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- 1. STRUCTURAL ANALYSIS OF BULKHEAD USING FEM Presented by Diana Augustine Reg. No: 95415011 Dept. of Ship Technology CUSAT External guide Internal Guide Dr. Smitha K.K. Dr. Manoj T Issac Associate Professor Asst. Professor SNGCE Dept. of Ship Technology CUSAT 1
- 2. INTRODUCTION KEY ELEMENTS OF A SHIP bottom and side shell plating deck plating transverse bulkheads fore end & aft end super structure 2 Fig 1: Key structural elements of a ship [ Manoj, 2016]
- 3. INTRODUCTION WHAT ARE BULKHEADS Bulkheads are stiffened-plate structures primarily subjected to normal loads and secondarily to in-plane loads. Similar to internal walls dividing a building into separate rooms. They subdivide the ship hull into a number of large water tight compartments. Bulkheads can either be arranged transversely or longitudinally. 3
- 4. BULKHEAD 4 Fig 2 : Bulkhead [www.marine-knowledge.com/bulk-head]
- 5. FUNCTIONS OF BULKHEAD An important function of bulkhead is to improve the general strength and rigidity of the entire hull structure. As transverse members, they contribute to hull stiffness . Transverse bulkhead prevents racking and torsional distortion of a ship. Longitudinal bulkheads contribute to the longitudinal strength of the ship. 5
- 6. WHY STIFFENED PLATE? In aircraft and ship construction, it is important to save weight to alleviate structures themselves. This necessity is met by using stiffened plates. Plates can be either longitudinally stiffened or stiffened both longitudinally and transversely . 6 Fig 3 : Model of a stiffened plate[ Jeom, 2002]
- 7. ADVANTAGES OF USING STIFFENERS Tremendous increase in strength and stability with minimum increase of weight to the overall structures. i.e. high strength-to-weight ratio. Increases the bending stiffness of the structure with a minimum of additional material. Also it subdivide the plate into smaller panels, thus increasing considerably the critical stress at which the plate will buckle. 7
- 8. ANALYSIS METHODS ORTHOTROPIC PLATE APPROACH Basis - convert the stiffened plate into an equivalent plate with constant thickness. Flexural and torsional rigidities in orthogonal directions represent the combined strength of stiffener and plating in the respective directions. 8 Fig 4 : Idealization of stiffened plate as equivalent plate [Dongqi, 2004]
- 9. ANALYSIS METHODS STRUT OR BEAM COLUMN APPROACH The stiffened plate is treated as a series of unconnected struts. A strut is composed of a stiffener with associated effective width of plate as shown in the Fig 9 Fig 5 : Strut/beam column approach[Dongqi, 2004]
- 10. ANALYSIS METHODS FINITE ELEMENT METHOD For the analysis of stiffened plates three different finite element models can be employed. - discrete model : plating is modeled using thin shell element and the stiffeners using ordinary beam elements. - smeared model : the stiffeners are smeared along the plate to form an equivalent plate - stiffened panel element : models the in-plane stiffness of a flat rectangular panel of stiffened plate having any number of parallel stiffeners in either one direction or in both directions. 10
- 11. OBJECTIVES The objectives of the present study are To conduct a study on the structural behaviour of bulkhead To conduct a linear static analysis of bulkhead, subjected to in-plane load and lateral pressure with various boundary conditions, using the finite element software, Abaqus. To conduct a parametric study on the behavior of bulkhead by varying the geometry of the stiffener, keeping the material volume a constant. 11
- 12. SCOPE OF THE WORK The stresses and displacements produced are affected by the thickness of the plate, geometry of the stiffeners, boundary conditions and grade of the steel used. In designing, the boundary condition assumed is simply supported where this assumption gives a large factor of safety. But in reality the bulkheads are neither simply supported nor fixed. [Hughes, 2010] The work done in this project is a step towards modelling a bulkhead with a more accurate boundary condition and thus analyse the stresses and displacements produced on application of lateral and in- plane loads. 12
