Analysis of stiffened isotropic and composite plate

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395 -0056
Volume: 03 Issue: 02 | Feb-2016 www.irjet.net p-ISSN: 2395-0072
© 2016, IRJET ISO 9001:2008 Certified Journal Page 1
Analysis of stiffened isotropic and composite plate
R. R. Singh1, Dr. P. Pal2
1 Research Scholar, Department of Civil Engineering, MNNIT Allahabad, U.P., India
2 Assistant Professor, Department of Civil Engineering, MNNIT Allahabad, U.P., India
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Abstract – This paper deals with the study of stiffened
isotropic and composite plates. Finite element technique is
used to model and analyze the stiffened plates. Anattempthas
been made to minimize the deformation of plate without
increasing the volume of material required to buildup the
stiffened plate. It is achieved by arbitrarily varying the length,
thickness and height of stiffener. The results are obtained for
both isotropic and composite plates and recommendations
have been made for both types of stiffened plate.
Key Words: Thin Plate, Composite, Stiffener, FEM, ANSYS.
1. INTRODUCTION
Stiffened panels are common structural elements in weight
sensitive structural, aerospace and marine applications.
Stiffened Plates are extensively used in lock gates, railway
wagons, plate girders, highway bridges, aircraftwings,cargo
containers, elevatedroadwaysetc.Thesestructural elements
can be defined as plates reinforced by a single or a set of
beams or ribs on one or both sides of the plate. The benefit
of reinforcing a plate by stiffeners lies in remarkable
increase of strength and stability whileminimumincrease of
weight to the overall structures. Stiffened plates can also be
fabricated with ease and simplicity.
Many researchers have done numerous work on isotropic
stiffened plates but the work on composite stiffened plate is
scanty. Mukhopadhyay et al.[1-2] used the eight-noded
isoparametric plate bending element to study the large
deflection behavior of stiffened plates. The author also
proposed a semi-analytical method for the analysis of bare
plates and extended it to the static analysis of stiffened
plates. Bedair[3] investigated the elastic behavior of
stiffened plates under non-uniform edge compression. A
finite element model was developed for optimizing
separately or simultaneously the critical buckling loads and
natural frequencies of the plates per unit volume of the
plates/stiffeners by Akl et al.[4]. Li and Xiaohui[5]variedthe
quantity, the collocation and the geometry of stiffeners to
improve the stiffness and the strength of stiffened laminated
plates. Authors used higher-order global–local theories to
study the bending behavior of stiffenedlaminatedplates. Liu
and Wang[6-7] discussed the strengthening effects of
stiffener on regular and arbitrarily stiffenedplatesthrougha
series of ANSYS buckling strength analyses. The authors
through several simulations and comparisons also proved
that the strengthening effectsofarbitrarilyorientedstiffener
can be approximated by those of regularlyorientedstiffener.
Thoi et al.[8] presented the static, free vibration and
buckling analyses of eccentricallystiffenedplates bythecell-
based smoothed discrete shear gap method (CS-FEM-DSG3)
using triangular elements. Ahmed and Rameez[9]
investigated strengthening effects of regular stiffened plates
subjected to uniaxial stress and arbitrarily stiffened plates
that are subjected to biaxial stress. Singhetal.[10]presented
a parametric study to estimate the maximum deflection and
stress in the isotropic stiffened plates.
2. FE MODELLING AND CONVERGENCE STUDIES
The modelling of any finite element problem includes
generally five steps;
a) Defining the material properties of the model, which are
presented in Table 1.
b) Creating the geometry of the model,
c) Discretizing the model into number of finite elements
(i.e. meshing of the geometry),
d) Applying boundary and loading conditions,
e) Solving the problem for its subsequent results.
Table 1: Material Properties
Isotropic
Composite
(Orthotropic)
Density = 7850
kg/m3 ,
E = 2 × 1011 Pa,
ν =0.3
Density = 154 kg/m3
Ex = 2.09 × 1011 Pa,
Ey = 9.450 × 109 Pa,
Ez = 9.450 × 109 Pa,
Gxy = 5.5 × 109 Pa,
Gyz = 3.9 × 109 Pa,
Gxz = 5.5 × 109 Pa,
νxy = 0.27, νyz = 0.4 ,
νxz = 0.27
For modeling the isotropic plate, the plate is modelled using
SHELL181 element and the stiffener is modelled using
SOLID186 element available in the ANSYS Workbench15.
Whereas forcompositeplate,onlySHELL181elementisused
for modeling both plate and stiffener. The description of
SHELL181 and SOLID186 are given below.
SHELL181 is suitable for analyzing thin to moderately-thick
shell structures. It is a four-node element with six degrees of

