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AN EFFICIENT CURVED BEAM FINITE ELEMENT
Author(s) -
LITEWKA PRZEMYSLAW,
RAKOWSKI JERZY
Publication year - 1997
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19970730)40:14<2629::aid-nme179>3.0.co;2-y
Subject(s) - finite element method , timoshenko beam theory , mathematical analysis , stiffness matrix , beam (structure) , mathematics , finite element limit analysis , mixed finite element method , bending stiffness , geometry , structural engineering , engineering
The plane two‐node curved beam finite element with six degrees of freedom is considered. Knowing the set of 18 exact shape functions their approximation is derived using the expansion of the trigonometric functions in the power series. Unlike the ones commonly used in the FEM analysis the functions suggested by the authors have the coefficients dependent on the geometrical and physical properties of the element. From the strain energy formula the stiffness matrix of the element is determined. It is very simple and can be split into components responsible for bending, shear and axial forces influences on the displacements. The proposed element is totally free of the shear and membrane locking effects. It can be referred to the shear‐flexible (parameter d ) and compressible (parameter e ) systems. Neglecting d or e yields the finite elements in all necessary combinations, i.e. curved Euler–Bernoulli beam or curved Timoshenko beam with or without the membrane effect. Applying the elaborated element in the calculations a very good convergence to the analytical results can be obtained even with a very coarse mesh without the commonly adopted corrections as reduced or selective integration or introduction of the stabilization matrices, additional constraints, etc., for the small depth–length ratio. © 1997 John Wiley & Sons, Ltd.