- 13. LITERATURE REVIEW Ji et al. [2001] derived simplified formulas to calculate the ultimate strength of corrugated bulkheads. The paper also provided the means to estimate the effect of shearing force on the ultimate strength of corrugated bulkheads. The axial compression induced by vertical shear force may reduce the ultimate strength. Khosrow et al. [2003] discussed the non linear large deflection analysis of stiffened plate. If lateral pressure is zero and the stiffened plate is under longitudinal compression, buckling takes place. 13
- 14. LITERATURE REVIEW With an increase in lateral pressure, the effect of buckling decreases and thus ultimate strength increases. The contribution of a large number of transverse bulkheads to general hull stiffness was analysed by Ivo et al. [2008]. Thin walled girder theory in combination with orthotropic plate theory is used. Transverse bulkheads are modelled by axial elastic springs at their joint to ship hull. Chikalthankar et al.[2013] presented Trigonometric Shear Deformation Theory, for the analysis of orthotropic plate. 14
- 15. LITERATURE REVIEW Bhaskar K and Anup Pydah [2014] derived analytical solution for stiffened plate. The plate is modelled using equations of 3D elasticity while the stiffener is modelled using a plane stress formulation. The effect of slenderness ratio (b/t) on ultimate strength of stiffened plate was studied experimentally by Shanmugan et al. [2014] Plate was kept simply supported at all four edges and was modelled using 8 noded doubly curved thin shell element. 15
- 16. LITERATURE REVIEW Deepak et al.[2015] carried out parametric study to estimate the maximum deflection and stress in the isotropic plates by varying the geometry of stiffener keeping the constant volume of material. Parametric study for different combination of stiffened plate geometry. Thickness of stiffener should be approximately equal to the thickness of the plate. 16
- 17. FINITE ELEMENT PROCEDURE The finite element method is an approximate technique by which an object is decomposed into pieces and treated as isolated, interacting sections. The advancement in computer technology enables us to solve even larger system of equations and to display the results quickly and conveniently. Another important feature is the meshing, i.e. discretization of a continuous domain into a set of sub-domains. 17
- 18. FINITE ELEMENT PROCEDURE A time-independent problem in finite element analysis is typically expressed by the following stiffness equation. {R} = [K]{U} where {R} = load vector, {U} = displacement vector and [K] = stiffness matrix. The stiffness matrix is a function of the structure’s geometric and material properties. If these properties are constant, the problem is linear. If these properties are dependent on either {R} or {U}, the problem is nonlinear. For finite element analysis ABAQUS software is used in this study. 18
- 19. VALIDATION OF ABAQUS SOFTWARE For validating Abaqus software, analysis of a stiffened and unstiffened plate is considered. The total volume of the stiffened and unstiffened plates and the plan dimensions have been kept equal so that the plate thickness for the stiffened plate has been reduced. The plates were meshed using a 4 noded plate shell element. For the anlalysis of unstiffened plate, a rectangular plate 1.4x1.4 and 15mm was considered. Uniformly distributed pressure load of 10kPa was applied laterally and the four edges were made simply supported. 19
- 20. VALIDATION OF ABAQUS SOFTWARE For the anlalysis of stiffened plate, a rectangular plate 1.4x1.4 stiffened orthogonally using 0.15x 0.0148 m flat bar with a spacing of 350mm was considered. The thickness of the plate is reduced to 6mm so that the unstiffened and stiffened plates have equal material volume. Uniformly distributed pressure load of 10kPa was applied laterally and the four edges were made simply supported. 20 Fig 6: Orthogonally stiffened plate model
- 21. VALIDATION OF ABAQUS SOFTWARE The analytical results for the deflection at the centre of an unstiffened plate have been taken from the book by Timoshenko [1959] w = α qa4/D where D = Eh3/12(1-υ2) w : deflection at the centre E : Young’s modulus h : thickness α : constant depending on b/a ratio b : major length of the plate a : minor length of the plate q : lateral pressure The differential equation for deflection surface is given by 21
