Design turbine blade Aeolian of vertical axis using laminated tin palm material using the
finite element method
Diseño de álabe de turbina eólica de eje vertical usando material laminado de Palma de Lata mediante el
método de los elementos finitos
Manuel del Jesús Martínez1*,
Juan Dayal Castro-Bermúdez2 ,
Iván Darío Ortega-Anillo3 .
This work focuses in analyze the mechanical behavior of a vertical axis wind turbine Blade, which
is constituted by a natural composite material of “Palma de Lata” and binder, constituents for which its
mechanical properties are obtained through mechanical tests and literature references. This study was made
under the wind conditions of the colombian “Cañon del Chicamocha”, whose aerodynamic loads (pressures)
were obtained in previus studies. The Design was made base on the layers layout of the composite, from
stress distribution analysis the critical regions to reinforce the blade were found. At last, the behavior of the
reinforced Blade was verified, obtaining in the “Palma de Lata” laminated a feasible alternative to be used
in the wind turbines design.
El presente trabajo se enfoca en analizar el comportamiento mecánico de un álabe de aerogenerador de
eje vertical, el cual está constituido por material natural compuesto de Palma de Lata y aglomerante,
constituyentes para los cuales se obtuvieron sus propiedades mecánicas por medio de ensayos mecánicos y
referencias de literatura. Este estudio se realizó bajo las condiciones de viento del Cañón del Chicamocha
colombiano, cuyas cargas aerodinámicas (presiones) fueron obtenidas en estudios previos. Se realizó el
diseño del álabe basado en la disposición de capas del material compuesto, a partir del análisis de las
distribuciones de esfuerzos se hallaron las regiones críticas para reforzar el álabe. Finalmente, se verificó el
comportamiento del álabe reforzado, obteniendo en el laminado de Palma de Lata una alternativa factible
para ser usada en el diseño de aerogeneradores.
Palabras clave:Palma de Lata,
Diseño, Teorías de
Falla, Método de
Composite materials are one of the most important
research topics of recent times, this has been due to
the great utility of fiberglass and carbon composites
in an appreciable amount of engineering applications,
in addition the study of composite materials has an
inherent complexity to their structure, manufacture
and anisotropy presented -, which makes it an
area of interest for research.
Materials and methods
Ecological and sustainable ideas have significantly
impacted the advancement of science, wanting to
narrow the gaps that still exist between nature and
technology, thanks to the desire to reduce the impact
of pollution and reduce the amount of solid waste
,. A controversial example is observed in wind
turbines , one of their main construction materials
being fiberglass composites that are potential
contaminants of water, affecting marine fauna 
and presenting problems such as reduced properties
or obsolescence when recycled . As shown in 
one of the desired alternatives for the handling of
synthetic compounds is to prevent the production of
waste; therefore, if the use of synthetic raw material is
reduced by replacing it with biodegradable materials
, both solid waste and the contamination inherent
in the manufacture of artificial compounds would be
significantly reduced . This project proposes as
an alternative the use of tin palm (Bactris Guineensis)
as a replacement for synthetic fibers for applications
with low loads, so that organic materials are used for
The Tin Palm is found in regions of South America
 and is used to obtain drinks with a high content
of antioxidants  and wines, its stem has been used
in reinforcements of old constructions but few studies
,  and  have focused on the mechanical
characterization of the Tin Palm, consequently, it
became necessary to study the mechanical behavior
of this palm and thus take the first steps to design
structural elements that take advantage of this raw
One of the best known applications for composite
materials are wind turbines, these have gained
popularity worldwide because of their ability to
generate “clean” energy with wind currents. However,
most of the global electrical energy still has a fossil
origin which worsens the current situation of climate
change due to the greenhouse effect generated by
these energy sources. In addition, because turbines
are built with these materials, they carry with them
a problem that goes against their purpose with the
In Colombia by 2010 more than 25% of the energy
produced in the country was of fossil origin ,
which is not bad compared to some countries that
have a much higher percentage in this category,
however, the goal according to scientists is to reduce
carbon emissions into the air as soon as possible,
which means that the target for the value shown is
This work investigates the behavior of the Palma de
Lata as a structural material for blades of vertical
axis wind turbines. With the purpose of contributing
from the academy in the sustainable development of
the country and in such a way to contribute with its
economic, cultural and social development.
