Abstract

In this paper, the exact stiffness matrix of curved beams with nonuniform cross section is derived using direct method. The considered element has two nodes and 12 degrees of freedom, with three forces and three moments applied at each node. The noncoincidence effect of shear center and center of area is also considered in this element. The deformations of the beam are due to bending, torsion, tensile, and shear loads. The line passing through center of area is a general three-dimensional curve and the cross section properties may change arbitrarily along it. The method is extended to deal with distributed loads on the curved beams. The stiffness matrix of some selected types of beams is determined by this method. The results are compared (where possible) with previously published results, simple beam finite element analysis and analytic solution. It is shown that the determined stiffness matrix is exact and that any type of beam can be analyzed by this method.

1.
Ashwell
,
D. G.
, and
Sabir
,
A. B.
, 1971, “
Limitation of Certain Curved Finite Elements When Applied To Arches
,”
Int. J. Mech. Sci.
0020-7403,
13
, pp.
133
139
.
2.
Dawe
,
D. J.
, 1974, “
Curved Finite Elements for the Analysis of Shallow and Deep Arches
,”
Comput. Struct.
0045-7949,
4
, pp.
559
580
.
3.
Choit
,
J. -K.
, and
Lim
,
J. -K.
, 1995, “
General Curved Beam Elements Based on the Assumed Strain Fields
,”
Comput. Struct.
0045-7949,
55
, pp.
379
386
.
4.
Stolarski
,
H.
, and
Belytschko
,
T.
, 1982, “
Membrane Locking and Reduced Integration for Curved Elements
,”
J. Appl. Mech.
0021-8936,
49
, pp.
172
176
.
5.
Prathap
,
G.
, and
Ramesh Babu
,
G.
, 1986, “
An Isoparametric Quadratic Thick Curved Beam Element
,”
Int. J. Numer. Methods Eng.
0029-5981,
23
, pp.
1583
1600
.
6.
Naganarayana
,
B. P.
, and
Prathap
,
G.
, 1990, “
Consistency Aspects of Out-of-Plane Bending, Torsion and Shear in a Quadratic Curved Beam Element
,”
Int. J. Numer. Methods Eng.
0029-5981,
30
, pp.
431
443
.
7.
Prathap
,
G.
, and
Naganarayana
,
B. P.
, 1990, “
Analysis of Locking and Stress Oscillation in a General Curved Beam Element
,”
Int. J. Numer. Methods Eng.
0029-5981,
30
, pp.
177
200
.
8.
Litewka
,
P.
, and
Rakowski
,
J.
, 1998, “
The Exact Thick Arch Finite Element
,”
Comput. Struct.
0045-7949,
68
, pp.
369
379
.
9.
Krishnan
,
A.
, and
Suresh
,
Y. J.
, 1998, “
A Simple Cubic Linear Element for Static and Free Vibration Analyses of Curved Beams
,”
Comput. Struct.
0045-7949,
68
, pp.
473
489
.
10.
Molari
,
L.
, and
Ubertini
,
F.
, 2006, “
A Flexibility-Based Finite Element for Linear Analysis of Arbitrarily Curved Arches
,”
Int. J. Numer. Methods Eng.
0029-5981,
65
, pp.
1333
1353
.
11.
Wu
,
J. -S.
, and
Chiang
,
L. -K.
, 2004, “
Free Vibration of a Circularly Curved Timoshenko Beam Normal to Its Initial Plane using Finite Curved Beam Elements
,”
Comput. Struct.
0045-7949,
82
, pp.
2525
2540
.
12.
Wu
,
J. -S.
, and
Chiang
,
L. -K.
, 2003, “
Out-of-Plane Responses of a Circular Curved Timoshenko Beam Due to a Moving Load
,”
Int. J. Solids Struct.
0020-7683,
40
, pp.
7425
7448
.
13.
Kulikov
,
G. M.
, and
Plotnikova
,
S. V.
, 2004, “
Non-Conventional Non-Linear Two-Node Hybrid Stress-Strain Curved Beam Elements
,”
Finite Elem. Anal. Design
0168-874X,
40
, pp.
1333
1359
.
14.
Spacone
,
E.
,
Ciampi
,
V.
, and
Filippou
,
F. C.
, 1996, “
Mixed Formulation of Nonlinear Beam Finite Element
,”
Comput. Struct.
0045-7949,
58
, pp.
71
83
.
15.
Ayoub
,
A.
, and
Filippou
,
F. C.
, 1998, “
Nonlinear Finite-Element Analysis of RC Shear Panels and Walls
,”
J. Struct. Eng.
0733-9445,
124
, pp.
298
308
.
16.
Taylor
,
R. L.
,
Filippou
,
F. C.
, and
Saritas
,
A.
, 2003, “
Finite Element Solution of Beam Problems
,”
Comput. Mech.
0178-7675,
31
, pp.
25
.
17.
Jafari
,
M.
, 2001, “
Analysis of a Commercial Vehicle Chassis Frame Using a Modified Stiffness Matrix: Comparison With Experimental Results
,” M.Sc. thesis, Mechanical Engineering Department, University of Tehran.
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