freedom at each node: translations in the x, y, and z
directions, and rotations about the x, y, and z-axes. It is well-
suited for linear, largerotation,and/orlargestrainnonlinear
applications. It accounts for follower (load stiffness) effects
of distributed pressures. It can be also used for layered
applications for modeling composite shells or sandwich
construction. The accuracy in modeling composite shells is
governed by the first-order shear-deformation theory
(usually referred to as Mindlin-Reissner shell theory).
SOLID186 is a higher order 3-D 20-node solid element that
exhibits quadratic displacement behavior. The element is
defined by 20 nodes having three degrees of freedom per
node: translations in the nodal x, y, and z directions. The
element supports plasticity, hyperelasticity, creep, stress
stiffening, large deflection, and large strain capabilities.
SOLID186 Homogeneous Structural Solid is well suited to
modeling irregular meshes (such as those produced by
various CAD/CAM systems).
Table 2: Geometric Dimensions
Bare Plate Stiffened Plate
Size of Plate 1000mm×1000mm×
10mm
1000mm×1000mm×
8mm
Size of
Stiffener
- (L×T×H)*
Total Volume
of material
used
10,000,000mm3 ≤10,000,000mm3
Fig.1 Geometry of Stiffened Plate
*For various length of stiffener (i.e. 700, 750 & 800 mm) and
varying aspect ratio (H/T), different sizes of stiffener can be
obtained. The height of stiffener with varyingaspectratiosis
presented in Table 3.
Table 3: Height of Stiffener for varying aspect ratio
The geometric properties of the plate (bare and stiffened)
considered for the present investigation are given in Table
2. The following boundary conditions are adopted.
1. All edges fixed. 2. All edges simply supported.
Following loading conditions are considered fortheanalysis
of plate.
1. Uniformly distributed load of 1 kN/m2.
2. Point load at the center of plate of 1 kN.
At first, a square bare plate subjected to transverse loading
condition for both fixed and simply supported condition is
considered for the study. A convergence study is carried out
to fix the mesh sizes of the bare isotropic plate subjected to
uniformly distributed load. Fig. 2 and Fig. 3 show the
maximum deflection of plate for fixed edges and simply
supported boundary conditions, respectively. For both the
support conditions, it is observed that the convergence of
results of maximum deflection occur at mesh size (20×20).
Fig.2 Convergence study for UDL with all edges fixed
Aspect
Ratio
(H/T) =
1 2 3 4 5 6 7 8
Height (in mm)
T = 10 mm 10 20 30 40 50 60 70 80
T = 12 mm 12 24 36 48 60 72 84 96
T = 14 mm 14 28 42 56 70 84 98 112
T = 16 mm 16 32 48 64 80 96 112 128
T = 18 mm 18 36 54 72 90 108 126 144
T = 20 mm 20 40 60 80 100 120 140 160

Fig.3 Convergence study for UDL with all edges simply
supported
3. RESULTS AND DISCUSSIONS
Various finite element models are developed using ANSYS
Workbench 15.0fordeterminingmaximumdeformation and
stress values.
The study on bare plate is establishedtovalidatetheanalysis
used for solving the problems of stiffened plate. The cases
considered herein, when the deformationofstiffenedplateis
less than that of bare plate for the same geometric and
materials properties. The whole study is based upon the
condition when the volume of material used for stiffened
plates do not exceed the volume of material required for
bare plate.
3.1 Bare Isotropic and Composite Plate
Example 1 In this example, a square isotropic bare
plate subjected to transverse loadings (udl of 1kN/m2 or
point load at the center of plate of 1kN) and the boundary
conditions (all edges fixed or simply supported) is
considered for the study. The bare plate is analyzed for
determining the maximum deflection and the results are
presented in Table 4. The same problem was studied by
Singh et al.[10].
The obtained results are compared withthereportedresults
published by Timoshenko & Krieger[11] and it is observed
that the present results are close to the reported one. It is
also observed that the percentage error in the case of point
load is quite smaller than the case of uniformly distributed
load. This may be caused due to the effectiveness of load
vector in global equation of FEM.
Fig. 4 shows the deformation and stress contour in the fixed
isotropic bare plate subjected to uniformly distributed load
of 1 kN/m2. The maximum deformationof0.0691mmoccurs
at the center of the plate and the maximum stress of 2.46
MPa occurs at the mid region of edges.
Table 4: Maximum deflections in isotropic bare plate
Fig. 4 Deformation and Stress in isotropic bare plate
S.
No.
Boundary
and
loading
conditions
Max.
Deflection
(mm)
obtained
by ANSYS
Max.
Deflection
(mm)
calculated
by formula
given by
Timoshenko
& Krieger[2]
Percentage
error (%)
1. All edges
fixed with
uniformly
distributed
load (1
kN/m2)
0.0691 0.0688 0.4360
2. All edges
fixed with
point load
at the
center of
bare plate
(1 kN)
0.3055 0.3058 0.0981
3. All edges
simply
supported
with
uniformly
distributed
load (1
kN/m2)
0.2225 0.2217 0.3608
4. All edges
simply
supported
with point
load at the
center of
bare plate
(1 kN)
0.6346 0.6334 0.1862

