STATIC,LINEAR AND FINITE ELEMENT ANALYSIS OF PRESSURE VESSEL
Volume III, Issue IV, April 2014IJLTEMASISSN 2278 - 2540Static, Linear and Finite Element Analysis of PressureVesselProf. Vishal V. SaidpatilProf. V.K.KulloliAssistant ProfessorMechanical Engineering DepartmentNBNSSOE, Pune.Vishal.saidpatil@sinhdad.eduAssistant ProfessorMechanical Engineering DepartmentNBNSSOE, Pune.Abstract— ‘Finite Element Method’ is a mathematicaltechnique used to carry out the stress analysis. In thismethod the solid model of the component is subdividedinto smaller elements. Constraints and loads are appliedto the model at specified locations. Various propertiesare assigned to the A pressure vessel is a closedcontainerdesignedtoholdgasesorliquids at a pressure different from the ambientpressure. The end caps fitted to the cylindrical body arecalled heads. The aim of this project is to carry outdetailed design & analysis of Pressure vessel used inboiler for optimum thickness, temperature distributionand dynamic behavior using Finite element analysissoftware.model like material, thickness, etc. The modelis then analyzed in FE solver. The results are plotted inthe post processor. Paper involves design of acylindrical pressure vessel to sustain 5 bar pressure anddetermine the wall thickness required for the vessel tolimit the maximum shear stress. Geometrical and finiteelement model of Pressure vessel is created using CADCAE tools. Geometrical model is created on CatiaV5R19 and finite element modeling is done usingHypermesh. Ansys is used as a solver. Ansys APDLprogramming is used for number of simulation in linearstatic, modal and thermal analysis.1. INTRODUCTIONA. General Informationpressure vessel is a closed container designed tohold gases or liquids at a pressure different fromthe ambient pressure. The end caps fitted to thecylindricalbodyarecalledheads.Pressure vessels are used in a variety ofapplications. These include the industry and theprivate sector. They appear in these sectorsrespectively as industrial compressed air receiversand domestic hot water storage tanks, other examplesof pressure vesselsare: diving utoclaves and many other vessels in mining or oilrefineries and petrochemical plants, nuclear reactorvessel, habitat of a space ship, habitat of a submarine,pneumatic reservoir, hydraulic reservoir underpressure, rail vehicle airbrake reservoir, road vehicleairbrake reservoir and storage vessels for liquefiedAwww.ijltemas.ingases such as ammonia, chlorine, propane, butaneand LPG.In the industrial sector, pressure vessels aredesigned to operate safely at a specific pressure andtemperature technically referred to as the "DesignPressure" and "Design Temperature".A vessel that is inadequately designed to handle ahigh pressure constitutes a very significant safetyhazard. Because of that, the design and certificationof pressure vessels is governed by design codes suchas the ASME Boiler and Pressure Vessel Code inNorth America, the Pressure Equipment Directive ofthe EU (PED), Japanese Industrial Standard (JIS),CSA B51 in Canada, AS1210 in Australia and otherinternational standards like Lloyd's, GermanischerLloyd, Det Norske Veritas, Stoomwezen etc.Pressure vessels can theoretically be almostany shape, but shapes made of sections of spheres,cylinders and cones are usually employed. Morecomplicated shapes have historically been muchharder to analyze for safe operation and are usuallyfar harder to construct. Theoretically a sphere wouldbe the optimal shape of a pressure vessel.Unfortunately the sphere shape is difficult tomanufacture, therefore more expensive, so most ofthe pressure vessels are cylindrical shape with 2:1semi elliptical heads or end caps on each end.Smaller pressure vessels are arranged from a pipe andtwo covers. Disadvantage of these vessels is the factthat larger diameters make them relatively moreexpensive, so that for example the most economicshape of a 1,000 liters (35 cu ft), 250 bars (3,600 psi)pressure vessel might be a diameter of 914.4millimeters (36 in) and a length of 1,701.8millimeters (67 in) including the 2:1 semi ellipticaldomedendcaps.Many pressure vessels are made of steel. Tomanufacture a spherical pressure vessel, forged partswould have to be welded together. Some mechanicalproperties of steel are increased by forging, butwelding can sometimes reduce these desirableproperties. In case of welding, in order to make thepressure vessel meet international safety standards,carefully selected steel with a high impact resistance& corrosion resistant material should also be used.Page 84
