FEM MidShip Project Report

Structural Analysis of Midship Section of General Cargo Ship

NAME 6098 FINITE ELEMENT METHODS TERM PROJECT

RAJESH KOPPARTHI AVINASH KARRI

NAME # 6098 Term Project

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Structural Analysis of Midship Section of General Cargo Ship TABLE OF CONTENTS 1. INTRODUCTION.................................................................................................. 3 2. METHODOLOGY ................................................................................................ 5 3. DESIGN REQUIREMENTS................................................................................. 6 3.1 Design Criteria ............................................................................................................................6 3.2 Design Loads................................................................................................................................6 3.3 Materials.......................................................................................................................................6 3.4 Geometrical Properties of the Model...........................................................................................7 3.5 Element Type...............................................................................................................................7 3.6 Finite Element Model...................................................................................................................8 3.7 Boundary Conditions..................................................................................................................10

4. STRENGTH ANALYSIS.....................................................................................12 4.1 Loading Condition # 1..............................................................................................................12 4.2 Loading Condition # 2..............................................................................................................14 4.3 Loading Condition # 3..............................................................................................................15 4.4 Loading Condition # 4…………..............................................................................................16 4.5 Loading Condition # 5..............................................................................................................17 4.6 Loading Condition # 6..............................................................................................................18 4.7 Loading Condition # 7..............................................................................................................19 4.8 Summary of Results…..............................................................................................................19

5. REFERENCES…............................................................................................... 20 6. APPENDIX……….............................................................................................. 21


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Structural Analysis of Midship Section of General Cargo Ship STRUCTURAL ANALYSIS OF MIDSHIP SECTION OF A GENERAL CARGO SHIP 1. INTRODUCTION: Structural analysis comprises the set of physical laws and mathematics required to study and predicts the behavior of structures. The subjects of structural analysis are engineering artifacts whose integrity is judged largely based upon their ability to withstand loads; they commonly include buildings, bridges, aircraft, and ships. Structural analysis incorporates the fields of mechanics and dynamics as well as the many failure theories. From a theoretical perspective the primary goal of structural analysis is the computation of deformations, internal forces, and stresses. To perform an accurate analysis a structural engineer must determine such information as structural loads, geometry, support conditions, and materials properties. The results of such an analysis typically include support reactions, stresses and displacements. This information is then compared to criteria that indicate the conditions of failure. There are three approaches to the analysis: the mechanics of materials approach (also known as strength of materials), the elasticity theory approach (which is actually a special case of the more general field of continuum mechanics), and the finite element approach. The first two make use of analytical formulations which apply mostly to simple linear elastic models, lead to closed-form solutions, and can often be solved by hand. The finite element approach is actually a numerical method for solving differential equations generated by theories of mechanics such as elasticity theory and strength of materials. The finite element method is perhaps the most restrictive and most useful at the same time. This method itself relies upon other structural theories (such as the other two discussed here) for equations to solve. It does, however, make it generally possible to solve these equations, even with highly complex geometry and loading conditions, with the restriction that there is always some numerical error. Effective and reliable use of this method requires a solid understanding of its limitations. The finite element method approximates a structure as an assembly of elements or components with various forms of connection between them. Thus, a continuous system such as a plate or shell is modeled as a discrete system with a finite number of elements interconnected at finite number of nodes. The behavior of individual elements is characterized by the element's stiffness or flexibility relation, which altogether leads to the system's stiffness or flexibility relation. NAME # 6098 Term Project

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Structural Analysis of Midship Section of General Cargo Ship This report presents the details of Static Strength Analysis done to the Midship Section of a General Cargo Carrier using ABAQUS. The design of Midship Section is considered according to the ABS Rules which are shown in the Appendix. Static Strength analysis is performed to ensure the stress levels in the structure are within allowable limits as per ABS Rules and AISC 9th Edition.

Vessel Specifications: The vessel which is considered is General Cargo Carrier with the following dimensions: Frame spacing = 1 m (spacing of transverse or longitudinal frames) Length = 105 m (length of vessel) Length of the midship section considered = 18 m Half Breadth of the vessel = 13 m Draft = 10 m (molded draft) Depth = 15 m (molded depth)


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Structural Analysis of Midship Section of General Cargo Ship 2. METHODOLOGY: A 3-D comprehensive finite element model is created in ABAQUS using shell S4 plate elements. For this purpose, the complete hull bottom, top and side shell top plating with transverse and longitudinal stiffeners and frames have been considered in the analytical model. The model used was of the hull structure for the Midship Section. Seven load combinations were used for analysis. Loading Conditions were taken by the combination of different loads on the structure like Hydrostatic pressure, Deck Load and Cargo Load. The material yield stresses and the allowable stresses are described in Section 3. It will be checked for maximum Von Misses stresses to ensure it’s less than Fy/1.45, where 1.45 is the Safety Factor. The maximum unity ratio for the plate and support beams should not exceed 1.0. The structural analysis and design reported in this document comply with the ABS Rules for Steel Vessels (2006) and AISC-ASD (9thedition). Units used are Pressures in Mpa (Mega Pascal) and dimensions in mm for ABAQUS model.


