Analysis of Pressure Hull

Analysis of Pressure Hull

Unit: Structural Application of Finite Elements (ENG781s1)

ReportOn Pressure Hull Enclosure for Sonar Equipment - Buckling and Vibration Predictions

Pressure Hull Enclosure for Sonar Equipment - Buckling and Vibration PredictionsPressure hulls are the main load bearing structures of naval submarines, commercial and research submersibles, and autonomous underwater vehicles (AUVs). Pressure hulls are closely related to many structures in the offshore oil and gas industry that withstand hydrostatic pressure, and axially-compressed shell structures used in the aerospace industry. The many similarities between pressure hull, offshore, aerospace and some civil engineering structures mean that advances in one group are often applicable to the others, and thus this document is sometimes concerned with the entire collection of thin-walled curved structures designed for instability, referred to hereafter as buckling-critical shells.A Pressure Hull is inside the outer hull. It withstands the outside pressure and has normal atmospheric pressure inside. High strength steel is used to construct a Pressure Hull. Weight is an Important Performance parameter and lowers the weight, better is the performance. Steel is generally used in constructing the Pressure Hull. But Pressure hulls made of steel are bulky. The use of composite materials such Carbon Fiber Composite improves the performance of the Hull and offers a significant amount of material savings. The hull should withstand the pressure that is exerted on it when it is submerged. Buckling is one of the major reasons of failure of such Hulls. Generally Stiffeners are added to the hull to increase its strength.Since it carries Sonar equipment the pressure hull needs to be designed taking in to account the vibration response of the structure. In this Project we have carried out a design study of Pressure Hull that houses Sonar equipment for sub-sea application. A pressure Hull has been designed and its performance has been analyzed for different materials cases. Firstly, a Steel Pressure Hull is considered and then it is analyzed for buckling strength at 150m its Vibration response in air and Weight of the Hull. Secondly Carbon fiber composite Pressure Hull is considered and then it is analyzed for buckling strength at 150m, its Vibration response in air and Weight of the Hull.

The aim for reducing cost, time, and effort applied in the manufacturing process has taken the companies to virtually create their products for testing them even before producing a single unit. Nowadays the manufacture process for the pressure hulls is done by the use of CNC techniques and processes, creating each part separately and assembling them by using hundreds of screws and fasteners. Simulation software such a SolidWorks and ANSYS help to evaluate a design from different aspects and tell the user whether to make changes or not, where a failure may occur and many other features. The virtual assessment must be performed by a person able to read and understand the complexity of the results and apply modifications avoiding reprocesses and wasted time, otherwise, the product would give negative results in the practice. Attention to the process temperature, vibration, motion and precise variables will give more accurate and reliable results, while ignoring details that can seem insignificant can yield completely wrong answers

Doing a vibration analysis for a device is highly essential to prevent it failing while operations. The vibrations a product may experience can reduce performance, shorten product life, or even cause a catastrophic failure. The effects of vibrations, which are simply time-varying or transient loads on your product, are difficult to predict:

Vibration loads can excite dynamic responses in a structure resulting in high dynamic stresses. Ignoring dynamic stresses could lead to assume that a product or structure has a higher factor of safety (FoS) than it actually does. Therefore using the vibration analysis natural frequencies and their relevant mode shapes were found.

There are two major categories leading to the sudden failure of a mechanical component: material failure and structural instability, which is often called buckling.For material failures you need to consider the yield stress for ductile materials and the ultimate stress for brittle materials.

Those material properties are determined by axial tension tests and axial compression tests of short columns of the material. Predicting material failure may be accomplished using linear finite element analysis. That is, by solving a linear algebraic system for the unknown displacements, K= F.The strains and corresponding stresses obtained from this analysis are compared to design stress (or strain) allowable everywhere within the component. If the finite element solution indicates regions where these allowable are exceeded, it is assumed that material failure has occurred.The load at which buckling occurs depends on the stiffness of a component, not upon the strength of its materials.Buckling refers to the loss of stability of a component and is usually independent of material strength. This loss of stability usually occurs within the elastic range of the material.The two phenomenon are governed by different differential equations.