Volume III, Issue IV, April 2014IJLTEMASTwo types of analysis are commonly appliedto pressure vessels. The most Common method isbased on a simple mechanics approach and isapplicable to “thin wall” Pressure vessels which bydefinition have a ratio of inner radius, r, to wallthickness, t, of r/t 10. The second method is based onelasticity solution and is always applicable regardlessthe r/t ratio and can be referred to as the solution for“thick wall” pressure vessels. Both types of analysisare discussed here, although for most engineeringapplications, the thin wall pressure vessel can beused.Drazan ,Pejo, Franjo and Darko (2010)considered influence of stresses resulting from weldmisalignment in cylindrical shell circumferentialweld joint on the shell integrity .The stressesestimated analytically by API recommended practiceprocedure and calculated numerically by using thefinite element method . [3]L.You, J.Z hang and X. You present anaccurate method to carry out elastic analysis of thickwalled spherical pressure vessels subjected to internalpressure. They considered two kinds of pressurevessels: one consists of two homogeneous layers nearthe inner and outer surfaces of the vessel and onefunctionally graded layer in the middle; the otherconsists of the functionally graded material only.They found that proposed approach converges veryquickly and has excellent accuracy [7].R. Patil, Dr. Bimlesh Kumar (et al 2011)studied the fracture pattern of perforated aluminumsheets experimentally and numerically using finiteelements models on two different length scales, tounderstand effect of small scale features such asvoids or hard particles on local deformation whichhave significant influence on the failure mode of amaterial .They found that the fracture path,successfully predicted without introducing softeningmaterial models. The softening phenomenon isnaturally taken into account by the formation oflocalized deformation bands [8].Manyworksincludinganalytical,experimental and numerical investigations have beendevoted to the stress analysis of nozzle connectionsin pressure vessels subjected to different externalloadings.II. LITERATURE REVIEWA. HistoryThe design of pressure vessels is animportant and practical topic which has beenexplored for decades. Even though optimizationtechniques have been extensively applied to designstructures in general, few pieces of work can befound which are directly related to optimal pressurevessel design. These few references are mainlyrelated to the design optimization of homogeneousand composite pressure vessels.L. P. Zick (1971) studied behavior ofstresses in large horizontal cylindrical pressurevessels on two saddle supports. Zick indicates theapproximate stresses that exist in cylindrical vesselsat various locations and develop formulae to covervarious conditions and charts.B. Review of PapersR. Carbonari, P Munoz-Rojas (et al 2011)discuses work on shape optimization of axisymmetricpressure vessels considering an integrated approachin which the entire pressure vessel model is used inconjunction with a multi-objective function that aimsto minimize the von-Mises mechanical stress fromnozzle to head. Representative examples areexamined and solutions obtained for the entire vesselconsidering temperature and pressure loading. Aproper multi-objective function based on alogarithmic of a p-root of summation of p-exponentterms has been defined for minimizing the tankmaximum von-Mises stress [1].V.N. Skopinskyand A.B. Smetankindescribes the structural model and stress analysis ofnozzle connections in ellipsoidal heads subjected toexternal loadings. They used Timoshenko shelltheory and the finite element method. The features ofthe structural model of ellipsoid-cylinder shellintersections, numerical procedure and SAIS specialpurpose computer program were discussed. Aparametric study of the effects of geometricparameters on the maximum effective stresses in theellipsoid-cylinder intersections under loading wasperformed. The results of the stress analysis andparametric study of the nozzle connections arepresented [2].www.ijltemas.inISSN 2278 - 2540 C. CommentsReview of literature gives idea about varioustypes of analysis of Pressure vessels. Designing apressure vessel using a handbook is troublesome andnot interactive. In this Paper further improvementachieve using following steps,Design Pressure Vessel as per Problem statementGeometrical model of Pressure vessel is created usingCATIA V5 R19.Optimization analysis of pressure vessel is carried outfor optimum wall thickness.Carried out Linear Static Structural analysis.Validate design Model using Finite Element Model.Carried out Dynamic analysis to identify the naturalfrequencies of loading that can be cause catastrophicdestruction and find out critical mode shapes.Carried out Thermal analysis.Compare results of FEA with ASME boiler andpressure vessel regulations.Page 85