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Structural Analysis of Midship Section of General Cargo Ship 3. DESIGN REQUIREMENTS: The design criteria and load conditions are described in the following sub-sections. 3.1 Design Criteria: The Structure has been designed in accordance with the applicable design criteria of the ABS Rules for Steel Vessels and the AISC-ASD (9th Edition). 3.2 Design Loads: When considering how our model should be loaded, the first step is to consult the classification society rules. They all have very good sections dedicated to calculating the loads expected for various locations on the ship. Following are the various loads considered according to the ABS Steel Rules.

S No 1 2 3 4 5

Load Hydrostatic Pressure Hydrostatic Pressure Deck Load Cargo Load Cargo Load

6

Water Ballast

Location Bottom Shell Side Shell Main Deck Tween Deck Tank Top Double Bottom

Magnitude (Mpa or N/mm2) 0.01 0.0075 0.005 0.0075 0.01

Type of Load External External Internal Internal Internal

0.002

Internal

Once we have decided on which values to use, applying them to the model is quite straightforward. Simply select the member to be loaded, assign the load value and select the orientation of the load. 3.3 Materials: The material generally used in the construction of ships is steel. So the material constants for steel are used. It is assumed that the steel does not go into the non linear state and we stay in the elastic range. Further it is an isotropic material. All steel is assumed to have minimum yield strength of 355 N/mm2 (=51 ksi) and Poison’s Ratio of 0.3. The allowable stress is determined from ABS Steel Rules, AISC and API RP 2A which is given as Allowable Von Misses = Fy / 1.45, Where safety factor = 1.45 NAME # 6098 Term Project

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Structural Analysis of Midship Section of General Cargo Ship 3.4 Geometric Properties of the Model: Only quarter of the midship section is used for analysis as it is symmetric in Longitudinal and Transverse directions. Before running the analysis, we ensured that all of the structural members are connected by common nodes. Two lines that intersect may look graphically as if they are intersecting and connected, but if they don’t share a common node, then they will not be mathematically connected. This is of vital importance for FEA models. Length of the Section = 18 m (Modeled as 9 m taking symmetry in Z direction) Breadth of the Section = 26 m (Modeled as 13 m taking symmetry in X direction) Depth of the Section = 15 m Thickness of the Main Deck and Tween Deck plate = 12 mm Thickness of the Tank top plate = 12 mm Thickness of the Bottom Shell Plate = 16 mm Section of the Stiffener = L 150x100x10 Beam Section = T 600x8+200x12 Section of the Girder = T 600x8+200x12 3.5 Element Type: Since thin structures can be modeled efficiently as shells, we'll use shell elements (S4) to build the finite-element model. Shell elements can support membrane and bending loads consistent with classical shell theory. Shell elements are appropriate when the thickness of the structure is small compared to the other dimensions.


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Structural Analysis of Midship Section of General Cargo Ship 3.6 Finite Element Model:

View 1


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View 2


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View 3

3.7 Boundary Conditions: Many designers find the application of boundary conditions quite daunting but be assured that it is very simple. All you have to do is consider how the structure will be restrained and constrain the degrees of freedom to make the model behave in a realistic manner. There are only six degrees of freedom to consider, 3 translation (tx,ty,tz) and three rotation, - the rotation about each axis (rx,ry,rz). One type of boundary condition to consider is the symmetric boundary condition. If we could model quarter of our structure and get an accurate result using symmetrical boundary conditions, we can size quarter of the model and significantly reduce the time to build and solve it. So for the 9m x 13m x 15 m model, symmetrical boundary conditions are given in X and Z directions so that it represents the full Compartment of 18 m x26m x 15m size.


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Structural Analysis of Midship Section of General Cargo Ship As there will be a Transverse Bulkhead at the end of the compartment, the model is fixed at the end in Longitudinal Direction. A transverse floor is considered at the mid of the compartment. So the double bottom is restrained in vertical (Y) direction at the mid of the Compartment (at end of the Model in Long direction towards symmetrical side). Pillars (Three in Long and Two in Tran directions which makes total of 5) are considered to support the loading on Decks and Stiffeners. As Pillars are not modelled as structure, it is taken as boundary condition which restrains the portion, where pillar connects the deck, in vertical direction. Also, the model is restrained in the Longitudinal direction (Z – axis).