Problem Matrix

Case ICase II

ParameterSteelCarbon fiber composite

1Buckling modes.YesYes

2Vibration response.YesYes

3Estimate of the mass of Pressure Hull designs.YesYes

Development and Justification of finite element model for Cylinder (Main Body) and Hemispherical Ends:Design of Pressure Hull Dimensions is Present in Annexure I. Based on these dimensions a Finite Element model (FE-Model) is generated. The FE model is made of SHELL281 and BEAM188 element Types. SHELL 281 is used to model the cylinder while BEAM188 is used for modeling the Ring Stiffeners. The details of the element spacing are explained in Annexure I.There is a single Geometry Model and Two FE-models due to two different materials. Case IFE-Model ISteel Isotropic material

Case IIFE-Model IICarbon Fiber CompositeOrthotropic material

Steel has Isotropic Properties and a corresponding Isotropic Material Model has been used for FEA analysis. Please Refer the Material Property data for steel in Annexure IIIThe Carbon Fiber Composite has orthotropic properties and a corresponding orthotropic Material Model has been used for FEA analysis. Please Refer the Material Property data for Carbon Fiber Composite in Annexure IV.The given depth of operation for the Hull is 150m. The pressure at this depth acting on the Pressure Hull is calculated. The method for Calculation is described in Annexure II.The Created FE-model is validated. A section of the hull with no stiffeners is taken the material properties of steel and the pressure is applied. The value calculated by FEA and by using hand calculations is compared. The method described in Annexure V. This Validated model has been used for all the further calculations. The nodal diameter is 5. Hence the FE model also has a nodal distance of 5.

Case I: Development and Justification of finite element model for Steel Hull (Isotropic):Buckling Analysis:At the depth of 150 m the pressure acting on the steel hull is 14.7 N/mm2. This value of pressure is applied on the entire body. The material model is Isotropic as described in Annexure III. The Hull is constrained at the ends. First a static analysis is run and after that an Eigen Value buckling analysis is done.The Results and detailed processing are described in Annexure VI. The Buckling factor is 1.48 as per FEA. Vibration Response:The hull has been constrained at its ends. A modal Analysis has been carried out. The frequency of the structure is 83.98 Hz. The detailed post processing is shown in Annexure VI.Mass of the Structure: The mass of structure is about 1.5387 kg. This confirms with the hand calculations done. This is another check for model Validation. Refer Annexure IIIHand Calculations

Steel Density =7850 kg/m3Volume Weight

Cylinder (main Body)0.000125664 m30.98646

Hemispherical Caps6.28402E-05 m30.493296

Stiffener 7.5 E-06 m30.0589

Total Weight 1.5 kg

Case II: Development and Justification of finite element model for Carbon Fiber Composite (Orthotropic):Buckling Analysis:At the depth of 150 m the pressure acting on the steel hull is 14.7 N/mm2. This value of pressure is applied on the entire body. The material model is Orthotropic as described in Annexure IV. The Hull is constrained at the ends. First a static analysis is run and after that an Eigen Value buckling analysis is done.The Results and detailed processing are described in Annexure VII. The Buckling factor is -2.35 as per FEA. Vibration Response:The hull has been constrained at its ends. A modal Analysis has been carried out. The frequency of the structure is 191.69 Hz. The detailed post processing is shown in Annexure VIIMass of the Structure: The mass of structure is about 0.392 kg as per FEA. This confirms with the hand calculations done. This is another check for model Validation. Refer Annexure IV.Hand Calculations

Carbon Fiber Composite Density =2000 kg/m3Volume Weight

Cylinder (main Body)0.000125664 m30.251327

Hemispherical Caps6.28402E-05 m30.125680461

Stiffener 7.5 E-06 m30.015

Total Weight 0.39 kg

Design ProposalThe FEA analysis of Steel and Carbon fiber composite for buckling reveals followingTypeDepthPressureBuckling FactorInterpretation

SteelMass = 1.5387 kg150m14.8 N/mm21.48

Applied Loads are less than estimated critical loads, hence buckling is not predicted at the depth of 150 m for a steel Hull.

Carbon Fiber CompositeMass = 0.392 kg150m14.8 N/mm2-2.35Load factor is negative; Buckling is not Predicted, even if all loads are reversed, at the depth of 150 m for a Carbon Fiber Composite.

The FEA analysis of Steel and Carbon fiber composite for Vibration reveals followingTypeFrequencyInterpretation

SteelMass = 1.5387 kg83.98 HzThe first mode for Steel is 83.98 Hz

Carbon Fiber CompositeMass = 0.392 kg191.69 HzThe first mode for Carbon Fiber Composite is191.69 Hz

So based on the careful observations following can be proposed about the designs1. The steel hull is 3.5 times heavier than the carbon composite hull. This can be expected as the density of steel is 3.5 times the carbon composite. 2. The Buckling factor for steel Hull is 1.48 for the depth of 150m. The Steel Hull is away from buckling. But the carbon composite factor is -2.3, which means that buckling is not even predicted at this depth.3. The Vibration Frequency response of steel structure is 83.98 Hz and for Carbon composite is 191.69 Hz. That means Carbon composite vibrates at 43% higher frequency than steel.4. Based on the Overall analyses of both the structures it can be said that Carbon composite Pressure hull is Preferred as it offers a serious advantage of weight among other parameters of buckling strength and Vibration response.