Volume III, Issue IV, April 2014IJLTEMASISSN 2278 - 2540III. PROBLEM STATEMENT AND OBJECTIVESA. Problem StatementA cylindrical pressure vessel, as shown inFigure 3.1, is to be used for a boiler. The vesselconsists of a cylindrical portion with the two endsclosed using hemispherical structure. A nozzle iswelded on at the mid-point of the length of the vesselwhich is supported on two supports. The vessel isconstructed using rolled steel plates.The internal pressure in the boiler isexpected to be 5 bar. In addition, the flange of thenozzle is subjected to forces and moments beingtransmitted to the vessel through connected piping.The magnitudes of these forces and moments aregiven in Table 1.Table 3.1 Forces and moments acting on the flange of the 0650600500used. Create a simple finite element model toanalyze the configuration used for the closed formsolution and check the accuracy of the closed formsolution against the simulated results. Discuss howclosing the open ends of the cylindrical tube affectsthe stress distribution in the vessel and, hence, itsstructural integrity. Create a detailed finite elementmodel of the vessel using appropriate element type,size and order. Provide suitable justifications forthe choices made. If auxiliary analysis is used toarrive at some decisions, provide short details ofthe same. Describe how the loads and boundaryconditions have been applied and provide thereasons for the approach used. Comment, withappropriate figures, on the key features of theresults and reasons for deviation from the closedform solutions. Suggest some methods forimproving the identified shortcomings in design.Fig 3.1 A typical cylindrical pressure vessel Using closed form solutions for the cylindrical partof the vessel, determine the wall thickness requiredfor the vessel to limit the maximum shear stress inthe vessel to half the yield strength of the material www.ijltemas.inB. ObjectivesTo review the literature on ASME pressure vesseldesign regulations, pressure vessel operation, andpressure vessel materials.To prepare 3 D model of the pressure vessel.Page 86
Volume III, Issue IV, April 2014 IJLTEMASTo carry out closed form structural FE analysis tofind optimum thickness to confine with ASMEstandardTo carry out structural FE analysis of completepressure vessel based on thickness calculated.To compare results obtained through FEA withASME regulations.ISSN 2278 - 2540safety of pressure vessels installed within itsboundaries. The code used for unfired pressurevessels is Section VIII of the ASME boiler andpressure vessel code. It is usually necessary that thepressure vessel equipment be designed to a specificcode in order to obtain insurance on the plant inwhich the vessel is to be used. Regardless of themethod of design, pressure vessels within the limitsof the ASME code specification are usuallychecked against these specifications.C. Methodology Literature review for ASME pressure vesselregulations, pressure vessel operation and materialused for pressure vessel will be carried out byreferring journals, books, manuals and relateddocuments. Based on reviewed literature, study will be carriedout for pressure vessel critical characteristics,bottlenecks & regulatory requirements. 3 dimensional CAD model will be created based onblue prints using commercial CAD tool CATIAV5. Structural FE analysis will be carried out to find theoptimum pressure vessel wall thickness usingcommercial FEM software ANSYS To carried out structural closed form FE analysis ofcomplete pressure vessel based on thicknessobtained to findout critical areas.C. Development and Scope of ASME CodeIn 1911, American Society of MechanicalEngineering established a committee to formulatestandard specifications for the construction ofsteam boilers and other pressure vessels. Thiscommittee reviewed the existing Massachusetts andOhio rules and inducted an extensive survey amongsuperintendents of inspection departments,Engineers, fabricators, and boiler operators. Anumber of preliminary reports were issued andrevised. A final draft was prepared in 1914 and wasapproved as a code and copy righted in 1915.The introduction to the code stated thatpublic hearings on the code