- 22. VALIDATION OF ABAQUS SOFTWARE In case of orthogonally stiffened plate, they are converted into an equivalent orthotropic plate. The thickness is obtained by equating the rigidities of the stiffened plate in two perpendicular directions to the equivalent plate rigidity. For a stiffened plate of thickness tp, the combined flexural rigidity of the plate and the stiffeners can be equated to the flexural rigidity of an equivalent plate as given below. Etp 3/(12(1-υ2)) + E (I/ unit length) = Eteq 3/(12(1-υ2)) 22
- 23. VALIDATION OF ABAQUS SOFTWARE The governing equation for orthotropic plate analysis known as Huber’s equation is as follows: 23 I1 : moment of inertia of one stiffener b1 : spacing of stiffener in x direction I1 and a1 : respective values in y direction Dx and Dy : Flexural rigidities in x and y directions respectively
- 24. RESULTS ABAQUS result for the deflection of an unstiffened plate 24 Fig 7 : Deflection of unstiffened plate
- 25. RESULTS ABAQUS result for the deflection of an stiffened plate 25 Fig 8 : Deflection of stiffened plate
- 26. RESULTS 26 The Abaqus and analytical results for maximum deflection at the centre of the plate is given in the table below. It is clear Abaqus software gives a good result in accordance with the analytical solution and thus Abaqus software can be further extended for the analysis of bulkheads. Analytical solution (m) FEM (m) Percentage Variation% Unstiffened plate 2.18x10-03 2.19x10-03 0.46 Orthogonally stiffened plate 8.112x10-05 8.59x10-05 5.89
- 27. STRUCTRE DESCRIPTION OF BULKHEAD Generally rectangular in shape and the dimensions may vary depending on the type of ship. On an average, the dimensions of a ship will be : 200m long, 40m wide and 24m deep. The minimum thickness of bulkheads is 8mm and this increases towards the bottom . Plate thickness is directly related to the pressure exerted by the head of the water. They are welded to the shell, deck and tank top. 27
- 28. STRUCTRE DESCRIPTION OF BULKHEAD Mild or high-tensile steel and aluminium alloy is commonly used. High-tensile steel is preferred in the highly stressed regions. This allows reduction in thickness of the members. The stiffener spacing is about 760mm for watertight bulkheads And the spacing between bulkheads is about 10m. 28
- 29. STRUCTURAL ARRANGEMENT OF A TYPICAL BULKHEAD The bulkhead plating is supported by three stiffening systems Primary stiffener : one or more deep horizontal girder spanning the width of the bulkhead. Secondary stiffener : vertical and span full depth of the bulkhead. Tertiary stiffener : oriented horizontally and are arranged to give a bulkhead plating panel an aspect ratio of about 1 29
- 30. STRUCTURAL ARRANGEMENT OF A TYPICAL BULKHEAD 30 Fig 9 : Cross section of a flat – plate bulkhead structure
- 31. BOUNDARY CONDITION Although the plates are neither simply supported nor clamped, in maritime engineering practice, it is often assumed that the plates are simply supported at their edges. [Hughes, 2010] The top and bottom of the bulkhead is welded to the deck plate and tank top respectively. Stiffeners are connected to deck plate and tank top using brackets. Though this provides a rigid connection, when lateral pressure is applied, bending of bulkhead takes place, but due to the elastic nature of the deck plate, the deck plate-bulkhead assembly tend to rotate as a whole. Thus as far as the connection is concerned, the connection is rigid at that particular point but the structure has the freedom to move in a limited manner. ie. , Limited rigidity and limited flexibility 31
- 32. STRUCTURAL BEHAVIOUR In a bulkhead, the stiffener and the plating between stiffeners undergo bending due to lateral load Most of the lateral load initially acts on the plating. Then through plate bending action, plating transmits the lateral load to the stiffeners The bulkhead platings undergo bending due to lateral loads and exhibit buckling due to axial compressive loads. Stiffened plates have high stiffness to weight ratio and high strength to weight ratios. The strength of the plate, as indicated by the yield stress, is proportional to the section modulus of the profile. 32
- 33. LOADS ON BULKHEADS The design lateral pressure on ordinary watertight bulkheads as given in Indian Register of Shipping [2014] Plat = 10 h [kPa] h : the vertical distance from the centre of loading to the top of bulkhead or to the flooded waterline if it is higher. 33 Fig 10 : Lateral pressure acting on a bulkhead
- 34. LOADS ON BULKHEADS Fig 11 : In-plane loads on a bulkhead 34
