MODELING WITH INCREASED EFFICIENCY AND VERSATILITY FOR FLEXURAL-TORSIONAL BUCKLING OF UNSYMMETRICAL THIN-WALLED STRUCTURES

2002 ◽  
Vol 02 (04) ◽  
pp. 431-456 ◽  
Author(s):  
S. S. MARZOUK ◽  
A. S. GENDY ◽  
S. N. MIKHAIEL ◽  
A. F. SALEEB
Keyword(s):  
Exact Solution ◽  
Cross Sections ◽  
Degrees Of Freedom ◽  
Performance Enhancement ◽  
Coupled System ◽  
Difficult Case ◽  
Torsional Buckling ◽  
Thin Walled Structures ◽  
Thin Walled ◽  
Flexural Torsional Buckling

Aiming at the performance-enhancement in coarse mesh modeling, we utilize a number of closed form solutions of a class of torsionally loaded thin-walled bars to formulate a two-noded element for spatial buckling analysis. The key in this relates to the use of the "exact" solution for the displacement fields (as oppose to the more conventional finite element approach where polynomial/Lagrangian-type interpolation is employed). That is, in addition to the well known "exact" solution for the coupled flexure/transverse-shear problem, we utilize a new "exact" solution for the more difficult case of coupled system of differential equations governing a torsionally loaded thin-walled beam using the higher-order theories of non-uniform twist/bi-moment with coupled warping-shear deformations. For the linear analysis, convergence and accuracy study indicated that the proposed model to be rapidly convergent, stable and computationally efficient; i.e. one element is sufficient to exactly represent an end loaded part of the beam. Such model has been extended to account for nonlinear analysis, in particular, the flexural torsional buckling of thin-walled structures. To this end, the effect of finite rotations in space is accounted for as per the modern theories of spatial buckling, resulting in second-order accurate geometric stiffness matrices. Compared with the classical theory of thin-walled structures, the present approach is more general in that all significant modes of stretching, bending, shear (due to both flexure and torsional/warping), torsion, and warping are accounted for. The inclusion of non-uniform torsion is accomplished through adoption of the principle sectorial area. This requires incorporation of a warping degree of freedom in addition to the conventional six degrees of freedom at each node. The element is derived for general cross sections including the Wagner-effect contributions. The model's properties and performance, particularly with regard to the resulting (significant) improvements in mesh accuracy, are assessed in a fairly complete set of numerical simulations.

Optimization of cold-formed steel pallet racking cross-sections for flexural–torsional buckling with constraints on the geometry

2009 ◽  
Vol 31 (11) ◽  
pp. 2711-2722 ◽  
Author(s):  
M.M. Pastor ◽  
M. Casafont ◽  
E. Chillarón ◽  
A. Lusa ◽  
F. Roure ◽  
...  
Keyword(s):  
Cross Sections ◽  
Torsional Buckling ◽  
Cold Formed Steel ◽  
Flexural Torsional Buckling

Numerical Investigation of Cross-Section on Aluminum A6063 Thin-Walled Structures under Low-Velocity Impact Loading

2014 ◽  
Vol 1019 ◽  
pp. 96-102
Author(s):  
Ali Taherkhani ◽  
Ali Alavi Nia
Keyword(s):  
Energy Absorption ◽  
Cross Section ◽  
Cross Sections ◽  
Peak Load ◽  
Circular Cross Section ◽  
Absorption Capacity ◽  
Energy Absorption Capacity ◽  
Thin Walled Structures ◽  
Thin Walled ◽  
Crush Strength

In this study, the energy absorption capacity and crush strength of cylindrical thin-walled structures is investigated using nonlinear Finite Elements code LS-DYNA. For the thin-walled structure, Aluminum A6063 is used and its behaviour is modeled using power-law equation. In order to better investigate the performance of tubes, the simulation was also carried out on structures with other types of cross-sections such as triangle, square, rectangle, and hexagonal, and their results, namely, energy absorption, crush strength, peak load, and the displacement at the end of tubes was compared to each other. It was seen that the circular cross-section has the highest energy absorption capacity and crush strength, while they are the lowest for the triangular cross-section. It was concluded that increasing the number of sides increases the energy absorption capacity and the crush strength. On the other hand, by comparing the results between the square and rectangular cross-sections, it can be found out that eliminating the symmetry of the cross-section decreases the energy absorption capacity and the crush strength. The crush behaviour of the structure was also studied by changing the mass and the velocity of the striker, simultaneously while its total kinetic energy is kept constant. It was seen that the energy absorption of the structure is more sensitive to the striker velocity than its mass.