Example 2 In this study, a square compositebareplate
subjected to transverse loading (udl of 1kN/m2 or pointload
at the center of plate 1kN) and boundary conditions (all
edges fixed or simply supported) is considered for the
analysis. A cross ply laminated composite plate madeoffour
layers [0/90/90/0] stacked one above another is taken for
the study. The obtained results are presented in Table 5.
Table 5: Maximum deflection in composite bare plate for
different boundary and loading conditions
3.2 Isotropic Stiffened Plate
Example 3 A stiffened isotropic plate subjected to
transverse loadings (udl of 1kN/m2 and point load at the
center of 1kN) and boundary conditions (all edges fixed and
simply supported) is studied in this example. The aspect
ratio (H/T) of stiffener varies from 1 to 8 for each different
length of stiffener (i.e. 700,750 & 800mm).
Fig. 5 (a-d) shows the deformation and stress contour of
stiffened plate for a stiffener of size 700×10×40mm
subjected to different loading and boundary conditions. The
maximum deformation and stress values are obtained as
0.063mm & 4.612MPa,0.233mm&26.949MPa,0.0193mm&
8.472MPa and 0.473mm & 33.221MPa, respectively which
are shown in Fig. 5 (a), (b), (c) and (d).
Further, the results for each length of stiffener with varying
aspect ratios for each set of boundaryandloadingconditions
are shown in Figs. 6-9.
It is observed that the pattern of deformation curve for each
length of stiffeners is similar. With the increase in aspect
ratio, change in deformation for the stiffener having smaller
thickness is more than that of the stiffener having larger
thickness.
Fig. 5 Deformation and Stress variations
The deformation and stress generally tendtodecreases with
the increase in size of stiffener. Insomecasesthevariationin
stress is haphazard whereas the deformation curves have
the uniform pattern. This can be attributed to the fact that
the deformation functionisonedegreehigherthanthestress
function. For instance in Fig. 6, the stresses (for stiffener
length of 750mm) increase beyond the aspect ratio of 6 for
the stiffener having thickness of 10 and 12mm.
Fig. 6 Maximum deformation (left) and stress (right)
curves for stiffened plate subjected to UDL and all edges
fixed
S.
No.
Boundary and loading
conditions
Max. Deflection
(mm) obtained
by ANSYS
1. All edges fixed with
uniformly distributed load
(1 kN/m2)
0.17212
2. All edges fixed with point
load at the center of bare
plate(1 kN)
0.87416
3. All edges simply supported
with uniformly distributed
load (1 kN/m2)
0.36003
4. All edges simply supported
with point load at the
center of bare plate (1 kN)
1.35740

curves for stiffened plate subjected to point load at the
center and all edges fixed
curves for stiffened plate subjected to UDL and all edges
simply supported
curves for stiffened plate subjected to point load at the
center and all edges simply supported
3.3 Composite Stiffened Plate (orthotropic)
Example 4 A stiffened composite plate subjected to
transverse loadings (UDL of 1kN/m2 or Point load at the
center of 1kN) and boundary conditions (all edges fixed or
simply supported) is considered for the study. The aspect
ratio (H/T) of stiffener varies from 1 to 8 for each different
length of stiffener (i.e. 700,750 & 800mm).
A cross ply laminated composite stiffened platemadeoffour
layers [0/90/90/0] stacked one above another is taken for
the study.
Fig. 10 Deformation and Stress variations

Fig. 10 (a-d) shows the deformation and stress contour of
stiffened plate for a stiffener of size 700×10×40mm
subjected to different loading and boundary conditions. The
maximum deformation and stress values are obtained as
0.169mm & 4.742MPa, 0.559mm & 11.968MPa, 0.336mm &
6.459MPa and 0.878mm&16.696MP,respectivelywhichare
shown in Fig.10 (a), (b), (c) and (d).
Further, the results for each length of stiffener with varying
aspect ratios for each set of boundaryandloadingconditions
are shown in Figs. 11-14.
Fig. 11 Maximum Deformation (left) and Stress (right)
Curves for Stiffened Plate subjected to UDL and all edges
Fixed
Fig. 12 Maximum Deformation (left) and Stress (right)
Curves for Stiffened Plate subjected to Point Load at the
center and all edges Fixed
Fig.13 Maximum Deformation (left) and Stress (right)
Curves for Stiffened Plate subjected to UDL and all edges
Simply Supported
Fig.14 Maximum Deformation (left) and Stress (right)
Curves for Stiffened Plate subjected to Point Load at the
center and all edges Simply Supported