Finite Element Analysis
The Finite Element Method (FEM)  is a
numerical technique used to solve problems with a
high degree of complexity, for which it is difficult to
solve analytically. The method has, therefore, great
application in engineering problems , .
In this work was studied the behavior of a H-Rotor
type wind turbine blade using F.E.M, with the
aerodynamic profile DU06W200 was studied by 
for the wind conditions of the Chicamocha Canyon
of Colombia, the design of the blade adds an internal
stiffener based on the results obtained in .
There are several methods to solve a finite element
problem, in this work is used the Galerkin method
which is commonly used by finite element software
such as ANSYS. This method is based on looking for
the solution by means of test functions, to the system
of linear equations. KU = F describing Hooke’s law,
where the term U is the vector of
forces and K the stiffness matrix of the material. (eq 1:).
Properties of the study material
To define the matrix of elasticity of an anisotropic material it is necessary to know the 36
constants, which allow to define the law of three-dimensional Hooke, in the case of
orthotropic materials due to the symmetry previously mentioned, the constants are reduced
define the elastic problem.
tensorial form of Hooke's law of elasticity in a solid can be written as: (eq 2 & 3:).
Palm presents a zone of high rigidity in the external bark of the stem  similar to
happens with Bamboo , therefore from this zone the sheets for the composite
were obtained, for this external bark a transverse isotropy behavior is assumed, an
assumption accepted for similar composite materials such as parallel fiber Bamboo (PSB)
thus reducing the constants that define the elasticity tensor to 5: S11, S12 ,S22 ,S66 ,S23 ó S44
in (4) the matrix form of Hooke›s law
is shown in terms of the engineering constants, as
considered for this study (eq 4 & 5:).
Composite Failure Theories
Failure criteria in finite element software are commonly represented from the failure index,
which is represented as: (eq 6 &7:).
In this case, the resistance is taken as the limit in which the breakage of the first can palm
fibers occurs, as shown in . In order to avoid failure, the failure rate must be greater
Maximum effort failure theory
In this criterion is not considered any interaction between different stress components, failure occurs when the stress in any direction exceeds the maximum value allowed by compound in that direction. In the same way the maximum deformation evaluates when material reaches its limit deformation in any direction so that the failure at this point have already occurred.
The maximum three-dimensional stress criterion is the maximum value found between following relationships , in the case of normal stresses: (eq 8:).
Being the normal effort in direction 1, 2 o 3, y the
resistance of the material in the same direction as the
stress, whether it is tensile or compressive. If σi is
less than zero, the compressive strength is used.
For shear forces: (eq 9:).
Where is the absolute value of the shear force in
directions 12, 13 o 23 and is shear resistance in the
Fault theory of Tsai-Hill
It is a criterion formulated referring to the energy of
distortion, i.e. it takes into account interplanar shear
stresses. The failure criterion is described by: (eq 12:).
Where again the parameters in the denominators are
the limits of the efforts in the indicated directions.
In this work it was decided not to show failure criteria
such as Tsai-Wu because biaxial testing properties
would be required that were not determined for Tin
For this simulation the DU06W200 profile is used,
the 3D model is created by importing the coordinates
of the points and then extruding them, then the
internal reinforcement of the blade is positioned, its
location is at 20% of the length of the rope, which for
this simulation is 25 cm, i.e. the stiffener is located
5 centimeters from the nose of the blade, distance
determined in previous works , , the length
of the blade is 2 meters, taking as a reference that
the aspect ratio (ratio between blade length and rope
length) for this type of turbines should not be less
than 7.5 .