- 35. LOADS ON BULKHEADS Pressure due to dry cargo, stores and equipment on the deck as per given in given in Indian Register of Shipping [2014] pdeck = q (10 + 5 av) [kN/m2] q : deck cargo load [t/m2] = 1 [t/m2] for weather decks and hatchcovers with cargo loading, in general = 1.6 [t/m2] for platform deck in machinery spaces av : vertical acceleration due to heave and pitch 35
- 36. LOADS ON BULKHEADS Static pressure acting on ship hull [kN/m2] pwater = 10 (1.4 T – z) for z < T = 0 for z ≥ T Where T : draught z : distance from the load centre of the structure to the base line [m] . 36
- 37. LOADS ON BULKHEADS Sloshing forces may be required to be taken into account for bulkheads with partially filled holds or tanks. In the analysis of bulkhead, the static pressure acting on ship hull is usually neglected as it is considerably too small compared to the lateral pressure and deck load acting on the bulkhead. So in the present study, the lateral pressure in a fully flooded condition and the deck load are only considered. As the bulkhead considered is fully flooded sloshing effects are also not considered 37
- 38. BULKHEAD FAILURES Fracture Damage Type - In most cases fractures are found at locations where stress concentration occurs. - If fracture occur under repeated stresses which are below the yielding stress, the fractures are called fatigue fractures. - There are also chances of brittle fracture, which is a catastrophic failure, in which failure ocuurs without prior plastic deformation and at extremely high speeds. Buckling Damage Type - Buckling is caused by excessive compressive and/or shear stresses resulting in out-of-plane deformation. - The buckling strength of a plate depends on the ratio of thickness to stiffener spacing. 38
- 39. BULKHEAD FAILURES - In overall buckling, the stiffeners buckle along with the plating; - in local buckling, either the stiffeners buckle prematurely because of inadequate rigidity or stability, or the plate panels buckle between the stiffeners, thus shedding extra load into the stiffeners Deformation Damage Type - Deformations are often caused by impact loads/contact and inadvertent loading. Damages due to Welding - Weld defects are associated with areas where stress concentrations are significant 39
- 40. BULKHEAD FAILURES - Full penetration welds are to be provided at regions with high stress concentration. - This is because, only full penetration welding can be inspected through the whole thickness by ultrasonic testing. Damages due through Thickness lamellar Tearing - Lamellar tearing is a crack parallel to the rolled surface of steel plates in layers after welding. - high sulphur content will create soft layers which will contribute to lamellar tearing. - So it is important to control the sulphur level of steel. 40
- 41. ANALYSIS OF BULKHEAD CLASSICAL METHOD Watertight bulkhead is a stiffened sheet of plating restrained in some way all round its edges and subjected to water pressure on one side. Let the water pressure at any position be w(x) where w is the weight per unit volume of the fluid and let the stiffener spacing be ‘s’. 41 Fig 12 : Cross section of a bulkhead
- 42. ANALYSIS OF BULKHEAD Then the basic equation for the bending analysis of bulkhead is given by On integration, deflection is given by 42
- 43. ANALYSIS OF BULKHEAD One of the primary failure modes of stiffened panels is the buckling and plastic collapse of the plates surrounded by support members. thus an evaluation of the buckling and plastic collapse behaviour of plates is essential to identify the failure of ship structures. Structural strength analysis may be based on linear elastic theory. Lateral pressures have effects on the buckling strength of stiffeners, so they are considered in the stiffener buckling strength assessment. 43
- 44. ANALYSIS OF BULKHEAD Plate behaviour always involves a large degree of deflection (geometric nonlinearity) and/or plasticity (material nonlinearity) before and after the ultimate strength has been reached. Plate behaviour depends on a variety of influential factors, namely the plate’s geometric and material properties, loading characteristics, boundary conditions, etc. TYPES OF ANALYSIS Linear Elastic Analysis Linear Buckling Analysis Non-linear Analysis 44