It is observed that the pattern of deformation curve is same
for both the type of stiffened plate and alsoobservedthat the
maximum stress decreases with the increase in aspect ratio
for both the cases but in Fig. 13 one exceptional behavior is
noticed where the maximum stress in the plate increases
with the increase in aspect ratio for the stiffener having
length of 750mm.
4. CONCLUSIONS
This paper presents the behavior of stiffened plate under
transverse loading conditions. Based on observations the
following concluding remarks are made.
1. The height of stiffener shall not be increased beyond six
times of thickness as it gives very less improvement in
deformation. Since, the maximum deformations in all
scenario of varying thickness & aspectratiotendtoconverge
towards a minimum value and beyond the aspect ratio of 6
the results are very close to each other.
2. The stiffener having lesser thickness gives almost equal
deformation with that of greater thickness stiffener having
more or less equal volume of material.
3. The stiffener having lesser height and greater thickness
can be used at the places where there is limitation of space
otherwise the stiffener having greater height and lesser
thickness may always be recommended.
4. The maximum deformation of compositeplateisabout 1.5
to 2.5 times than that of isotropic plate.
5. The maximum stress in composite plate is on lower side
than that of isotropic plate.
The aim of this study is to highlight the effectiveness of
stiffeners in the plate. The results presented herein are for
deformation and stresses which can be useful for fixing the
geometry of stiffener in the plate. The cost effectiveness of
the stiffened plate may be studied further for achieving the
economy in the construction of real life structures having
stiffened plates.
REFERENCES
[1] D. Venugopal Rao, A. H. SheikhandM.Mukhopadhyay,
“A finite element large displacement analysis of
stiffened plates,” Computers & Structures, Vol. 47,
No.6, 1993, pp. 987-993.
[2] M. Mukhopadhyay, “Stiffened plates in bending,”
Computers & Structures Vol.500,No.4,1994,pp.541-
548.
[3] Osama K. Bedair, “Influence ofstiffenerlocationonthe
stability of stiffened plates under compressionandin-
plane bending,” Int. J. Mech. Sci. Vol. 39, No. 1, 1997,
pp. 33-49.
[4] W. Akl, A. El-Sabbagh and A. Baz, “Optimization of the
static and dynamic characteristics of plates with
isogrid stiffeners,” Finite Elements in Analysis and
Design, Vol.44, 2008, pp. 513 – 523.
[5] Li Li and Ren Xiaohui, “Stiffened plate bending
analysis in terms of refined triangularlaminatedplate
element,” Composite Structures, Vol. 92, 2010, pp.
2936–2945.
[6] Yucheng Liu and Qingkui Wang, “Computational study
of strengthening effects of stiffeners on regular and
arbitrarily stiffened plates,” Thin-Walled Structures,
Vol. 59, 2012, pp. 78–86.
[7] Yucheng Liu andQingkuiWang,“Strengthening effects
of stiffeners on arbitrarily stiffened plates and
regularly stiffened plates subject to biaxial stress,”
Thin-Walled Structures, Vol. 68, 2013, pp. 85–91.
[8] T. Nguyen-Thoi,T.Bui-Xuan,P.Phung-Van,H.Nguyen-
Xuan and P. Ngo-Thanh, “Static, free vibration and
buckling analyses of stiffened plates by CS-FEM-DSG3
using triangularelements,”ComputersandStructures,
Vol. 125, 2013, pp. 100–113
[9] Ahmed and Rameez, “Study of strengtheningeffectsof
stiffeners on regular and arbitrarily stiffened plates
(eigen buckling analysis) using ansys,” International
conference on mechanical and industrial engineering,
2014.
[10] D. K. Singh, S. K. Duggal and P. Pal, “Analysis of
stiffened plates using FEM – a parametric study,”
International research journal of engineering and
technology, Vol. 02, July 2015.
[11] Timoshenko and Woinowsky-Krieger, “Theory of
plates and shells,” McGraw–Hill New York, 1959.
BIOGRAPHIES
Mr. R. R. Singh is M.Tech Scholar in
the Department of Civil
Engineering at Motilal Nehru
National Institute of Technology,
Allahabad, India.
Dr. P. Pal is currently Assistant
Professor in the Department of
Civil Engineering at Motilal Nehru
National Institute of Technology,
Allahabad, India.

Analysis of stiffened isotropic and composite plate

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