The laminate is made in normal direction to the
surface, for the internal reinforcement, sheets are
placed on both sides of the base geometry that is
inside, in addition, the joint between the stiffener
and the walls of the blade is made in the form of “T”
adhering through a layer of material. (Fig 1:).
In order to simulate the blade and verify the failure
criteria, it was necessary to mechanically characterize
the Can Palm, using as a guide the ASTM D3039,
E132-04, D1037 and D7078 standards to obtain the
great majority of the engineering constants required
in (5) when testing: Traction in direction 1 and 2,
Poisson Coefficient and Cutter in direction 12. (tab 1:).
The remaining properties of the Palm are obtained
by averaging or comparing proportions. In the first
instance, the maximum compressive stress was
taken from  for the stem of dry and complete
canned palm. The was taken as the average of this
property for hardwoods presented in  of woods,
which together with was calculated by means of
(5). Huang’s work  compares the limits: y for
the maximum shear force in PSB, obtaining that
is 44.3% less than , for La Palma was obtained
experimentally and conserving the proportion of the
PSB is a approximate. Finally, in order to determine
F( 2c), the comparison process is repeated using as a
guide the PSB.
Polyvinyl alcohol (PVA)  was used as a binder,
which was chosen as an adherent because it is of
natural origin and soluble in water so that it can be
removed with a relatively simple process, in addition
to this, PVA is commonly used as for the union of
wood pieces , the limit stress to traction and the
modulus of elasticity of the work were taken from
Chan’s work , and the Poisson coefficient from
Chen’s work . (tab 2:).
Lamination is performed by placing a layer of PVA
between two layers of Tin Palm as shown in Figure
2, the thicknesses of the Palm sheets are taken to be
1 mm due to the limited thickness of the Palm bark,
and the thickness of the PVA layer is taken to be 0.3
millimetres. (Fig 2:).
Contour and mesh conditions
The blade is supported by 2 rectangular structural
steel bars that are directly attached to the internal
stiffener in order to approximate the contour
conditions to which the blade would be subjected
when in a turbine. However, this is a simplification
as the supports must actually go from edge to wind
and must have the shape of an aerodynamic profile
that produces low lift when it produces little drag, so
as not to hinder the operation of the turbine.
The load conditions imposed in the model are
taken from , in this case only the pressure
distribution was taken, which in  was determined
bidimensionally around the profile, which is
considered constant along the blade for this study. (Fig 3:).
The parameterization of the number of elements and
the maximum total displacement was carried out, in
order to look for a sufficiently fine mesh so that the
results are independent of the quantity of elements,
finding that close to 8000 elements this behavior
is observed, working this way the final model with
40360 elements type SHELL 181 with 6 degrees of
freedom, recommended to analyze structures thin to
Results and discussion
Blade with a composite layer
A first simulation was performed to visualize the
behavior of the Palma-PVA compound with a
single layer as shown in Figure 2, this was arranged
both in the profile and in the internal stiffener, the
distribution of displacements, stresses and failure
criteria were visualized to identify the critical regions
in the model.
Figure 4 shows the total displacements of the blade, a
maximum value can be seen in the center of the area
that is not subject, which is in line with expectations.
It can also be seen that the zone of maximum
displacement is located in the upper region of the
blade where the sustentation occurs. The maximum
value of total displacements is 0.075 [mm] which
will not affect the structural integrity of the blade. (Fig 4:).
When analyzing the distribution of efforts, it is
noticed that the blade has 2 critical regions: the
distant exit edge to the supports and the entry edge
in the region adjacent to the supports, in both failing
in the direction of the matrix the Palma de Lata
(direction 2), but not in the same sheet.
As can be seen in figure 5 (a), the leading edge has
maximum stresses on the palm outer sheet with a
value of 22.7. [MPa], that when compared to the
limit value in Table 1 of 3.55 [MPa] by means of
(7) and (8) an inverse fault index value of 6.39 is
obtained indicating a fault in this zone.