scholarly journals On incorporating warping effects due to transverse shear and torsion into the theories of straight elastic bars

2020 ◽  
Author(s):  
T. Lewiński ◽  
S. Czarnecki
Keyword(s):  
Cross Sections ◽  
Transverse Shear ◽  
Explicit Construction ◽  
Effective Characteristics ◽  
Warping Function ◽  
Torsional Buckling ◽  
Lateral Buckling ◽  
First Order ◽  
Thin Walled ◽  
Scientific Tool

Abstract By endowing El Fatmi’s theories of bars with first-order warping functions due to torsion and shear, a family of theories of bars, of various applicability ranges, is effectively constructed. The theories thus formed concern bars of arbitrary cross-sections; they are reformulations of the mentioned theories by El Fatmi and theories by Kim and Kim, Librescu and Song, Vlasov and Timoshenko. The Vlasov-like theory thus developed is capable of describing the torsional buckling and lateral buckling phenomena of bars of both solid and thin-walled cross-sections, which reflects the non-trivial correspondence, noted by Wagner and Gruttmann, between the torsional St.Venant’s warping function and the contour-wise defined warping functions proposed by Vlasov. Moreover, the present paper delivers an explicit construction of the constitutive equations of Timoshenko’s theory; the equations linking transverse forces with the measures of transverse shear turn out to be coupled for all bars of asymmetric cross-sections. The modeling is hierarchical: the warping functions are numerically constructed by solving the three underlying 2D scalar elliptic problems, providing the effective characteristics for the 1D models of bars. The 2D and 1D problems are indissolubly bonded, thus forming a unified scientific tool, deeply rooted in the hitherto existing knowledge on elasticity of elastic straight bars.

Crashing Behaviour Analysis of TWB Tubular Structures with Different Cross-Sections

2013 ◽  
Vol 814 ◽  
pp. 159-164
Author(s):  
Vlad Andrei Ciubotariu
Keyword(s):  
Finite Element ◽  
Cross Sections ◽  
Fuel Efficiency ◽  
Tubular Structures ◽  
Tailor Welded Blanks ◽  
Thin Walled Structures ◽  
Prediction And Control ◽  
Thin Walled ◽  
Crushing Behavior ◽  
Bimetallic Structures

The present paper investigates the crashing behavior and energy absorption characteristics of thin-walled (tubular) structures with different cross-sections made from tailor welded blanks (TWB) which were subject of axial quasistatic loadings. Resulted data were obtained by using explicit nonlinear finite element code LS_Dyna V971. Implementing the TWB into the auto industry was an efficient method to decrease the general weight of different structures. By far, these kind of bimetallic structures are largely utilized in auto and naval industries because it led to important decrease of scarp quantities and general manufacturing costs, improved material use and probably the most important, great fuel efficiency. After reviewing the literature it was concluded that proper combination between mechanical characteristics of sheet metals, different thicknesses and cross-section shapes into the same thin-walled structure is far too little researched and understood. The aims of this study are better understandings of the crashing behavior regarding thin-walled structure with various cross-sections made from TWB blanks subject to quasistatic loadings. The non-linear finite element platform LS_Dyna V971 was used for the numerical analysis of the crushing behavior regarding the thin-walled structures. Having two materials constituting the thin-walled structures, the crashing behavior changed during the quasistatic loading. Thus, the crashing inertia of the structure is somehow limited and controlled. It is noted that material ratio should not be randomly chosen due to the unexpected crashing mode which could aggravate the prediction and control of the crashing behavior of the thin-walled structure.

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