1Annexure I Geometry

2Annexure II Pressure Calculation

3Annexure III Case I, Steel Isotropic, Mass of steel model

4Annexure IVCase II, Carbon fiber composite , Mass of model

5Annexure VValidation

6Annexure VI Steel Buckling and Vibration Analysis and Post Processing

7Annexure VIICarbon fiber composite Buckling and Vibration Analysis and Post Processing

Annexure IThere was a choice of choosing the end of the cylinder. Following is the brief review of heads available.Ellipsoidal Head, Hemispherical Head and Tori-spherical Head are three types of ASME Pressure vessel Dished Heads. Hemispherical head is the ideal shape for a head, because the pressure in the vessel is divided equally across the surface of the head. The radius (R) of the head equals the radius of the cylindrical part of the Hull.Length of the cylindrical part is 200mm. The radius of the cylinder and the hemispherical ends is 50mm. There are three stiffener rings attached at the central part at a distance of 50mm from each other. The wall Thickness is 2mm.

GeometryDescription:1. Total Length=300mm2. Cylinder Diameter=100mm3. Hemispherical CAP Radius=50mm

Annexure II

Pressure Calculations P= Pa+*g*hP=Pressure acting on the submerged body

Pa=1.013E5Pa(N/m2)Atmospheric Pressure

=1000Kg/m3Density of fluid (water)

g=9.81m/s2Gravity

h=1500mDepth under fluid.

P=1.48E+07Pa(N/m2)This is the Pressure acting on Hull.

Annexure IIICase I

Steel Pressure HullDesign / FEA RationaleIsotropic

Material Property DataValue

1Youngs Modulus200GPa

2Poisson Ratio0.3

3Density 7850 kg/m3

Element Property DataValue

1End and Cylinder partSHELL281

2Ring-Stiffeners modeled BEAM188

3Beam DataB = 4 H = 2 and Remarks: Y offset to 3 for Actual modeling of real conditions.

GeometryDescription:4. Total Length=300mm5. Cylinder Diameter=100mm6. Hemispherical CAP Radius=50mm

MeshDescription:1. Nodal Distance = 52. 32 elements around the perimeter3. 3 Rings of 32 beam element

Mass of modelTotal Mass of Model= 1.5387 kg

.Element TYPE 1 = SHELL281-----Pressure HullElement TYPE 2= BEAM188------Ring Stiffners

Annexure IVCase II

Carbon Fiber Composite HullDesign / FEA RationaleCarbon Fiber Composite Material Property DataOrthotropic

Density= 2000 kg/m3

Element Property DataValue

End and Cylinder partSHELL281

Ring-Stiffeners modeled BEAM188

Beam DataB = 4 H = 2 and Remarks: Y offset to 3 for Actual modeling of real conditions.

GeometryDescription:7. Total Length=300mm8. Cylinder Diameter=100mm9. Hemispherical CAP Radius=50mm

MeshDescription:4. Nodal Distance = 55. 32 elements around the perimeter6. 3 Rings of 32 beam element

Mass of modelTotal Mass of Model= 0.392 kg .Element TYPE 1 = SHELL281-----Pressure HullElement TYPE 2= BEAM188------Ring Stiffeners

Annexure VValidation Methodology

The following equation by Donell* describes a cylindrical shell which is supported at its ends and subjected to uniform external pressure Pc.

Where,Pe =Pcr=critical buckling load in N/m2,A=radius of cylinder in m,E=young's modulus of cylinder material N/m2,L=longitudinal length of cylinder m,h=thickness in m,n= nodal distance *DON.O.BRUSH &BO.O.ALMROTH:-buckling of bars, plates and shells

Pcr9.3E+07N/m2Taking n=5

Pcr93N/mm2

Validation Methodology

Calibration Model

Description:1. A section of Pressure Hull is taken without Stiffeners.2. n=5 3. Boundary condition and Pressure are applied.

Validation Methodology

Validation Model

Boundary Condition and Pressure AppliedDescription:Read Arrows describe the Pressure and DOF is on the end.

Results Comparison

Results Comparison

MethodValue

FEA88 N/mm2

Donell relation93 N/mm2

Error of 5%

An Validated Model with Node spacing of 5 has been used to perform all the Analysis

Annexure VI

Steel Pressure HullBuckling Analysis

Factor =1.48

Steel Pressure HullVibration Analysis

FREQUENCY=83.98 Hz

Annexure VIICarbon Fiber Composite HullBuckling Analysis

FACTOR=-2.35

Carbon Fiber Composite HullVibration Analysis

FREQUENCY=191.69 Hz

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