Now, when observing figure 5 (b) it was found that
it is the inner sheet that presents the greatest efforts,
with a maximum of 60.54 [MPa], resulting in an
inverse failure rate of 17.55, this region being more
critical than the leading edge. (Fig 5:).
The trailing edge region is the one that obtains
higher inverse failure index values, greater than 15
for all the fault criteria analyzed, and the fault is
present in the inner sheet of Palma de Lata, this may
be due to the fact that in this region the upper and
lower surfaces come together creating a vertex that
generates a concentration of stresses.
Blade reinforced with more layers
Because the previous blade was faulty, the blade
was reinforced by adding 2 external layers of PVAPalma
to stiffen the entire blade. Two more layers
of PVA-Palma were added to the inlet and outlet
edges in the internal region, as shown in Figure 6,
to support and reduce the concentration of stresses
without affecting the aerodynamic profile. (Fig 6:).
Figure 7 shows the total displacements for the reinforced blade, obtaining a maximum
equal to 0.1295 [mm] at the edge of the blade again this values does not affect the integrity of the blade, even so it must be noted that this value is greater than that found for the blade whit a single layer of
laminate, this is because the reinforcements make
the displacements are distributed evenly throughout
the body of the blade by introducing a rotation of the
point further away from the supports, unlike the local
deformation shown in the figure, which is different
from the local deformation shown in the figure. (Fig 7:).
Finally, to corroborate that reinforcements also
help to reduce stress and avoid material failure, the
Tsai-Hill maximum stress failure criteria are shown
in Figure 8 (a) and 8 (b), obtaining inverse failure
index values of 0.2872 and 0.168 respectively, which
indicate that there is no material failure, even so it
should be noted that the entry edge zone located just
in front of the supports, is still an area of interest. (Fig 8:).
A comparison with the literature shows that the work
done gives similar results in terms of deformations
and stresses. As shown in Wang , the deformation
increases to a maximum in the blade as it moves
away from the support, in Raciti  the trailing
edge is observed to rise as it deforms. As far as the
stresses are concerned, Liu  describes how the
maximum stress occurs in the area where the blade
supports are located, in the same way as the results
found in this work.
The displacements in the composite blade of canned
palm with PVA do not present critical values, with
maximums of only 0.075 [mm] for the single-layer
blade and 0.1295 [mm] for the reinforced blade.
The reinforcement layers in the blade help to
substantially reduce the stresses obtained, leading to
a substantial reduction in failure, showing that the
inverse failure rate for the maximum stress theory can
be reduced more than 60 times, from 17.55 obtained
for a single layer to 0.2872 with reinforcements.
Because for the 3 tested failure theories the inverse
failure rates are significantly lower than 1, it can be
said that the reinforced blade does not fail with the
loads that were imposed.
Finally, it can be said that the tin palm and PVA
composite material provides a viable alternative,
which can be used as a replacement for synthetic
compounds in both wind turbines and low load
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1* Doctor en Mecánica Computacional, Orcid: 0000-0001-7069-6400, Universidad Industrial de Santander, Bucaramanga, Colombia, email@example.com
2 Ingeniero Mecánico, Orcid: 0000-0002-5127-4904, Universidad Industrial de Santander, Bucaramanga, Colombia, firstname.lastname@example.org
3 email@example.com, Orcid: 0000-0002-1750-4315, Universidad Industrial de Santander, Bucaramanga, Colombia, firstname.lastname@example.org
Received on January 21, 2018 - Approved on June 12, 2018.
How to cite :M.J. Martínez, J.D. Castro-Bermúdez and I.D. Ortega-Anillo, “Design turbine blade Aeolian of vertical axis using
laminated tin palm material using the finite element method”, Respuestas, vol. 23, no. 2, pp. 43-52, 2018
Received on January 17, 2018 - Approved on June 09, 2018.