Model with Loads and Boundary Conditions NAME # 6098 Term Project

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Structural Analysis of Midship Section of General Cargo Ship 4. STRENGTH ANALYSIS: Static strength analysis of the structure was performed using ABAQUS. The following plots are of the finite element results, there were a total of 7 conditions run as follows. S No 1 2 3 4 5 6 7

Loading Conditions Lightship LS + Ballast LS + MD LS + Ballast + MD 80 % cargo load 100% cargo without Ballast Full Loading

Main Deck x x x x x

Tween Deck Tank Top x x x

x x

DB x x x

Hydrostatic x x x x x

x

x x

To pass the strength Check, unity ratio at the critical location must be less than or equal to 1.0. Unity Ratio = (Von misses Stress * 1.45) / Fy Where Yield Strenth, Fy = 355 N/mm2 4.1 Loading Condition # 1:


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As there is only Hydrostatic Pressure, side shell and Bottom shell are bulged inwards.

LC No 1

Max Von misses Stress (Mpa) 117.7


Unity Ratio Strength Check 0.480746479 Ok

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Structural Analysis of Midship Section of General Cargo Ship 4.2 Loading Condition # 2:

LC No 2



Unity Ratio 0.47584507

Strength Check Ok

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LC No 3




Strength Check Ok

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LC No 4




Strength Check Ok

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LC No 5




Strength Check Ok

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4.6 Loading Condition # 6:

LC No 6




Strength Check Ok

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LC No 7



Strength Check Ok

Unity Ratio 0.480746479 0.47584507 0.485647887 0.480746479 0.472985915 0.548140845 0.547732394

Strength Check Ok Ok Ok Ok Ok Ok Ok

4.8 Summary of Results: LC No 1 2 3 4 5 6 7

Max Von misses Stress (Mpa) 117.7 116.5 118.9 117.7 115.8 134.2 134.1

Though the Structure passes the Strength check, it deflects more which is not feasible design. So, more local stiffening is to be done to reduce the deformation of the structure. NAME # 6098 Term Project

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Structural Analysis of Midship Section of General Cargo Ship 5. REFERENCES

1. NAME # 6098 Lecture Handouts by Dr. Pingsha Dong 2. ABS Rules for Steel Vessels 2006 3. AISC – Allowable Stress Design, 9th Edition


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6. APPENDIX ABS REGULATIONS FOR MINIMUM THICKNESS: We examined ABS Rules for Building and Classing Steel Vessel 2007 to find requirements that would apply to the bottom, side shell and deck plating, stiffeners design for the vessel. We made the assumption that our designed plate will have thickness greater than the minimum requirements of the specified ABS requirements below. An additional requirement is a 15:1 (approximately) ratio for the stiffener length to width/depth dimensions. This requirement was made based on the application of the stiffened plate. In this problem we are considering the length to depth as 11 (approximately) 3.9 Side Shell Plating The minimum thickness, t, of the side shell plating throughout the amidship 0.4L, for vessels having lengths not exceeding 427 m (1400 ft), is to be obtained from the following equation: t = ( s/645 ) (L − 15.2)(d / Ds ) + 2.5 mm for L ≤ 305 m where, s = spacing of transverse frames or longitudinals, in mm L = length of vessel, as defined in 3-1-1/3.1, in m d = molded draft, as defined in 3-1-1/9, in m Ds = molded depth, in m 3.13.2 Bottom Shell Plating

The thickness, t, of the bottom plating amidships is not to be less than obtained from the following equations or the thickness determined by 3-2-2/3.17, whichever is greater. 3.13.2(a) For Vessels with Transversely-framed Bottoms t = ( s/519 ) L − 19.8)(d / Ds ) + 2.5 mm for L ≤ 183 m 3.13.2(b) For Vessels with Longitudinally-framed Bottoms t = ( s/671 ) (L −18.3)(d / Ds ) + 2.5 mm for L ≤ 122 m Strength Deck Outside Line of Openings With Transverse Beams 1a and 1b (note 1) t = 0.01sb + 2.3 mm for sb ≤ 760 mm t = 0.0066sb + 4.9 mm for sb > 760 mm Reference: ABS Rules for Steel Vessels 3-2-2 3.12 Page 69 NAME # 6098 Term Project

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FEM MidShip Project Report

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