A finite element formulation for beams with thin walled cross-sections

1982 ◽  
Vol 15 (6) ◽  
pp. 691-699 ◽  
Author(s):  
Geir A. Gunnlaugsson ◽  
P. Terndrup Pedersen
Keyword(s):  
Finite Element ◽  
Cross Sections ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Thin Walled

Analysis of Thin-Walled Closed Beams With General Quadrilateral Cross Sections

1999 ◽  
Vol 66 (4) ◽  
pp. 904-912 ◽  
Author(s):  
J. H. Kim ◽  
Y. Y. Kim
Keyword(s):  
Finite Element ◽  
Cross Sections ◽  
Distortion Function ◽  
Element Formulation ◽  
Numerical Work ◽  
New Approach ◽  
One Dimensional ◽  
Static And Dynamic Analysis ◽  
Thin Walled ◽  
The One

This paper deals with the one-dimensional static and dynamic analysis of thin-walled closed beams with general quadrilateral cross sections. The coupled deformations of distortion as well as torsion and warping are investigated in this work. A new approach to determine the functions describing section deformations is proposed. In particular, the present distortion function satisfies all the necessary continuity conditions unlike Vlasov's distortion function. Based on these section deformation functions, a one-dimensional theory dealing with the coupled deformations is presented. The actual numerical work is carried out using two-node C0 finite element formulation. The present one-dimensional results for some static and free-vibration problems are compared with the existing and the plate finite element results.

Modelling of rotors with three-dimensional solid finite elements

2001 ◽  
Vol 36 (4) ◽  
pp. 359-371 ◽  
Author(s):  
A Nandi ◽  
S Neogy
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Cross Sections ◽  
Three Dimensional ◽  
Element Model ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Two Dimensional ◽  
Inertia Effects ◽  
Solid Finite Elements

A shaft is modelled using three-dimensional solid finite elements. The shear-deformation and rotary inertia effects are automatically included through the three-dimensional elasticity formulation. The formulation allows warping of plane cross-sections and takes care of gyroscopic effect. Unlike a beam element model, the present model allows the actual rotor geometry to be modelled. Shafts with complicated geometry can be modelled provided that the shaft cross-section has two axes of symmetry with equal or unequal second moment of areas. The acceleration of a point on the shaft is determined in inertial and rotating frames. It is found that the finite element formulation becomes much simpler in a rotating frame of reference that rotates about the centre-line of the bearings with an angular velocity equal to the shafts spin speed. The finite element formulation in the above frame is ideally suited to non-circular shafts with solid or hollow, prismatic or tapered sections and continuous or abrupt change in cross-sections. The shaft and the disc can be modelled using the same types of element and this makes it possible to take into account the flexibility of the disc. The formulation also allows edge cracks to be modelled. A two-dimensional model of shaft disc systems executing synchronous whirl on isotropic bearings is presented. The application of the two-dimensional formulation is limited but it reduces the number of degrees of freedom. The three-dimensional solid and two-dimensional plane stress finite element models are extensively validated using standard available results.

On a Finite Element Formulation of Dynamical Torsion of Beams Including Warping Inertia and Shear Deformation Due to Nonuniform Warping

1983 ◽  
Vol 105 (4) ◽  
pp. 476-483
Author(s):  
A. Potiron ◽  
D. Gay
Keyword(s):  
Finite Element ◽  
Shear Deformation ◽  
Cross Section ◽  
Experimental Results ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Secondary Effects ◽  
Mass Matrices ◽  
Warping Displacement ◽  
Thin Walled

We start from the energetical expressions of dynamical torsion of beams in terms of angular and warping displacement and velocity. We derive the stiffness and two mass matrices including both secondary effects for torsion: the shear deformation due to nonuniform warping and the warping inertia. The suitability of these matrices for evaluation modified torsional frequencies is investigated in the case of thick, as well as thin-walled, cross section beams by comparison with analytical and experimental results.

Shear-deformable hybrid finite-element formulation for lateral-torsional buckling analysis of composite thin-walled members

2020 ◽  
Author(s):  
Emre Erkmen ◽  
Vida Niki ◽  
Ashkan Afnani
Keyword(s):  
Finite Element ◽  
Beam Theory ◽  
Buckling Analysis ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Lateral Torsional Buckling ◽  
Torsional Buckling ◽  
Hybrid Finite Element ◽  
Thin Walled ◽  
Shear Deformable

A shear deformable hybrid finite element formulation is developed for the lateral-torsional buckling analysis of fiber-reinforced composite thin-walled members with open cross-section. The method is developed by using the Hellinger-Reissner functional. Comparison to the displacement-based formulations the current hybrid formulation has the advantage of incorporating the shear deformation effects easily by using the strain energy of the shear stress field without modifying the basic kinematic assumptions of the thin-walled beam theory. Numerical results are validated through comparisons with results based on other formulations presented in the literature. Examples illustrate the effects of shear deformations and stacking sequence of the composite layers in predicting bucking loads.

scholarly journals Shear deformable hybrid finite element formulation for buckling analysis of composite columns

2018 ◽  
Vol 45 (4) ◽  
pp. 279-288
Author(s):  
Vida Niki ◽  
R. Emre Erkmen
Keyword(s):  
Finite Element ◽  
Shear Stress ◽  
Shear Deformation ◽  
Cross Sections ◽  
Buckling Analysis ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Composite Columns ◽  
Hybrid Finite Element ◽  
Shear Deformable

The objective of this study is to develop a shear deformable hybrid finite element formulation for the flexural buckling analysis of fiber-reinforced laminate composite columns with doubly symmetric cross sections. The hybrid finite element formulation is developed by using the Hellinger-Reissner functional which is obtained by introducing the conditions of compatibility as auxiliary conditions to the potential energy functional. The shear deformation effects due to bending are included by equilibrating shear stress. In comparison to the displacement-based formulations the current hybrid formulation has the advantage of incorporating the shear deformation effects easily by using the strain energy of the shear stress field without modifying the basic kinematic assumptions of the beam theory. The agreement with Engesser formulation for flexural buckling analysis of columns with shear-weak cross sections shows the applicability and accuracy of the current hybrid finite element method for composite structural elements. The applicability of the developed method herein to sandwich and built-up columns are also illustrated.

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