finite element analysis of composite hat-stiffened panels … finite element analysis of composite...

Jordan Journal of Civil Engineering, Volume 14, No. 2, 2020

‐ 137 - © 2020 JUST. All Rights Reserved

Received on 15/10/2019. Accepted for Publication on 24/2/2020.

Finite Element Analysis of Composite Hat-Stiffened Panels Subjected to

Edge Compression Load

Shashi Kumar 1)*, Rajesh Kumar 2) and Sasankasekhar Mandal 3)

1) Assistant Professor, Department of Civil Engineering, Sitamarhi Institute of Technology, Sitamarhi, India. * Corresponding Author. E-Mail: [email protected]

2), 3) Professor, Department of Civil Engineering, Indian Institute of Technology (BHU) Varanasi, India. E-Mails: [email protected]; [email protected]

ABSTRACT

This paper deals with optimizing smeared extensional stiffness ratio of stiffeners to that of skin of laminated

composite hat-stiffened panel with the variation of pitch length stiffeners, depth of stiffeners and panel

orthotropy ratio for three different plie configurations to maximize buckling capacity of the panel. Critical

buckling load and global buckling mode shape of the laminated composite hat-stiffened panel are studied for

the design of lightweight structures. Parametric studies of hat-stiffened panel under in-plane compressive load

are presented with simply supported boundary conditions. Models are analyzed by applying Finite Element

method using ABAQUS. A database is provided based on smeared stiffness approach for two different hat-

stiffened (600-hat-stiffened and 750-hat-stiffened) panels with variation of pitch length stiffeners, depth of

stiffeners, panel orthotropy ratio and smeared extensional stiffness ratio of stiffeners to that of skin with three

different plie configurations. On the basis of the study, optimum smeared extensional stiffness ratio is

increased with increasing of orthotropy ratio for all similar skin, but it is also increased with decreasing

extensional stiffness ratio to maximize buckling capacity of hat-stiffened panel and general guidelines are

developed for the design of better hat-stiffened panel.

KEYWORDS: Buckling, Composite panel, Finite element (FE), Fiber-reinforced polymers (FRPs), Numerical analysis.

INTRODUCTION

The design of laminated composite panel should be

such that it can achieve good performance with specific

buckling capacity. Shear force, compressive load and

their combination can be applied on stiffened panel to

check its stability. In stiffened panels, generally, local

buckling, global buckling and collapse occur under

shear, compression and their combination. The influence

of the variation of plate thickness and stiffener on the

buckling strength of stiffened panels can be studied

using analytical and numerical methods. Fiber-

reinforced polymers (FRPs) meet this requirement to

some extent since their development in 1960s. A

lightweight structure is an ongoing task for the

engineering community, which has been used

extensively in defense, aircraft and automobiles area and

now it is currently employed in structural applications.

FRP-stiffened panels are being used as the load shared

walls of the compressive member of structures.

Composite panels are also used in multi-storey buildings

to reduce the dead load of the structure. FRP-laminated

panels are currently used in heritage buildings for

retrofitting due to their high strength and aesthetic

appearance. Bakis et al. (2002) presented a detailed

study on buckling of the laminated composite stiffened

structure and its application in civil engineering.

Terminology Description

A11, A12,A22, A66

D11, D12,D22, D66

p D1/D2

Extensional stiffness component of skin. Bending stiffness component of skin. Pitch length (center-to-center spacing of stiffeners). Panel orthotropy ratio.

Finite Element… Shashi Kumar, Rajesh Kumar and Sasankasekhar Mandal

- 138 -

Many researchers have worked on buckling of

stiffened panels under different types of loading

conditions with blade-type, I-shaped, T-shaped and

J-shaped stiffeners. Ni et al. (2016) presented a review

of recent research based on two aspects; application of

finite element method and experimental work with

different loading conditions. Stroud and Anderson

(1981) studied the numerical formulation to find the

buckling of blade type, hat-stiffeners and corrugated

stiffened panel. Engineering analysis language has

been used to analyze the buckling behaviour of

laminated composite panel subjected to various types

of in-plane loading with different types of stiffeners by

Stroud et al. (1984). Guo et al. (2002) presented a

parametric study of stiffened panels with variation of

skin thickness to length ratio, ply configuration,

stiffener depth to skin thickness ratio and panel aspect

ratio. Bisagni and Vescovini (2009) used T-shaped

stiffeners in the composite panels to study local

buckling and post-buckling analysis by using an

analytical method. Barbero et al. (1995) investigated

laminated composite plates and presented a numerical

analysis of connection between them. The orthotropic

surfaces of FRP materials were modeled by using two-

friction coefficients (orthogonal) and applying

constitutive law. Kong et al. (1998) studied analytically

and experimentally the two-laminated composite panel

using blade-shaped and I-shaped stiffeners.

Zimmermann et al. (2006) studied experimentally the

buckling behaviour of stiffened panels with different

skin thicknesses and a number of I-shaped stiffeners.

Pevzner et al. (2008) proposed an extended effective

width method to study the torsion, bending and

buckling of curved stiffened panels with T-shaped and

J-shaped stiffeners. Shatnawi et al. (2010) studied an

analytical solution for determination of elastic critical

buckling pressures and mode shapes of long corroded

cylindrical steel shells subjected to external pressure

for symmetrical and anti-symmetrical cases. Elaldi

(2010) studied composite stiffened panels through

experiments and compared post-buckling capacity of

structural efficiency of hat-shaped and J-shaped

stiffened panels. Perret et al. (2012) studied post-

buckling analysis to predict the numerical models of

composite fuselage panel by experimental work.

Blazquez et al. (2012) studied the buckling response of

stiffened panels with the effects of thickness, ply

orientation and shape of the stringers. Boni et al.

(2012) developed a validated procedure of modeling

strategies. Pre-buckling and post-buckling simulations

were done by ABAQUS. Liu et al. (2014) performed

an experimental study of buckling behavior and failure

mode of stiffened panels with M-type stiffeners

subjected to compressive loading. Zhu et al. (2015)

conducted experimental work to study the buckling

load and failure load of I-section composite laminated

stiffened panels subjected to compressive loading.

Borrelli et al. (2015) investigated kinematic coupling

approaches for FE simulation of the buckling

behaviour of laminated I-shaped stiffened structures.

Wang et al. (2015) studied I-shaped stiffened panels to

find out their buckling and ultimate load-carrying

capacity.

Kalyanaraman and Upadhyay (2003) discussed the

behaviour of FRP box girders and proposed a

computationally efficient method to study single-cell

FRP box-girder bridges made with angle-shaped, T-

shaped or blade-shaped stiffened panels using FEM-

based software ANSYS. Qablan et al. (2009) analyzed

buckling load of square cross-ply laminated plates with

variation of parameters: cutout size, cutout location,

fiber orientation angle and type of loading by using

ABAQUS. The buckling load was reduced

significantly due to the increase of cutout size for shear

loading as compared to uniaxial and biaxial

compression. Almasri and Noaman (2014) studied

nonlinear FE analysis of steel column stability under

cyclic loading using ANSYS and the results were

compared with experimental results. Kumar et al.

(2018) used an artificial neural network (ANN) to

obtain an analytical tool for the prediction of buckling

capacity of laminated composite stiffened panels under

axial compression load. Falzon and Faggiani (2012)

presented genetic algorithms (GAs) and FE package

ABAQUS for optimization of the global-local

modeling of I-stiffened composite panel. Rahimi et al.

(2013) analyzed the buckling response of shell

structure due to stiffeners subjected to axial

compressive load by ANSYS. Huang et al. (2015)

computed the performance of stiffened panels using FE

technique and arbitrated the accuracy of the proposed

model. Fathallah et al. (2015) studied the optimization

of ply orientation and number of layers of composite

structure with T700/5505 born and other laminated


- 139 -

composite materials to find the minimum buoyancy

factor for composite elliptical submersible pressure

hull. Sudhirsastry et al. (2015) performed the buckling

analysis of laminated stiffened panels using ABAQUS

based on FEM with carbon fiber and other composite

materials. Square stiffened panel was fabricated with 8

layers of plates and 16 layers of differently shaped

stiffeners. Fenner and Watson (2012) performed

buckling analysis on a stiffened panel with application

of the FE program MSC NASTRAN and suggested the

influence of fillet radius along the line junction

between the stiffener webs and skin on buckling of the

panel. Ambur et al. (2004) presented the progressive

failure of panels and damage in the post-buckling

regime of stiffened panels including matrix cracking,

fiber failure and shear failure between fiber-matrix.

Satish Kumar and Paik (2004) obtained the buckling

loads of plates subjected to uniaxial compressive load,

biaxial compressive load and in-plane shear by using

an FE method based on hierarchical trigonometric

functions. Mahapatra and Panda (2016) investigated

nonlinear free vibration behaviour of laminated

composite spherical shell panel by FE method based on

higher-order shear deformation theory. Sridharan and

Zeggane (2001) analyzed local buckling and overall

buckling in stiffened plates and cylindrical shells with

the application of a specially formulated shell element,

which has additional degrees of freedom to generate

and control the relevant local buckling modes together

with the associated second-order fields. Nayak et al.

(2006) investigated a nine-node plate bending element

with assumed strains based on a refined higher-order

theory, which considers the effect of initial stresses in

the dynamic analysis of plates, to determine the small

deflection transient response of composite sandwich

plates due to initial stresses effect. Xie and Ibrahim

(2000) analyzed buckling mode localization in rib-

stiffened plates with varied spaced stiffeners. The finite

strip method has given satisfactory results for

determination of the buckling phenomenon of rib-

stiffened plates. Kalavagunta et al. (2017) obtained

ultimate capacity of the strengthened cold steel

columns with CFRP by using finite element analysis

software.

Many researchers have worked on parametric

studies of buckling of laminated composite panel with

blade type, I-shaped and T-shaped stiffeners in the

presence of in-plane shear, compression and their

combined loading, but parametric studies of buckling

response of laminated composite panels with hat-

stiffeners under compressive loading gained less

consideration. For the design of stiffened panel,

computation of stiffened panels by numerical analysis

is not efficient due to the presence of a large number of

variables. A database is provided by application of FE

studies and on the basis of the study, parametric study

on buckling of laminated composite hat-stiffened

panels under compressive loading is presented.

Methodology for FE Modeling of Laminated

Composite Hat-stiffened Panels

Mathematical Approach

Linear buckling analysis predicts the theoretical

buckling capacity of an ideal linear elastic structure.

On the other hand, nonlinear buckling analysis

develops a non-linear static model with gradually

increasing loads to seek the load level at which the

structure becomes unstable. Therefore, non-linear

buckling analysis is an efficient approach which is

recommended for the design of compressive members

of complex structural problems in civil engineering.

Co-ordinate system and displacement field are

shown in Fig. 1. The vectors u, v and w are the

displacements and θx, θy and θz are the average

rotations of a line initially perpendicular to the

longitudinal plane along the x, y and z directions,

respectively. Displacements and rotations within each

element can be described in terms of the nodal

unknowns with the help of the shape functions (Ni)

given as;

u = uN i

n

ii

1 v = vN i

n

ii

1 w = wN i

n

ii

1 (1)

θx = xN i

n

ii

1 θy = yN i

n

ii

1

θz = zN i

n

ii

1

(2)

where n represents the number of nodes of the finite

element.

ABAQUS provides both triangular and

quadrilateral shell elements with linear interpolation

for larger-strain and small-strain formulations. For

most of applications, large-strain conventional shell

elements S4R (Shell, 4-node, Reduced integration) are

appropriate to these considerations. In this work, four-


- 140 -

node S4R quadrilateral shell element is considered for

buckling analysis of a stiffened panel which possesses

both bending and membrane capabilities.

For each node, it is convenient to write the vector

of unknowns as:

Figure (1): Co-ordinate system and

displacement field

{qi}= { ui, vi, wi, θxi, θyi, θzi}T (3)

The strain-displacement relationship from the

Mindlin-Reissner assumptions by Barbero et al. (1995)

can be shown as:

{ϵ}= [ B0 ]{qi} (4)

where [B0] = strain-displacement matrix.

The stress – strain relation can be determined from

the constitutive law as:

{σ} = [C]{ϵ} (5)

where [C] represents the material constant matrix.

The total potential energy (V) of the plate subjected

to in-plane and transverse loadings consists of the

strain energy (U) and the work done (W) by load.

V= U-W = T}{ dv - λ {q} T {f} (6)

where λ is the single load factor to increment the

load vector {f}.

As a first step in the linear buckling analysis,

mathematical formulation of the stiffness matrix [K0] is

carried out as:

[K0] = dv]B][C[]B[V

0T

0 (7)

Therefore, the pre-buckling solution can be found

from:

[K0] {q} = {f0} (8)

In the second step, the critical stage along with the

fundamental path are determined. Therefore, it is

needed to compute the geometric stiffness matrix [Kσ]

as given by Barbero et al. (1995):

[Kσ] = dv]G][[]G[V

T (9)

The linear Eigenvalue problem is given by:

}0{}{][][ 0 xKK (10)

The critical load λc can be determined from

Equation (10) corresponding to Eigenvector {x}. The

buckling analysis is done with variation of different

parameters with two different types of hat-stiffeners of

the stiffened panel through models generated in

ABAQUS.

FE Modeling of the Panel

Modeling of the laminated composite hat-stiffened

panel is developed carefully to define the material

properties of skin and stiffeners, number of layers,

thickness and fiber orientation of the ply configuration.

Uniformly distributed compressive loading of 1 kN/m

is applied on the edge of the panel in the stiffeners’

direction. The simply supported boundary conditions

are applied on all the sides of the panel and a model is

submitted for the Eigenvalue buckling analysis. The

buckling load is obtained by multiplying the edge

compressive load and the Eigenvalue as obtained from

the FE analysis.

Validation Studies

The FE model is validated for a hat-stiffened panel

with the Engineering Analysis Language (EAL) results

presented by Stroud et al. (1984). The FE analysis is

carried out on a hat-stiffened panel of dimensions 762

mm x 762 mm with six hat stiffeners (taken by Stroud

et al. (1984)). The variation of Eigenvalue with the

global size of shell element (S4R) of the panel is

studied as shown in Fig. 2. The Eigenvalue is

approximately constant for the further increase in


- 141 -

global size of element (38.1 mm). In the present study,

38.1 mm global size of element is taken for the analysis

of stiffened panels and the Eigenvalue from the present

study is in good agreement with EAL results of hat-

stiffened panels reported by Stroud et al. (1984). The

hat-stiffened panel is discretized in shell elements

(S4R) and a total of 820 elements have been generated

of the panel as shown in Fig. 3. The results from the

present study are in good agreement with EAL results

reported by Stroud et al. (1984) for a hat-stiffened

panel under compression and combination of

compression-shear as shown in Table 1. The global

buckling mode shapes of the present study are obtained

to be symmetrical for compression and combination of

compression-shear, which is similar to the global

buckling mode presented by Stroud et al. (1984).

Figure (2): Effect of Eigenvalue with variation of

global size of element (S4R) of hat-stiffened panel

Table 1. Validation FE modeling of the panel

Applied load (kN/m)

FE analysis (Eigenvalue) % Difference

𝒃 𝒂

𝒂*100

FE analysis mode shape

Stroud et al. (1984)

(a)

Present study (b)

Stroud et al. (1984) Present study

NX NXY

175.1 0 3.0042 3.0158 0.38 Symmetric Symmetric

175.1 175.1 2.3268 2.2386 -3.79 Symmetric Symmetric

Figure (3): Hat-stiffened panel discretized with shell element (S4R)

Numerical Panel Studies

Numerical study is carried out by analyzing the

laminated composite hat-stiffened panel of dimensions

762 mm x 762 mm under edge compressive loading, as

shown in Fig. 4. Pitch length of the stiffener is varied

from 84.67 mm to 381 mm (number of the hat-

stiffeners is varied from 9 to 2, respectively) and a

fixed top width of 25mm. Two different types of hat-

stiffeners (600-hat-stiffener and 750-hat-stiffener) are

used to analyze the panel. The carbon fiber composite


- 142 -

(CFC) material properties of each ply of 0.125 mm

thickness are given in Table 2. Three types of ply

configurations of skin are used for plate and stiffener

component of the stiffened panel as illustrated in Table

3. A program is developed on the basis of smeared

stiffness approach by using the following formulae for

different pre-decided orthotropy ratios with variation of

pitch length of stiffener for finding the corresponding

hat-stiffener depth by trial and error for three different

skins considered separately. The obtained depth of

stiffener is used for the FE modeling of the panel. The

buckling of the stiffened panel subjected to uniformly

distributed edge compressive load is analyzed with

variation of different parameters obtained from Stroud

and Anderson (1981) using the following formulae.

Table 2. Material properties of CFC used in the analysis (Sudhirsastry et al. (2015))

Quantity Symbol Units CFC

Young’s modulus 00

Young’s modulus 900

Shear modulus in planes 12 and 13

Shear modulus in plane 23

Poisson’s ratio in plane 12

Ultimate tensile strength 00

Ultimate compressive strength 00

Ultimate tensile strength 900

Ultimate compressive strength 900

Ultimate shear strength in plane 12



Density

E11

E22

G12

G23

υ12

X1t

X1c

X2t

X2c

S12

S13

S23

ρ

GPa

GPa

GPa

GPa

-

MPa

MPa

MPa

MPa

MPa

MPa

MPa

Kg/m3

164

12.8

4.5

2.5

0.32

2724

111

50

1690

120

137

60

1800

Table 3. Ply configurations of panel elements

Panel component (plate and stiffener of same skin)

Ply configuration Each ply thickness

(mm) A11/A22 D11/D22

Skin – 1 Skin – 2 Skin – 3

[[300/-300/900/00]s]s [[450/-450/900/00]s]s [[600/-600/900/00]s]s

0.125 0.125 0.125

1.68 1.00 0.59

1.81 0.95 0.49

Figure (4): Structural geometry of hat-stiffened panel


- 143 -

Flexural stiffness of the panel (D1) in the direction

of stiffener:

𝐷 =

∑ 𝐴 𝑏 𝑧 2sin +

𝑏 𝐷 2cos (11)

Flexural stiffness of panel (D2) in the direction

transverse to stiffener:

D2 = (D22)Plate (12)

The smeared extensional stiffness of element per

pitch:

𝐸𝐴 =

∑ 𝐴 𝑏 (13)

= smeared extensional stiffness ratio of stiffener

to that plate per pitch:

Twisting stiffness of panel (D3) per pitch:

D3 = 3D +

3D (14)

For open-section panels given by:

3D = ∑ 𝑏 𝐷 𝐷 (15)

For closed-section panels given by: 3D

∑ (16)

where i = type of element of the panel (plate or

stiffener).

bi = width of the element, p = pitch length of the

panel.

Zi = distance from the neutral axis of the cross-

section to the centroid of the element.

ϴ = inclination of the element with the horizontal

direction.

Ā = area enclosed by closed-section in one period.

(a) 600-hat-stiffener with skin-2 (b) 750-hat-stiffener with skin-3

Figure (5): Global buckled mode shapes of the panel for (a) D1/D2 = 500 and pitch length = 127 mm, (b) D1/D2 = 300 and pitch length = 95.25 mm

The parameters influencing the buckling load of the

panel are identified on the basis of generated data by

trial and error. The parameter A11/A22 is the extensional

stiffness in the longitudinal direction to the transverse

direction of skin, D1/D2 gives the global flexural panel

properties, (EA)S/(EA)P gives the general concept

about material strength of skin, as well as depth and

pitch length of stiffener. The parameters D1/D2 and

(EA)S/(EA)P are increased upto a certain limit, which

depends upon the skin of panel components (plate and

stiffener), pitch length and depth of stiffener. For the

given skin of panel, D1/D2 and (EA)S/(EA)P of stiffened

panel are increased only by increasing pitch length and

depth of stiffener. Local buckling of the panel is

increased with increasing the depth of stiffener.

Therefore, less depth of hat-stiffener is required to be

used to reduce the local bucking of the stiffened panel.

The global buckling mode of the 600-hat-stiffened

panel under compressive load is shown in Fig. 5(a) for

a pitch length of 127 mm. The global buckling mode of

the 750-hat-stiffened panel under compressive load is

shown in Fig. 5(b) for a pitch length of 95.25 mm.


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RESULTS AND DISCUSSION

Parameters affecting the bucking behavior of hat-

stiffened panel are identified on the basis of the

generated database in the present study with two

different types of hat-stiffeners.

Influence of Panel Orthotropy Ratio

For different pitch lengths of the stiffener and

different skins, variation of buckling load of hat-

stiffened panels with D1/D2 is shown in Fig. 6(a)-(f). It

is observed that buckling load increases with increasing

D1/D2 in all cases of pitch lengths and all three types of

skins for 600-hat-stiffener and 750-hat-stiffener.

Initially, the increase of rate of buckling load is high,

but it is reduced further increasing D1/D2. It is also

observed that the buckling load of 600-hat-stiffener is

greater than that of 750-hat-stiffener of the panel in all

cases of given skin. For given skin and D1/D2, buckling

load is decreased with increasing pitch length of

stiffeners. 600-hat-stiffened panel with skin-3 has more

buckling capacity in compression in all cases of skin

and stiffener inclination. For the design of maximum

buckling capacity hat-stiffened panel, 600-hat-stiffened

panel is preferable with skin-3 and with lower pitch

length of stiffener and greater D1/D2.

Influence of Smeared Extensional Stiffness Ratio of

Stiffeners to That of Skin

For different D1/D2 and skin, variation of buckling

load per unit area of the panels with (EA)S/(EA)P is

shown in Fig. 7(a)-(f). It is observed that with the

increase in (EA)S/(EA)P, initially, buckling load per

unit area increases rapidly, after that increases

gradually and further it is approximately constant in all

cases. This type of behavior is more expressive in case

of high D1/D2. The buckling load per unit area is much

less important with the increase of (EA)S/(EA)P in case

for lower D1/D2. It is also observed that 600-hat-

stiffener is more significant as compared to 750-hat-

stiffener in all cases of skin for the maximum buckling

load per unit area.

In the above discussion, it is observed that the

buckling load per unit area is increasing upto certain

values of (EA)S/(EA)P for all D1/D2 in different cases

and then it is almost constant. Further increasing the

cross-sectional area of stiffener, buckling capacity per

unit area of the hat-stiffened panel is not significantly

improved, but (EA)S/(EA)P increases for any D1/D2

ratio. Therefore, (EA)S/(EA)P and D1/D2 depend upon

the depth and number of stiffeners for given skin.

Hence, depth and number of stiffener of hat-stiffened

panel are increased to a certain limit for efficient

bucking performance of the panel without increasing

the panel weight and local buckling. In addition, local

buckling of panel is increased with increasing the depth

of stiffener, so that less depth of hat-stiffener of the

panel is required to reduce the local bucking of the hat-

stiffened panel.

Ply configuration (skin) acts significantly in

buckling performance of hat-stiffened panel. It affects

the A11/A22 ratio, which is significant for affecting the

other parameters. In the present study, A11/A22 for three

different values; 1.68 (skin-1), 1.00 (skin-2) and 0.59

(skin-3), is taken as shown in Table 3 for determination

of buckling load of the panel. The minimum value of

(EA)S/(EA)P is determined from Fig. 7(a)-(f) for

different skins and D1/D2 at which the hat-stiffened

panel has the maximum buckling load per unit area.

This minimum value is defined as optimum

(EA)S/(EA)P of the hat-stiffened panel. Further, with

increase of (EA)S/(EA)P, the buckling capacity per unit

area curve becomes approximately constant.

The optimum (EA)S/(EA)P is studied with variation

of D1/D2 for different skin (A11/A22) of the panel as

shown in Fig. 8(a)-(b) for 600-hat-stiffener and 750-hat-

stiffener, respectively. It is observed that the optimum

(EA)S/(EA)P increases with decreasing A11/A22 for all

different D1/D2. It is also observed that the optimum

(EA)S/(EA)P increases with D1/D2 for all the same skin.

For skin-1, with increase of D1/D2 from 100 to 500, the

optimum (EA)S/(EA)P is varied from 0.34 to 0.68 with

600-hat-stiffened panel and from 0.33 to 0.64 with 750-

hat-stiffened panel, respectively. For skin-2, with

increase of D1/D2 from 100 to 500, the optimum

(EA)S/(EA)P is varied from 0.51 to 0.83 with 600-hat-

stiffened panel and from 0.49 to 0.78 with 750-hat-

stiffened panel respectively. For skin-3, with increase

of D1/D2 from 100 to 500, the optimum (EA)S/(EA)P is

varied from 0.59 to 0.99 with 600-hat-stiffened panel

and from 0.56 to 0.92 with 750-hat-stiffened panel,

respectively.


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Figure (6): Buckling load of hat-stiffened panel with D1/D2 for different pitch lengths of stiffener and skin


- 146 -

Figure (7): Buckling load/area of hat-stiffened panel with (EA)S/(EA)P for different D1/D2 and skin


- 147 -

Figure (8): Optimum (EA)S/(EA)P for different skin and D1/D2

CONCLUSIONS

Linear buckling analysis is performed on laminated

composite hat-stiffened panel with two different types

of hat-stiffener under edge compressive loading.

Parametric studies on buckling of hat-stiffened panels

are carried out with variation of pitch length of

stiffeners, number of stiffeners, panel orthotropy ratio

and smeared extensional stiffness ratio of stiffeners to

that of skin with three different ply configurations for

600-hat-stiffeners and 750-hat-stiffeners. The following

conclusions are drawn:

For the design of maximum buckling capacity

stiffened panel, 600-hat-stiffened panel is preferable

with less pitch length and greater D1/D2. Also, the

depth of stiffener should be as small as possible to

prevent local buckling of the panel.

For optimization of (EA)S/(EA)P of the hat-stiffened

panel, the optimum (EA)S/(EA)P increases with

decreasing A11/A22 for all different D1/D2 and it also

increases with increasing D1/D2 for all similar skin.

For maximum buckling load per unit area of the

panel, 600-hat-stiffeners gave significant results in

comparison to 750-hat-stiffeners in all cases.

For better design of the hat-stiffened panel, the

pitch length and depth of the hat-stiffener can be

obtained with the help of optimum (EA)S/(EA)P for

different skin and orthotropy ratio D1/D2 of the

panel.

REFERENCES

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evaluation of steel columns buckling under cyclic

loading”. Jordan Journal of Civil Engineering, 8 (3),

353-362.

Al-Qablan, H, Katkhuda, H., and Dwairi, H. (2009).

“Assessment of the buckling behavior of square

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