JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - 56

simulation
These results are truly comparable
to those obtained by fully 3D-FEM
computations in the major interior
part of the beam, even if the slenderness is small.

Fig. 3: CSection results: stress fields for a [0, 90,-45, 60]s laminated section

from the free edge (known as the "free
edge effect").

CBeam

CBeam is used to simulate the 3D
elastic behaviour of homogeneous
or composite beams subjected to any
loading and boundary conditions. The
section is considered to be constant
with respect to the beam axis.
CBeam computations, which use the
MCS previously computed by CSection, are performed by 1D finite elements, conforming to the Advanced
Beam Theory (ABT) [5]. ABT is a
higher order beam theory based on
a displacement model including, as
in- and out-of-plane sectional deformation, its "own" Poisson's effects,
warpings and distortions of the section previously computed by CSection. Due to this enrichment, this
beam theory can take into account the
3D localization of the loading applied
to the beam and thus better satisfy the

boundary conditions. Practically, ABT
might be seen as a refinement of Saint
Venant's theory including a significant
part of the edge effects.
Regarding loading (Figure 4), the
beam is considered as a 3D body and
the loads have to be introduced as
they are applied to the beam. The
loads are punctual forces or (line,
surface, volume) distributed forces.
Regarding the displacement boundary conditions, the degrees of freedom that can be constrained are the
individual components of the crosssectional (CS) displacements (translations and rotations), the CS-out-ofplane warping and the CS-in-plane
deformation.
Once the 1D beam problem is solved,
the 1D results are used to generate the
corresponding 3D displacement and
stress fields (Figure 4, right side).

Fig. 4: Bending-torsion of a short (1/5) open-walled composite beam - 3D displacements and 3D sectional
stresses right to the embedded section

56 jec composites magazine / No85 November - December 2013

In the current version of CBeam, the
beam axis is straight, the section is
constant and only the static analysis
is proposed. Dynamic and buckling
analyses will be included in the next
versions.
The current version is a general one.
However, specific versions for particular applications such as composite
springs, wind turbine or helicopter
blades, etc., including studies for
curved beams and (slowly) variable
sections, can be developed. n

More information:
rached.elfatmi@enit.rnu.tn
References
[1] El Fatmi. A Matlab tool to compute
the mechanical characteristics of any
composite section. Journal of Composite and Advanced Materials, RCMA,
no.3, p.395-413, 2012.
[2] Iesan. Saint-Venant's problem for
inhomogeneous and anisotropic elastic bodies. Journal of Elasticity, Vol. 6,
p.277-294, 1976.
[3] Ladevèze & Simmonds. New
concepts for linear beam theory with
arbitrary geometry and loading. European Journal of Mechanics, 17 (3),
p.377-402, 1998.
[4] El Fatmi & Zenzri. On the structural
behavior and Saint Venant's solution
in the exact beam theory. Application to laminated composite beams.
Computers and Structures, 80 p. 14411456, 2002.
[5] El Fatmi & Ghazouani. Higher order
composite beam theory built on Saint
Venant's solution. Part-I: Theoretical
developments. Part-II: Built-in effects
influence on the behavior of endloaded cantilever beams. Composite
Structures, Vol. 93, p. 557-581, 2011.



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

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

Cover
Edito
Point of view: bespoke equipment
Contents
Agenda of Events
COMPANY & BUSINESS In Brief
APPLICATIONS
Large parts
Skateboard
Second life
Truck
Pipe
MARKET Process
FEATURE CONSTRUCTION
Roofing
PFRP house
Sandwich panels
GFRP grid
Gelcoat
Windows
Bridge
RESEARCH & DEVELOPMENT
Cure monitoring
Design
TECHNOLOGY & INNOVATIONS
NDC
Simulation
CBeam
Index
In the world
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - Cover
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - 2
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - Edito
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - Point of view: bespoke equipment
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - 5
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - Contents
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - 7
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - Agenda of Events
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - 9
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - COMPANY & BUSINESS In Brief
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - 11
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - Large parts
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - 13
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - Skateboard
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - 15
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - Second life
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - 17
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - Truck
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - 19
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - Pipe
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - 21
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - 22
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - MARKET Process
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - 24
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - 25
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - 26
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - 27
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - Roofing
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - 29
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - 30
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - PFRP house
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - 32
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - Sandwich panels
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - 34
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - 35
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - GFRP grid
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - 37
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - Gelcoat
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - 39
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - Windows
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - 41
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - Bridge
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - 43
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - 44
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - Cure monitoring
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - 46
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - 47
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - Design
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - 49
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - 50
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - 51
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - NDC
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - 53
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - Simulation
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - 55
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - CBeam
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - Index
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - In the world
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - 59
JEC COMPOSITES MAGAZINE - Issue #85 - November/December 2013 - 60
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