should be held everytwo years. In 1918, a revised edition of the ASMEcode was issued. In 1924, the code was revisedwith the addition of a new section VIII, whichrepresented a new code for unfired pressurevessels.IV. DESIGN APPROACH OF PRESSUREVESSELA. Factors Influencing Pressure Vessel DesignD. Selection of The Type of VesselRegardless of the nature of application of thevessels, a number of factors usually must beconsidered in designing the unit. The mostimportant consideration often is the selection of thetype of vessel that performs the required services inthe most satisfactory manner. In developing thedesign, a number of other criteria must beconsidered such as the properties of material used,the induced stresses, the elastic stability, and theaesthetic appearance of the unit. The cost offabricated vessel is also important in relation to itsservice and useful life.The first step in the design of any vessel is theselection of the type best suited for the particularservice in question. The primary factors ressure.ii. Function and location of the vessel.iii.Natureoffluid.iv. Necessary volume for storage or capacity forprocessing.It is possible to indicate some generalities inthe existing uses of the common types of vessels.For storage of fluids at atmospheric pressure,cylindrical tanks with flat bottoms and conicalroofs are commonly used. Spheres or spheroids areemployed for pressure storage where the volumerequired is large. For smaller volume underpressure, cylindrical tanks with formed heads aremore economical.B.Design of PressureSpecificationVessels toCodeAmerican, Indian, British, Japanese, Germanand many other codes are available for design ofpressure vessels. However the internationallyaccepted for design of pressure vessel code isAmerican Society of Mechanical Engineering(ASME).Various codes governing the procedures forthe design, fabrication, inspection, testing andoperation of pressure vessels have been developed;partly as safety measure. These procedures furnishstandards by which, any state can be assured of thewww.ijltemas.in E. Material SelectionThe Material selection is done considering thefollowing factors:StrengthCorrosion ResistanceResistance to hydrogen attackFracture toughnessPage 87
Volume III, Issue IV, April 2014 IJLTEMASManufacturing (Fabrication)ISSN 2278 - 2540Geometrical model of Pressure vessel is as shownin figure 5.1The materials selected for the boiler is SA516Gr 70, for which the yield stress is 260MPa andminimum tensile stress is 480MPa. ASME,Maximum allowable stress. According to givencondition, to limit the shear stress to half of Yieldstrength of material, the design calculations aredevised using the maximum shear stress theory.According to this theory the maximum shear stressis half the algebraic difference of the maximum andminimum principal stress. The maximum principlestress is the hoop stress (σt1) and minimumprinciple stress is the longitudinal stress (σt2).τ (σ t1) - (σt2) / 2τ σy / 2 (σt1) - (σt2) / 2σy (σ t1) - (σt2)σy 2 (σt2) - (σt2) (σt2) since,(σt1) 2(σt2)σy 260 MPa (σt2)(σt1) 520 MPaThe Hoop stress in a vessel is given by(σt1) p. d / 2. TORT p. d / 2. (σt1)T (0.5 x 1500) / (2 x 520)T 0.7mmThe corrosion and weld efficiency, 1.5mmand 0.95mm respectively are added to abovethickness, hence the thickness becomes, T 3.17mm .The above value is rounded to 3mm, asthe standards sheet size is available in 3mm.Hoopstresses are calculated for 3 mm thickness.Hoop stress (σhoop),σhoop P.r/T 0.5*750/3 125 (N/mm2)V. FINITE ELEMENT MODELLINGModeling is the process of producing a model; amodel is a representation of the construction andworking of some system of interest. A model issimilar to but simpler than the system it represents.One purpose of a model is to enable the analyst topredict the effect of changes to the system. On theone hand, a model should be a close approximationto the real system and incorporate most of its silentfeatures. On the other hand, it should not be socomplex that it is impossible to understand andexperiment with it. A good model is a judicioustradeoff between realism and simplicity.www.ijltemas.inFig 5.1 Geometrical model of pressure vesselA. Pre-ProcessingFinite element modeling is done usingHypermesh 9.0. Hypermesh is high performancefinite element pre and post processor for majorfinite element solver helps to design condition inhighly interactive and visual environment. Properselection of element type, order and size playsimportant role in finite element analysis.Fig 5.2 Axisymmetric FE Model1). Element Type: For most of