Analysis of active closed cross-section slender beams based on asymptotically correct thin-wall beam theory

2007 ◽  
Vol 16 (1) ◽  
pp. 221-229 ◽  
Author(s):  
F Khouli ◽  
R G Langlois ◽  
F F Afagh
Keyword(s):  
Cross Section ◽  
Beam Theory ◽  
Thin Wall ◽  
Slender Beams

First and Second Order Elastoplastic Analyses of Thin-Walled Metal Members using Generalized Beam Theory

2018 ◽  
Author(s):  
Miguel Abambres
Keyword(s):  
Finite Element ◽  
Stainless Steel ◽  
Cross Section ◽  
Beam Theory ◽  
Second Order ◽  
Flow Rule ◽  
Non Linear ◽  
Thin Walled ◽  
Shell Finite Element ◽  
Generalized Beam Theory

Original Generalized Beam Theory (GBT) formulations for elastoplastic first and second order (postbuckling) analyses of thin-walled members are proposed, based on the J2 theory with associated flow rule, and valid for (i) arbitrary residual stress and geometric imperfection distributions, (ii) non-linear isotropic materials (e.g., carbon/stainless steel), and (iii) arbitrary deformation patterns (e.g., global, local, distortional, shear). The cross-section analysis is based on the formulation by Silva (2013), but adopts five types of nodal degrees of freedom (d.o.f.) – one of them (warping rotation) is an innovation of present work and allows the use of cubic polynomials (instead of linear functions) to approximate the warping profiles in each sub-plate. The formulations are validated by presenting various illustrative examples involving beams and columns characterized by several cross-section types (open, closed, (un) branched), materials (bi-linear or non-linear – e.g., stainless steel) and boundary conditions. The GBT results (equilibrium paths, stress/displacement distributions and collapse mechanisms) are validated by comparison with those obtained from shell finite element analyses. It is observed that the results are globally very similar with only 9% and 21% (1st and 2nd order) of the d.o.f. numbers required by the shell finite element models. Moreover, the GBT unique modal nature is highlighted by means of modal participation diagrams and amplitude functions, as well as analyses based on different deformation mode sets, providing an in-depth insight on the member behavioural mechanics in both elastic and inelastic regimes.

Bending Vibrations of Variable Section Beams

1956 ◽  
Vol 23 (1) ◽  
pp. 103-108
Author(s):  
E. T. Cranch ◽  
Alfred A. Adler
Keyword(s):  
Cross Section ◽  
Rectangular Cross Section ◽  
Circular Cross Section ◽  
Beam Theory ◽  
Cantilever Beams ◽  
Constant Depth ◽  
Bending Vibrations ◽  
Variable Section

Abstract Using simple beam theory, solutions are given for the vibration of beams having rectangular cross section with (a) linear depth and any power width variation, (b) quadratic depth and any power width variation, (c) cubic depth and any power width variation, and (d) constant depth and exponential width variation. Beams of elliptical and circular cross section are also investigated. Several cases of cantilever beams are given in detail. The vibration of compound beams is investigated. Several cases of free double wedges with various width variations are discussed.

On Torsion and Transverse Flexure of Orthotropic Elastic Plates

1980 ◽  
Vol 47 (4) ◽  
pp. 855-860 ◽  
Author(s):  
E. Reissner
Keyword(s):  
Cross Section ◽  
Beam Theory ◽  
Bending Moment ◽  
Rate Of Change ◽  
Elastic Plates ◽  
Shear Center ◽  
Explicit Consideration ◽  
The Difference ◽  
Shear Deformable ◽  
Shear Deformable Plates

The equations of transverse bending of shear-deformable plates are used for the derivation of a system of one-dimensional equations for beams with unsymmetrical cross section, with account for warping stiffness, in addition to bending, shearing, and twisting stiffness. Significant results of the analysis include the observation that the rate of change of differential bending moment is given by the difference between torque contribution due to plate twisting moments and torque contribution due to plate shear stress resultants; a formula for shear center location which generalizes a result by Griffith and Taylor so as to account for transverse shear deformability and end-section warping restraint; a second-order compatibility equation for the differential bending moment; a contracted boundary condition of support for unsymmetrical cross-section beam theory in place of an explicit consideration of the warping deformation boundary layer; and construction of a problem where the effect of the conditions of support of the beam is such as to give noncoincident shear center and twist center locations.