- 45. ANALYSIS OF BULKHEAD In the present study linear static analysis of bulkhead subjected to both lateral pressure and in-plane compressive deck load is conducted. The analysis is concerned with the linear behaviour of elastic continnum under prescribed boundary conditions and statically applied loads. Linear static analysis can be used to find the displacements, stresses etc. 45
- 46. MODELLING OF BULKHEAD Bulkheads are idealized as stiffened plates, generally stiffened in a grillage form i.e. the stiffeners run along both the directions. For the numerical analysis and simulation, the finite element analysis software - Abaqus is used. 4 noded quadrilateral plate-shell elements are used to model the plate and stiffeners. Bulkheads are modelled as plate stiffened using angle stiffeners, flat bars and T- stiffeners 46
- 47. MODELLING OF BULKHEAD represents a transverse bulkhead along with the adjoining longitudinal bulkheads, transverse bulkheads, bottom shell and deck plating. 47 Fig 13 : Meshed model of a bulkhead
- 48. MODELLING OF BULKHEAD ELEMENT DESCRIPTION Bulkheads are modelled using Abaqus by selecting a suitable element from Abaqus/Standard shell element library Triangular and quadrilateral elements with linear interpolation are used. In the present study, S4R and S3 elements are used to mesh the bulkhead model. bulkhead was meshed using 69193 elements of which 66474 are S4R elements and 2719 are S3 elements. 48
- 49. MODELLING OF BULKHEAD ELEMENT DESCRIPTION S3 elements are 3-noded triangular general purpose shell element with a finite membrane strain formulations. These elements have six degrees of freedom per node. Provides accurate results in most loading situations S4R element is a shear flexible, isoparametric quadrilateral shell with four nodes. These elements have six degrees of freedom per node. 49
- 50. FINITE ELEMENT RESULTS AND DISCUSSIONS The variation in the deflection of a bulkhead, by varying the boundary condition and the geometry of the stiffeners is studied. Simply supported, fixed and a condition which is partially fixed and simply supported is considered in the study. The geometry of the stiffeners used is shown in the Fig 6.1 below. 50 Fig 14 : Geometry of Stiffener
- 51. FINITE ELEMENT RESULTS AND DISCUSSIONS EFFECT OF GEOMETRY OF THE STIFFENERS AND BOUNDARY CONDITION Lateral load(triangular loading) with peak value of 150kPa and in-plane load (compressive loading) of 32kPa are applied in the model for the analysis. The maximum deflection values are as below 51 Type of Stiffener Fixed Partially fixed and Simply Supported Simply Supported Angle bar 1.708 x 10-02 4.745x10-02 1.712x10-0.2 Flat bar 4.717x10-02 6.285x10-02 4.743x10-02 T- Stiffener 1.794x10-02 1.911x10-02 1.796x10-02
- 52. FINITE ELEMENT RESULTS AND DISCUSSIONS 52 Fig 15 : Abaqus result for deflection in a bulkhead
- 53. FINITE ELEMENT RESULTS AND DISCUSSIONS The actual boundary being neither fixed nor simply supported, a condition which is partially fixed and partially simply supported is considered to be a more appropriate boundary condition. And in the analysis, the result obtained is such that, this boundary condition gives more deflection than the fixed and simply supported conditions. 53
- 54. FINITE ELEMENT RESULTS AND DISCUSSIONS EFFECT OF IN-PLANE LOAD ON A LATERALLY LOADED BULKHEAD Lateral loaded bulkhead is considered and the in-plane load is varied. 54 Fig 16 : Abaqus result for stress variation in a bulkhead
- 55. FINITE ELEMENT RESULTS AND DISCUSSIONS EFFECT OF IN-PLANE LOAD ON A LATERALLY LOADED BULKHEAD Case 1 55 0 100 200 300 400 500 600 700 800 0 20 40 60 80 100 120 140 160 Stress (MPa) Load (kPa) angle bar T- stiffener flat bar Fig 17 : Graph showing variation of stress (in x direction) - case1
- 56. FINITE ELEMENT RESULTS AND DISCUSSIONS EFFECT OF IN-PLANE LOAD ON A LATERALLY LOADED BULKHEAD Case 1 56 Fig 18: Graph showing variation of stress (in y direction) - case1 0 100 200 300 400 500 600 700 800 0 20 40 60 80 100 120 140 160 Stress (MPa) Load (kPa) angle bar T- stiffener flat bar
- 57. FINITE ELEMENT RESULTS AND DISCUSSIONS EFFECT OF IN-PLANE LOAD ON A LATERALLY LOADED BULKHEAD Case 1 57 Fig 19: Graph showing variation of deflection- case1 0 10 20 30 40 50 60 70 0 20 40 60 80 100 120 140 160 Deflection (mm) Load (kPa) angle bar T- stiffener flat bar
