Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Efficient formulation of a two-noded curved beam element under finite
  rotations   The paper extends the formulation of a 2D geometrically exact beam element
proposed in our previous paper [1] to curved elastic beams. This formulation is
based on equilibrium equations in their integrated form, combined with the
kinematic relations and sectional equations that link the internal forces to
sectional deformation variables. The resulting first-order differential
equations are approximated by the finite difference scheme and the boundary
value problem is converted to an initial value problem using the shooting
method. The paper develops the theoretical framework based on the
Navier-Bernoulli hypothesis but the approach could be extended to
shear-flexible beams. The initial shape of the beam is captured with high
accuracy, for certain shapes including the circular one even exactly. Numerical
procedures for the evaluation of equivalent nodal forces and of the element
tangent stiffness are presented in detail. Unlike standard finite element
formulations, the present approach can increase accuracy by refining the
integration scheme on the element level while the number of global degrees of
freedom is kept constant. The efficiency and accuracy of the developed scheme
are documented by five examples that cover circular and parabolic arches and a
spiral-shaped beam. It is also shown that, for initially curved beams, a cross
effect in the relations between internal forces and deformation variables
arises, i.e., the bending moment affects axial stretching and the normal force
affects the curvature.

2
The categories of this paper are: math
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci