Behaviour of plates with circular cutout

1. Proceedings of the International Conference on Emerging Trends in Engineering and Management (ICETEM14)
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BEHAVIOUR OF PLATES WITH CIRCULAR CUTOUT
DINU PAULOSE1
, DIPU V.S2
1
(M.Tech Student, Sree Narayana Gurukulam College of Engineering, Ernakulam, Kerala, India)
2
(Civil Department, Sree Narayana Gurukulam College of Engineering, Ernakulam, Kerala, India)
ABSTRACT
Steel plates are often used as the main components of steel structures such as webs of plate girders, box girders,
ship decks and hulls and platforms on oil rigs. Perforations are often included in the stressed skin cover of air plane
wings. In plates, cut-outs are provided to decrease the self-weight, to provide access, services and even aesthetics. When
these structures are loaded, the presence of cut outs will cause changes in the member mechanical properties,
consequently there will be change in the buckling characteristics of the plate as well as on the ultimate load capacity of
the structure. In marine and offshore structures, the perforated panels are used to make a way of access or to reduce the
total weight of the structure. When these plates are subject to compression loads, the structure could buckle if the load
exceeds the critical load. Thus, to know how this phenomenon occurs and to analyze the buckling behaviour of these
perforated panels has great importance for an efficient structural design. In this study, the finite element analysis
package, ANSYS is used to analyze the behavior of unstiffened plate with circular opening.
Keywords: Circular Opening, Design, Steel Plates, Ultimate Strength, Unstiffened Plates.
1. INTRODUCTION
The buckling behaviour of perforated plates has been the object of a large number of researches in the last
decade. Like other types of structures such as aerospace structures and land based structures, ships and offshore
structures now tend to be designed based on ultimate strength instead of allowable working stress. Therefore, it is
increasingly required to identify the ultimate strength characteristics of various types of structural components.
Perforated plates are used in ships and ship shaped Offshore structures to make a way of access or to lighten the
structure. Since these perforations may reduce the ultimate strength of the plate, it is necessary to investigate the effect of
perforations on the ultimate strength of the plate. The introduction of openings in plated structures (e.g. ship grillages,
stressed skins of airplane wings. etc.) for access and service results in changes in the stress distribution within the
member and causes a reduction of strength. The performance of such a plate is influenced by the type of applied stress, as
well as by the shape, location, sizeand number of holes.
Unstiffened plates are integral part of all kinds of structures such as ship and offshore oil platforms. Openings
are unavoidable and absolutely reduce the ultimate strength of structures. In this study, the finite element analysis
package, ANSYS is used to analyze the behaviour of unstiffened plate with circular opening. Stiffened and unstiffened
steel flat panels form the basic members for the deck structure and habitation units in ship as well as offshore structures.
Even though for stiffened panels, thin plates between stiffeners are integral part of flat panels. The ultimate strength of
these elements is important from view point of design and safety since collapse of plate due to local buckling is one of
the important basic failure modes. The bending rigidities of the boundary edges of plates between transverse frames and
longitudinal stiffeners are quite high compared with that of the plate itself. The rotational restraints along the plate edges
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can be assumed to be small for plates subjected to axial compression. Hence, the plate elements in the current study are
considered as simply supported along all edges [1].
Steel plates are often used as the main components of steel structures such as webs of plate girders, box girders,
ship decks and hulls and platforms on oil rigs. Perforations are often included in the stressed skin cover of air plane
wings. In plates, cut-outs are provided to decrease the self-weight, to provide access, services and even aesthetics. When
these structures are loaded, the presence of cut outs will cause changes in the member mechanical properties,
consequently there will be change in the buckling characteristics of the plate as well as on the ultimate load capacity of
the structure.
Fig.1: A typical ship deck in between the bulkhead
2. SCOPE
• Unstiffened plates are integral part of all kinds of structures such as ship and offshore oil platforms.
• Openings are unavoidable and absolutely reduce the ultimate strength of structures
• ANSYS is used to analyze the behaviour of unstiffened plate with circular opening.
3. OBJECTIVES
• To study the structural behaviour of plates under different loading & boundary conditions
• To determine the ultimate strength of plate without circular cutout using ANSYS
• To determine the ultimate strength of plate with circular cutout using ANSYS
• To compare the ultimate strength of plates with & without circular cutout.
• To study the structural behaviour of plates with circular cutout which will serve as a design aid.
4. METHODOLOGY
• Literature review
• Identification of geometry, boundary conditions & loading
• Problem solving by software package
• Result interpretation
5. GEOMETRY GENERATION & PROBLEM FORMULATION
Ultimate strength of unstiffened plate without opening is found to be maximum for an aspect ratio of A/B = 1.0.
So, an unstiffened plate of size 500 mm x 500 mm (A x B) is considered for the study. The circular type cutout are
considered in this study. Also, it is assumed that the cutout is located at the centre of the plate.The yield strength of plate
σy is assumed as 250 N/mm2
with Young’s modulus of elasticity (E) as 2 x 105
N/mm2
and Poisson’s ratio (υ) of 0.3. All
the edges of the plate are assumed to be simply supported.

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5.1 GEOMETRY OF THE PLATE
Ultimate strength of unstiffened plate without opening is found to be maximum for an aspect ratio of A/B = 1.0.
So, an unstiffened plate of size 500 mm x 500 mm (A x B) is considered for the study. The thickness of plate is varied as
5 mm, 6 mm, 8 mm, 10 mm, 12 mm and 15 mm to obtain plate slenderness ratio in the practical range of 1.0 - 4.5 used in
ship construction. The diameter of the circular hole is varied as 80 mm,113 mm,138 mm.160 mm.Area ratio (AR) of
opening is defined as the ratio of area of opening (AC) to area of plate (AP). In this study, the area ratio (AR) is varied as
0.02, 0.04, 0.06, 0.08. The unloaded edges are allowed to deform inplane but remains straight. This is achieved by
coupling the deformation of nodes in that direction. This condition is to generate the actual situation of unstiffened plate
between longitudinal and transverse stiffeners. The reaction edge is constrained to obtain an equal force caused due to
loading edge.
Fig 5: Geometry of the plate
5.2 BOUNDARY CONDITIONS OF PLATE
All the edges of the plate are assumed to be simply supported. The unloaded edges are allowed to deform
inplane but remains straight. This is achieved by coupling the deformation of nodes in that direction. This condition is to
generate the actual situation of unstiffened plate between longitudinal and transverse stiffeners. The reaction edge is
constrained to obtain an equal force caused due to loading edge.
5.3 NONLINEAR FINITE ELEMENT ANALYSIS
A general purpose finite element software ANSYS is used for modeling, analysis and post processing of
unstiffened plate with rectangular opening under axial compression. Modeling of unstiffened plate involves generation of
a square of size 500 mm x 500 mm. To create the opening, area is generated using key points and connecting it by means
of area command available in preprocessor. Using the ‘Subtract areas’ option available in the ‘Booleans’ operation under
the ‘modeling’ part, the area is deleted. Thus the geometry of an unstiffened plate with opening at the centre of the plate
is developed. The lines are meshed set using the ‘size controls’ available with the ‘mesh tool’ in ‘meshing’ part. Four
noded finite linear strain element (SHELL181) available in the ANSYS element library is used for discretisation of
unstiffened plate. The element has six degrees of freedom per each node; three translations (UX, UY and UZ) and three
rotations (RX, RY and RZ). This element is well suitable for analysing the linear, large rotation, and/large strain
nonlinear applications. The finite element model of the square plate with circular and square opening is done. Simply
supported boundary conditions along all the edges of the plate are used in the analysis. All the nodes along the four edges
of the plate are constrained for deflection and rotation along the thickness direction (UZ, RZ = 0). Apart from it, the
reactive edge is constrained against axial deformation (UY = 0). All the nodes along the unloaded edges are coupled for
inplane displacement (UX) such that the displacements along the length of the plate are uniform. Both geometric and
material nonlinearities are considered in the analysis. Large displacement static analysis with stress stiffening option is
activated in geometric nonlinear analysis. Bilinear isotropic rate independent hardening with von Mises yield criteria is
used in material nonlinear analysis [2].
6. VALIDATION
Unstiffened plate of size 500 mm x 500 mm (A x B) is considered for the study. The thickness of plate is 5 mm.
Rectangular opening is provided in the centre of the plate. The depth of opening (a) is 100 mm & The width of opening

4. Proceedings of the International Conference on Emerging Trends in Engineering and Management (ICETEM14)
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137
(b) is250 mm. The yield strength of plate σy is assumed as 250N/mm2
with Young’s modulus of elasticity (E) as 2 x 105
N/mm2
and Poisson’s ratio (υ) of 0.3. All the edges of the plate are assumed to be simply supported. The unloaded edges
are allowed to deform in plane but remains straight. This is achieved by coupling the deformation of nodes in that
direction. This condition is to generate the actual situation of unstiffened plate between longitudinal and transverse
stiffeners. The reaction edge is constrained to obtain an equal force caused due to loading edge.
Fig 3: Axial deformation contour for specimen P5
Fig 4: VonMises stress contour for specimen P5 at ultimate load

5. Proceedings of the International Conference on Emerging Trends in Engineering and Management (ICETEM14)
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Table 1: Validation details
7. PRESENT STUDY
Unstiffened plate of size 500 mm x 500 mm (A x B) is considered for the study. The thickness of plate is varied
as 5 mm, 6 mm, 8 mm,10 mm, 12 mm, 15 mm. Rectangular opening is provided in the centre of the plate. The diameter
of the plate varies as 80 mm, 113 mm, 138 mm, 160 mm. The yield strength of plate σy is assumed as 250N/mm2
with
Young’s modulus of elasticity (E) as 2 x 105
N/mm2
and Poisson’s ratio (υ) of 0.3. All the edges of the plate are assumed
to be simply supported.
Dimensions Of Plate
• Ultimate strength of unstiffened plate without opening is found to be maximum for an aspect ratio of A/B = 1.0
• So, an unstiffened plate of size 500 mm x 500 mm is considered for the study.
• The thickness of plate is varied as 5 mm, 6 mm, 8 mm, 10 mm, 12 mm and 15 mm to obtain plate slenderness
ratio in the practical range of 1.0 - 4.5 used in ship construction.
Properties of Plate
• The yield strength of plate σy is assumed as 250 N/mm2
• Young’s modulus of elasticity (E) as 2 x 105
N/mm2
• Poisson’s ratio (υ) of 0.3.
• All the edges of the plate are assumed to be simply supported.
Dimensions of cutout
• Area ratio (AR) of circular opening is defined as the ratio of area of opening (AC) to area of plate (AP).
• In this study, the area ratio (AR) is varied as 0.02, 0.04, 0.06, 0.08.
• Diameter of circular cutout-80,113,138,160 mm
Numerical Analysis
• ANSYS is used
• generation of a plate of size 500 mm x 500 mm
• Cutout area created
• Cutout is created by using booleans
• Meshing is done
• (SHELL181) available in the ANSYS element library is used for discretisation of unstiffened plate
• Loading is given
• Solution of problem & Interpretation of results
Fig 5: Boundary conditions & loading of plate
Sl. no Specimen
dimensions(mm)
Cutout
size(axb)mm
Ultimate load(PU)
kN
Ultimate stressσu/σy
1 500x500x5 100x250
Present
study
As per
journal
Present
study
As per
journal
278.15 277.05 0.44 0.44

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Fig 6: Axial deformation contour for specimen P3 (β=3.54) at ultimate load
Fig 7: VonMises stress contour for specimen p1 (β=3.54) at ultimate load

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Table 2: Details of parametric study
Sl.No Specimen Diameter
of opening
(D)mm
Thickness
of plate,
(t)mm
Plate
slenderness
ratio,(β)
Area of
opening to
plate
(AR=AC/AP)
Ultimate
load(PU)
kN
σu/σy
1 P1 80
5 3.54
0.02
564.62 0.90
6 2.93 686.15 0.91
8 2.27 936.98 0.94
10 1.77 1187.74 0.95
12 1.48 1443.45 0.96
15 1.17 1920.62 1.02
2 P2 113
5 3.54
0.04
513.45 0.82
6 2.93 635.23 0.85
8 2.27 891.89 0.89
10 1.77 1116.46 0.893
12 1.48 1362.44 0.91
15 1.17 1833.75 0.98
3 P3 138
5 3.54
0.06
496.38 0.79
6 2.93 598.64 0.798
8 2.27 820.00 0.82
10 1.77 849.35 0.85
12 1.48 1320.58 0.88
15 1.17 1802.23 0.96
4 P4 160
5 3.54
0.08
463.55 0.74
6 2.93 566 0.75
8 2.27 755.45 0.755
10 1.77 949.67 0.76
12 1.48 1209.38 0.81
15 1.17 1728.53 0.92
Fig 8: Stress on varied area ratio

8. Proceedings of the International Conference on Emerging Trends in Engineering and Management (ICETEM14)
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Table 3: Ultimate load of plate without cut-out
Sl. no: Plate thickness
(mm)
Ultimate load(PU)
kN
σu/σy
1 5 626.84 1.00
2 6 752.48 1.00
3 8 1004.56 1.00
4 10 1228.31 1.00
5 12 1522.58 1.00
6 15 1979.78 1.00
Table 4: Ultimate load of plates with different area ratio
Sl no: Dimensions of
plate(mm)
Area of opening to
plate
(AR=AC/AP)
Ultimate load(PU)
kN
σu/σy
1 (500x500x5)
0 626.84 1.00
0.02 564.62 0.90
0.04 513.45 0.82
0.06 496.38 0.79
0.08 463.55 0.74
Fig. 9: Effect of area ratio on ultimate stress (P3)
8. CONCLUSION
• Effect of circular opening of a square plate on ultimate strength under axial compression is found.
• Effect of slenderness ratio (β), area ratio (AR) on ultimate strength is determined using nonlinear finite element
analysis.
• Design aid for plate with circular cutout subjected to inplane loading is prepared.
9. SCOPE FOR THE FUTURE WORK
The study can be further extended to propose a design equation for plates with circular opening under axial
compression.

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