Elastave Bucking of Whole-Corrugate Web H-Beam

2011 ◽  
Vol 368-373 ◽  
pp. 23-27
Author(s):  
Yong Chen ◽  
Chun Yu Zhang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Cross Section ◽  
Engineering Application ◽  
Thin Wall ◽  
Constant Cross Section ◽  
Buckling Strength ◽  
Corrugated Web ◽  
Variable Section ◽  
H Beam

Contradiction between thin wall and stability of H-beam is a kind of problem in engineering field, the corrugated web H-beam researched in this paper relieve the contradiction to some extent. This paper apply finite element method of variable section beam and high programming language of MATLAB to analyze buckling strength under axis pressure and effect of critical load of parameter of whole-corrugated web H-beam and contrast to constant cross section H-beam, declaration superiority of whole-corrugated web H-beam with example, supply theory to this kind of H-beam in engineering application.

Buckling Behavior of Pultruded Monosymmetric Members

2005 ◽  
Vol 297-300 ◽  
pp. 1259-1264
Author(s):  
Seung Sik Lee ◽  
Soon Jong Yoon ◽  
S.K. Cho ◽  
Jong Myen Park
Keyword(s):  
Cross Section ◽  
Ritz Method ◽  
Beam Theory ◽  
Fiber Reinforced Polymer ◽  
Structural Members ◽  
Uniform Compression ◽  
Torsional Mode ◽  
Axial Forces ◽  
Reinforced Polymer ◽  
Buckling Behavior

Pultruded fiber reinforced polymer (FRP) structural members have been used in various civil engineering applications. T-shapes are commonly used for chord members in trusses and for bracing members. In these cases, T-shapes are mainly subjected to axial forces, and stability of a member is one of the major concerns in the design. Due to the monosymmetry existing in the cross-section of T-shapes, T-shapes are likely to buckle in a flexural-torsional mode. An energy solution, using the Ritz method, to the buckling problem of a pulturuded T-shape under uniform compression is derived based on a composite thin-walled beam theory developed by Bauld and Tzeng. The solution accounts for the bending-twisting and bending-extension coupling effects. The derived energy solutions are compared to the experimental results of buckling tests conducted on seventeen pultruded T-shapes. It is found that the ratios of the experimental to analytical results are in the range of 1.00 to 1.32.

Systematic design of cantilever beams for muscle research

1977 ◽  
Vol 42 (5) ◽  
pp. 786-794 ◽  
Author(s):  
R. J. McLaughlin
Keyword(s):  
Elastic Modulus ◽  
Cross Section ◽  
Experimental Studies ◽  
Circular Cross Section ◽  
Design Procedure ◽  
Structural Materials ◽  
Thick Wall ◽  
Beam Parameter ◽  
Thin Wall ◽  
Cantilever Beams

Experimental studies of muscle contraction often involve difficult problems in the design of cantilever beams for movable levers, transducers, or mechanical supports. Equations are presented for the calculation of mass, inertia, stress distribution, strain, deflection curve, compliance, and resonant frequency of uniform or nonuniform cantilever beams made of structural materials of different density or elastic modulus. Formulas are listed for solid, thick-wall, and thin-wall uniform beams of rectangular and circular cross section. Physical properties including density, elastic and torsional moduli, stress and strain limits, thermal expansion coefficients, Poisson's ratio, and certain elastic-modulus-to-density ratios are tabulated for structural materials including common metals, glass, plastic, and wood. A graphical design procedure is presented based on a chart containing loci of constant beam parameter values as a function of beam length and height or diameter, for the simple geometries. The choice of structural material is discussed for design problems with typical constraints, and examples are given of the design of beams of nonuniform cross section. Methods for extending the design chart to other geometries and materials are included.

Increasing the Production Accuracy of Profile Bending with Methods of Computational Intelligence

2009 ◽  
Vol 17 (4) ◽  
pp. 561-576 ◽  
Author(s):  
Alessandro Selvaggio ◽  
Uwe Dirksen ◽  
A. Erman Tekkaya ◽  
Marco Schikorra ◽  
Matthias Kleiner
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Closed Loop ◽  
Fuzzy Controller ◽  
Structure Optimization ◽  
Quality Criteria ◽  
Closed Loop Control ◽  
Software System ◽  
Thin Wall ◽  
Loop Control

Important quality criteria for profile bending are an accurate profile contour and an accurate cross section. During the bending process, torsion of the profile, deformation of the cross section, and deviations at the profile contour can occur. If these undesired effects are too large, the bent profile is not usable. Critical causes of profile cross section deformation are thin wall thicknesses with hollow sections. The profile torsion is favored by asymmetrical profile cross sections. These effects can be minimized by a production-correct profile design, whereby a trade-off between a production-correct design and the boundary conditions exists. Furthermore, undesired variations in the profile material properties and the profile cross section lead to deviations in the profile contour. These deviations cannot be reduced by design but by usage of a closed-loop control during bending. In this article, a software system for three-roll bending is presented that minimizes undesirable effects during bending by structure optimization of the profile cross section and application of closed-loop control. The structure optimization is based on an evolutionary algorithm and the process control uses a neuro-fuzzy controller. The structure of the software system and results of experiments are presented and discussed. 1

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