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.

scholarly journals Finite element formulation of slender structures with shear deformation based on the Cosserat theory

2007 ◽  
Vol 44 (24) ◽  
pp. 7785-7802 ◽  
Author(s):  
Dongsheng Liu ◽  
D.Q. Cao ◽  
Richard Rosing ◽  
Charles H.-T. Wang ◽  
Andrew Richardson
Keyword(s):  
Finite Element ◽  
Shear Deformation ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Cosserat Theory ◽  
Slender Structures

B-Spline Finite Element Formulation for Laminated Composite Shells

2008 ◽  
Author(s):  
Antonio Carminelli ◽  
Giuseppe Catania
Keyword(s):  
Finite Element ◽  
Tensor Product ◽  
Shear Deformation ◽  
Laminated Composite ◽  
Finite Element Formulation ◽  
Spline Functions ◽  
Element Formulation ◽  
Shape Functions ◽  
Composite Shells ◽  
B Spline

This paper presents a finite element formulation for the dynamical analysis of general double curvature laminated composite shell components, commonly used in many engineering applications. The Equivalent Single Layer theory (ESL) was successfully used to predict the dynamical response of composite laminate plates and shells. It is well known that the classic shell theory may not be effective to predict the deformational behavior with sufficient accuracy when dealing with composite shells. The effect of transverse shear deformation should be taken into account. In this paper a first order shear deformation ESL laminated shell model, adopting B-spline functions as approximation functions, is proposed and discussed. The geometry of the shell is described by means of the tensor product of B-spline functions. The displacement field is described by means of tensor product of B-spline shape functions with a different order and number of degrees of freedom with respect to the same formulation used in geometry description, resulting in a non-isoparametric formulation. A solution refinement method, making it possible to increase the order of the displacement shape functions without using the well known B-spline “degree elevation” algorithm, is also proposed. The locking effect was reduced by employing a low-order integration technique. To test the performance of the approach, the static solution of a single curvature shell and the eigensolutions of composite plates were obtained by numerical simulation and are then compared with known solutions. Discussion follows.

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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