- 58. FINITE ELEMENT RESULTS AND DISCUSSIONS EFFECT OF IN-PLANE LOAD ON A LATERALLY LOADED BULKHEAD Case 1 It is clear that for a particular of in-plane load, the stress and the deflection in the bulkhead is less when stiffened using T-stiffeners. But, for the stiffener size chosen in this case, the thickness of the plate is too large which cannot be practical in the actual case. So a study by varying the dimensions of the stiffeners is conducted so that the thickness can be made within feasible limits. 58
- 59. FINITE ELEMENT RESULTS AND DISCUSSIONS EFFECT OF IN-PLANE LOAD ON A LATERALLY LOADED BULKHEAD Case 2 59 Fig 20 : Geometry of Stiffener for case 2
- 60. FINITE ELEMENT RESULTS AND DISCUSSIONS EFFECT OF IN-PLANE LOAD ON A LATERALLY LOADED BULKHEAD Case 2 60 Fig 21: Graph showing variation of stress (in x direction) - case1 0 50 100 150 200 250 300 350 400 450 0 20 40 60 80 100 120 140 160 Stress (MPa) Load (kPa) angle bar T- stiffener flat bar
- 61. FINITE ELEMENT RESULTS AND DISCUSSIONS EFFECT OF IN-PLANE LOAD ON A LATERALLY LOADED BULKHEAD Case 2 61 Fig 22: Graph showing variation stress (in y direction) - case2 0 100 200 300 400 500 600 0 20 40 60 80 100 120 140 160 Stress (MPa) Load (kPa) angle bar T- stiffener flat bar
- 62. FINITE ELEMENT RESULTS AND DISCUSSIONS EFFECT OF IN-PLANE LOAD ON A LATERALLY LOADED BULKHEAD Case 2 It is clear that for a particular in-plane load , the stress and deflection in bulkhead stiffened using flat bar stiffeners is the least. 62 Fig 23: Graph showing variation of deflection - case2 0 5 10 15 20 25 0 20 40 60 80 100 120 140 160 Deflection (mm) Load (kPa) angle bar T- stiffener flat bar
- 63. CONCLUSIONS Bulkhead with a boundary condition which is much closer to the condition that exist in reality (which is neither simply supported nor fixed) was modelled. There is more deflection in this special boundary case compared to the other two boundary conditions. The effect of in-plane load on a laterally loaded bulkhead was studied by varying the in-plane load and also the stiffener geometry. For the stiffener sizes chosen in the first case, T- stiffened bulkhead showed better load carrying capacity. But as the thickness required is too large for this stiffener size, the dimensions of the stiffeners are altered. 63
- 64. CONCLUSIONS For the stiffener dimensions chosen in the case 2, bulkhead stiffened using flat bar showed good results. This may be because, in the case 2, the thickness of the whole structure is reduced and the stiffeners becomes more slender. Due to this, local buckling effect comes into play, which is absent in case 2, as web thickness is too large. Considering the material volume, the case2 requires only nearly half the amount of the volume as required in case 1 and gives a better load carrying capacity. overall performance of the bulkhead is greatly dependent on the stiffener geometries chosen. 64
- 65. REFERENCES 1. Bhaskar K., Anup Pydah, “An elasticity approach for simply-supported isotropic and orthotropic stiffened plates”, International Journal of Mechanical Sciences, Volume 89, 2014, PP No. 21-30 2. Chikalthankar S.B., I.I.Sayyad, V.M.Nandedkar, “Analysis of Orthotropic Plate By Refined Plate Theory”, International Journal of Engineering and Advanced Technology, Volume-2, Issue-6, August 2013. 3. Deepak Kumar Singh, S K Duggal, P Pal, “Analysis of Stiffened Plates using FEM – A Parametric Study”, International Research Journal of Engineering and Technology, Volume: 02, Issue: 04, July-2015. 4. Eyres D.J., “Ship Construction”, Elsevier, 2007, PP No.191 5. Ivo Senjanovi´c, Stipe Tomaˇsevi´c, Smiljko Rudan, Tanja Senjanovi´c, “Role of transverse bulkheads in hull stiffness of large container ships”, Engineering Structures, Volume 30, 24 March 2008, PP No. 2492-2509 65
- 66. REFERENCES 6. Ji H.D., Cui W.C., Zhang S.K., “Ultimate strength analysis of corrugated bulkheads considering influence of shear force and adjoining structures”, Journal of Constructional Steel Research, Volume 57, 2001, PP No. 525-545 7. John P. Comstock, “Principles of Naval Architecture”, The Society of Naval Architects and Marine Engineers, 1967, PP No. 224 8. Owen F. Hughes and Jeom Kee Paik, “Ship Structural Analysis And Design”, The Society of Naval Architects and Marine Engineers, 2010. 9. Shanmugam N.E,Zhu Dongqi, Y.S.Choo, M.Arockiaswamy, “Experimental studies on stiffened plates under in-plane load and lateral pressure”, Thin- Walled Structures, Volume 80, 2014, PP No. 22-31 10. Timoshenko S. , Woinowsky-Krieger, “Theory of Plates and Shells”, McGraw- Hill, 1959, PP No. 120 66