the pressurevessels the element selection is made from eitheraxisymmetric solid elements, shell/plate elementsor 3-D brick elements. However, 3D elements takemuch computation time than other two. As thevessel is to be modelled with the nozzle it cannotbe treated as axisymmetric. Shell elements canrepresent curved surface. As the ratio of thicknessof the vessel to radius (r) is less than 0.1, shellelements are used. The nozzle applies forces andmoments in all three directions, i.e. in-plane andnormal loads have to be considered while selectingthe element type. Shell63 element is used as it asboth bending and membrane capabilities.2). Element order: As the geometry is not muchcomplex, first order elements are used. Also thePage 88
Volume III, Issue IV, April 2014IJLTEMAScomputation time taken is less compared to higherorder elements.3). Element size: As the stress concentration will beat the nozzle neck and cylinder intersection, it ismodelled with denser mesh. Curvature at the nozzlearea is studied with the chord deviation withdifferent element size. The element size is selectedto be 50 starting from the nozzle area. Mesh modelof Pressure vessel is shown in figure 5.3Fig 5.3 Finite Element Mesh ModelISSN 2278 - 2540VI. STRUCTURAL ANALYSISStructural analysis consists of linear and non-linearmodels. Linear models use simple parameters andassume that the material is not plasticallydeformed. Non-linear models consist of stressingthe material past its elastic capabilities. A staticanalysis calculates the effects of steady loadingconditions on a struct
pressure vessel using a handbook is troublesome and not interactive. In this Paper further improvement achieve using following steps, Design Pressure Vessel as per Problem statement Geometrical model of Pressure vessel is created using CATIA V5 R19. Optimization analysis of pressure vessel is carried out for optimum wall thickness.
Finite element analysis DNV GL AS 1.7 Finite element types All calculation methods described in this class guideline are based on linear finite element analysis of three dimensional structural models. The general types of finite elements to be used in the finite element analysis are given in Table 2. Table 2 Types of finite element Type of .
The Finite Element Method: Linear Static and Dynamic Finite Element Analysis by T. J. R. Hughes, Dover Publications, 2000 The Finite Element Method Vol. 2 Solid Mechanics by O.C. Zienkiewicz and R.L. Taylor, Oxford : Butterworth Heinemann, 2000 Institute of Structural Engineering Method of Finite Elements II 2
Nonlinear Finite Element Method Lecture Schedule 1. 10/ 4 Finite element analysis in boundary value problems and the differential equations 2. 10/18 Finite element analysis in linear elastic body 3. 10/25 Isoparametric solid element (program) 4. 11/ 1 Numerical solution and boundary condition processing for system of linear
1 Overview of Finite Element Method 3 1.1 Basic Concept 3 1.2 Historical Background 3 1.3 General Applicability of the Method 7 1.4 Engineering Applications of the Finite Element Method 10 1.5 General Description of the Finite Element Method 10 1.6 Comparison of Finite Element Method with Other Methods of Analysis
Finite Element Method Partial Differential Equations arise in the mathematical modelling of many engineering problems Analytical solution or exact solution is very complicated Alternative: Numerical Solution – Finite element method, finite difference method, finite volume method, boundary element method, discrete element method, etc. 9
3.2 Finite Element Equations 23 3.3 Stiffness Matrix of a Triangular Element 26 3.4 Assembly of the Global Equation System 27 3.5 Example of the Global Matrix Assembly 29 Problems 30 4 Finite Element Program 33 4.1 Object-oriented Approach to Finite Element Programming 33 4.2 Requirements for the Finite Element Application 34 4.2.1 Overall .
2.7 The solution of the finite element equation 35 2.8 Time for solution 37 2.9 The finite element software systems 37 2.9.1 Selection of the finite element softwaresystem 38 2.9.2 Training 38 2.9.3 LUSAS finite element system 39 CHAPTER 3: THEORETICAL PREDICTION OF THE DESIGN ANALYSIS OF THE HYDRAULIC PRESS MACHINE 3.1 Introduction 52
Figure 3.5. Baseline finite element mesh for C-141 analysis 3-8 Figure 3.6. Baseline finite element mesh for B-727 analysis 3-9 Figure 3.7. Baseline finite element mesh for F-15 analysis 3-9 Figure 3.8. Uniform bias finite element mesh for C-141 analysis 3-14 Figure 3.9. Uniform bias finite element mesh for B-727 analysis 3-15 Figure 3.10.
