JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - 55

(e)): in-plane Poisson's effects and
distortions (very important for thinwalled sections), and out-of-plane
warpings;
- full (6x6) matrix of the structural
(1D) behaviour of the beam (Figure
2-(f )) from which one can derive
all the conventional sectional char-acteristics (elastic centre, orientation of inertia axes, shear centre,
axial, flexional and torsional ri-gidities) and all the constants of
the elastic couplings between tension
bending and torsion that can occur
for an arbitrary anisotropic and
composite section.

Fig. 1: Homogeneous and composite sections

Here, it is important to note that these
MCS go far beyond the sole conventional sectional constants; they constitute a set of mechanical information
that can really help to understand the
section's mechanics and the beam's
structural behaviour. These MCS
computed by CSection will be later
used by CBeam.

Fig. 2: Snapshots of the CSection interface: (a) section with the position of the elastic centre, the shear centre
and the inertia axis; (b) sectional axial stresses due to a unit bending/x, (c) Poisson's effect, (d) distortions, (e)
warpings , (f) (6x6) 1D rigidity matrix and classical sectional constants

heterogeneous structural tests that
need an adequate numerical tool to be
properly exploited.
CSection & CBeam is briefly presented in Figure 1.

CSection
CSection [1] is a software application
devoted to the computation of MCS
by 2D finite elements. The section
(Figure 1) may be solid or walled,
open or closed, symmetric or not,
and made of elastic and anisotropic
materials (perfectly bonded together).
To define a section, the user selects
the 2D geometry and the material(s);
each anisotropic material can be freely
oriented, and winding can also be

taken into account.
For a given section (Figure 2-(a)) defined by the user, CSection provides,
in a systematic way, the following
MCS:
- sectional 3D stress fields related to
each of the 6 internal forces (axial
force, shear forces, torsional
moment, bending moments). Figure
2-(b) depicts the sectional axial
stress field σzz for a unit bending
moment with respect to x ([x,y] are
related to the sectional axes and z to
the beam axis);
- "natural" deformability modes of the
composite section (Figure 2-(c)-(d)-

From a theoretical point of view, it
is very important to emphasize that
the MCS computation is free from all
classical beam assumptions. They are
derived from the effective computation of the 3D Saint Venant's solution
extended to composite and anisotropic sections [2, 3]. This is achieved by a
numerical method [4] which consists
in solving, by 2D finite elements, a
set of elastic problems on the section
from which the MCS are deduced.
Details and quality of the stress results
provided by CSection: Figure 3 shows
the sectional stress fields obtained
for an 8-layer composite section [0,
90,-45, 60]s. The left side shows the
sectional shear field σyz related to a
unit shear force Ty; note that shear,
as expected, appears continuous right
to the interfaces and it vanishes at
the ends. The right side shows, for
a given tension, the variation of the
inter-laminar stresses σyy right to the
0/90 interface, which can explain the
delamination of the layers that starts

No85 November - December 2013

/ jec composites magazine 55
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013

Table of Contents for the Digital Edition of JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013
