◽  
Stress Function ◽  
Flexural Rigidity ◽  
Rectangular Cross Section ◽  
Shear Lag ◽  
Transverse Vibrations ◽  
Thin Walled ◽  
Flexural Vibrations ◽  
Walled Cylinder ◽  
Natural Transverse

SummaryThe natural transverse vibrations of a long cylindrical box of doubly symmetrical rectangular cross section are considered. Explicit stress-function solutions are obtained for the webs and the top and bottom surfaces so that the effects of shear lag and shear deflection are inherently included. The results are expressed simply in terms of an effective flexural rigidity, which may be determined with the aid of a number of graphs.

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