Finite beam element with exact shape functions for torsional analysis in thin-walled single- or multi-cell box girders

Starting with total potential energy variational principle, the governing equilibrium coupled equations for the torsional-warping static analysis of open thin-walled beams under various torsional and warping moments are derived. The formulation captures shear deformation effects due to warping. The exact closed form solutions for torsional rotation and warping deformation functions are then developed for the coupled system of two equations. The exact solutions are subsequently used to develop a family of shape functions which exactly satisfy the homogeneous form of the governing coupled equations. A super-convergent finite beam element is then formulated based on the exact shape functions. Key features of the beam element developed include its ability to (a) eliminate spatial discretization arising in commonly used finite elements, and (e) eliminate the need for time discretization. The results based on the present finite element solution are found to be in excellent agreement with those based on exact solution and ABAQUS finite beam element solution at a small fraction of the computational and modelling cost involved.

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A finite element with exact shape functions for shear lag analysis in multi-cell box girders

Computers & Structures ◽

10.1016/0045-7949(91)90083-x ◽

1991 ◽

Vol 39 (1-2) ◽

pp. 155-163 ◽

Cited By ~ 22

Author(s):

A.G. Razaqpur ◽

H.G. Li

Keyword(s):

Finite Element ◽

Shear Lag ◽

Shape Functions ◽

Box Girders ◽

Exact Shape

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Exact shape functions of imperfect beam element for stability analysis

Advances in Engineering Software ◽

10.1016/j.advengsoft.2006.08.020 ◽

2007 ◽

Vol 38 (8-9) ◽

pp. 576-585 ◽

Cited By ~ 3

Author(s):

R. Adman ◽

H. Afra

Keyword(s):

Stability Analysis ◽

Beam Element ◽

Shape Functions ◽

Exact Shape

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Exact Shape Functions for Timoshenko Beam Element

IOSR Journal of Computer Engineering ◽

10.9790/0661-1903041220 ◽

2017 ◽

Vol 19 (03) ◽

pp. 12-20

Author(s):

Sri Tudjono ◽

Aylie Han ◽

Dinh-Kien Nguyen ◽

Shota Kiryu ◽

Buntara S. Gan

Keyword(s):

Timoshenko Beam ◽

Beam Element ◽

Shape Functions ◽

Exact Shape ◽

Timoshenko Beam Element

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Finite element formulation for shear deformable thin-walled beams

Canadian Journal of Civil Engineering ◽

10.1139/l11-007 ◽

2011 ◽

Vol 38 (4) ◽

pp. 383-392 ◽

Cited By ~ 3

Author(s):

Liping Wu ◽

Magdi Mohareb

Keyword(s):

Finite Element ◽

Differential Equations ◽

Boundary Conditions ◽

Element Formulation ◽

Shape Functions ◽

Stationary Potential ◽

Cross Sectional ◽

Exact Shape ◽

Thin Walled ◽

Shear Deformable

Starting with the principle of stationary potential energy, this paper develops the governing differential equations of equilibrium and boundary conditions for shear deformable thin-walled beams with open cross-section. Unlike conventional solutions, the formulation is based on a non-orthogonal coordinate system, in which the selected origin is generally offset from the section centroid. The exact solution of the resulting coupled differential equations of equilibrium is derived and used to develop exact shape functions. A finite element based on the exact shape functions is then formulated. Through a series of examples, the adoption of non-orthogonal coordinates is shown to enable the seamless modelling of structural members with eccentric boundary conditions and (or) stepwise cross-sectional variations.

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Derivation of an Efficient Non-Prismatic Thin Curved Beam Element Using Basic Displacement Functions

Shock and Vibration ◽

10.1155/2012/786191 ◽

2012 ◽

Vol 19 (2) ◽

pp. 187-204 ◽

Cited By ~ 7

Author(s):

Ahmad Shahba ◽

Reza Attarnejad ◽

Mehran Eslaminia

Keyword(s):

Special Functions ◽

Free Vibration Analysis ◽

Beam Element ◽

Point Of View ◽

Curved Beam ◽

Shape Functions ◽

Curved Beams ◽

Curved Beam Element ◽

Exact Shape ◽

Basic Displacement Functions

The efficiency and accuracy of the elements proposed by the Finite Element Method (FEM) considerably depend on the interpolating functions, namely shape functions, used to formulate the displacement field within an element. In this paper, a new insight is proposed for derivation of elements from a mechanical point of view. Special functions namely Basic Displacement Functions (BDFs) are introduced which hold pure structural foundations. Following basic principles of structural mechanics, it is shown that exact shape functions for non-prismatic thin curved beams could be derived in terms of BDFs. Performing a limiting study, it is observed that the new curved beam element successfully becomes the straight Euler-Bernoulli beam element. Carrying out numerical examples, it is shown that the element provides exact static deformations. Finally efficiency of the method in free vibration analysis is verified through several examples. The results are in good agreement with those in the literature.

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