COMPARATIVE STUDY OF DIFFERENT APPROACHES · PDF fileTo obtain a suitable stress concentration...

http://www.iaeme.com/IJMET/index.asp 142 [email protected]

International Journal of Mechanical Engineering and Technology (IJMET)

Volume 7, Issue 5, September–October 2016, pp.142–155, Article ID: IJMET_07_05_017

Available online at

http://www.iaeme.com/ijmet/issues.asp?JType=IJMET&VType=7&IType=5

Journal Impact Factor (2016): 9.2286 (Calculated by GISI) www.jifactor.com

ISSN Print: 0976-6340 and ISSN Online: 0976-6359

© IAEME Publication

COMPARATIVE STUDY OF DIFFERENT

APPROACHES TO ESTIMATE SCF IN PRESSURE

VESSEL OPENING

Avinash R.Kharat*, Suyash B. Kamble, Amol V. Patil, I.D. Burse

Assistant Professor, Mechanical Department, BVCOEK, Maharashtra, India

ABSTRACT

Pressure vessels are used for storage, transportation and application of energy and fluids and

also for carrying out reactions and many other purposes. Openings in tanks and pressure vessels are

necessary to carry on normal operations. Openings are generally made in both vessel shells as well

as heads. Unfortunately, these openings also result in penetrations of the pressure restraining

boundary, and are seen as discontinuities. Nozzles represent one of the most common causes for

stress concentration in pressure vessels and stress concentration factors can be very useful in

pressure vessel design. FEM analysis is very efficient method for determination of stress

concentration factors; however reliability of FEM analysis should always be assessed.

In this paper comparison of the different approaches are done for determining SCF’s for various

geometries. The experimental data is taken from previous work done by one of the author. Finite

element analysis is carried out using ANSYS commercial code for different nozzle diameter. The

graph of SCF v/s d/D is plotted for different nozzle diameters. To study the effect to stress distribution

around nozzle area a case study is carried out by changing the nozzle radius, shell thickness and

nozzle by keeping internal pressure constant.

Key words: Pressure, Analysis, Opening, Stress Concentration factor (SCF), FEA, Stress

distribution.

Cite this Article: Avinash R.Kharat, Suyash B. Kamble, Amol V. Patil, I.D. Burse, Comparative

Study of Different Approaches To Estimate SCF In Pressure Vessel Opening. International Journal

of Mechanical Engineering and Technology, 7(5), 2016, pp. 142–155.

http://www.iaeme.com/ijmet/issues.asp?JType=IJMET&VType=7&IType=5

1. INTRODUCTION

Pressure vessel cylinders find wide applications in thermal and nuclear power plants, process and chemical

industries, in space and ocean depths, and fluid supply systems in industries. The failure of pressure vessel

may result in loss of life, health hazards and damage of property. Discontinuities like opening in cylindrical

part weaken the containment strength of a pressure vessel because stress intensification is created by the

existence of a void in an otherwise symmetrical section [1]. Openings in tanks and pressure vessels are

necessary to carry on normal operations. They allow for the mounting of equipment, the insertion of

instrumentation, and the connection of piping facilitating the introduction and extraction of content but they

also leads to the high stress concentration which get to the failure of pressure vessel [3]. In recent years,

Comparative Study of Different Approaches To Estimate SCF In Pressure Vessel Opening


researchers have put enormous amount of effort in investigating techniques for analysis stress concentration

near openings. The failure of structures due to stress concentration at any discontinuity/opening has been

baffling engineers for long. It has been found that structure failures in ships, offshore structures, boilers or

high rise buildings subjected to natural calamities is due to stress concentration. Stress concentration mainly

occurs due to discontinuities in continuum [4]. Due to stress concentration the magnitude of the maximum

stress occurring in any discontinuity is comparatively higher than the nominal stress. Stress concentration

cause strength degradation and premature failure of structures because of fatigue cracking and plastic

deformation frequently occurring at these points.

To avoid such type of pressure vessel failure the design engineer must have positive assurance that

stresses generated will never exceed the strength. Stress analysis of a pressure vessel is a very sophisticated

area [2].

2. STRESS CONCENTRATION FACTOR: (SCF)

In a cylindrical shell weakened by a hole, the stress distribution caused by an internal pressure load applied

to the shell will differ considerably from that in an un-weakened shell. The maximum stress will be much

larger if there is a circular hole in the shell than in the case where there is no penetration. This causes the rise

in the stress distribution around the hole to study the effect of stress concentration and magnitude of localized

stresses, a dimensionless factor called Stress Concentration Factor (SCF), calculate this stress rising around

hole the stress concentration factor where mostly used in practice. The determination of S.C.F includes basic

concept of engineering like maximum stress/strain and nominal stress etc. This factor is ratio between the

maximum average stress generated in the critical zone of discontinuity and the stress produce over the cross

section of that zone. Kt as defined by Eq. (1) is used.

(1)

3. VARIOUS APPROACHES TO ESTIMATE THE SCF

The SCF is defined as the ratio of the maximum stress to the nominal stress. For internal pressure loading

the nominal stress is given by; where P is the internal pressure, and T and D are respectively the thickness

and mean diameter of the vessel. The maximum stress is variously defined as the largest normal stress, the

largest equivalent stress (VonMises).

Here the comparison of different approaches used in estimating the stress concentration factor with

different d/D ratio is assessed by using all the available formulas. A specific case study is taken to compare

the different approaches by estimating the theoretical results.

3.1. Flat Plate with circular hole

According to Roukars stress and strain formulae the static stress concentration factor for a plate containing

a centrally located hole in which the plate is loaded in tension depends on the ratio 2r=D, The equation for

Kt is defining here is,

(2)

Where,

Kt = 3.00 –3.13(2r/D) + 3.66(2r/D) 2 -1.53(2r/D) 3 (3)

For the hole, the stress gradient is extremely large compared with the nominal stress, and hence the term

stress concentration applies. This provides the means to evaluate the static stress concentration factors in

the elastic range for many cases that apply to fundamental forms of geometry and loading conditions. [13]

Avinash R.Kharat, Suyash B. Kamble, Amol V. Patil, I.D. Burse


Figure 1 loaded plate in tension

3.2. Roukars formula for calculating SCF of radial hole in a hollow or solid circular shaft

For radial hole in a hollow or solid circular shaft with elastic stress and axial tension loading conditions

stress concentration factor Kt for various dimensions is define as: [12]

Kt = C1+C2 (2r/D) + C3 (2r/D) 2 + C4 (2r/d) 3 (4)

Where,

C1= 3.00

C2=2.773 + 1.529 d/D -4.379 (d/D) 2

C3= -04.21- 12.782(d/D) + 22.781 (d/D) 2

C4=16.841 + 16.678 (d/D) – 40.007 (d/D) 2

Figure 2 Cylindrical shaft with hole

3.3. Leckie and Penny Charts

Two cases will be considered here, namely that for spherical vessels and for cylindrical vessels. Leckie and

Penny treat the case of nozzles in spherical vessels in their analysis of an intersecting cylinder and sphere.

The maximum stress occurring in the sphere was presented in a graphical form. Both flush and protruding

nozzles were considered in the analysis. The stress concentration factors have been calculated in terms of

the maximum stress in the sphere by neglecting the bending stresses. In its most basic form, a radial nozzle

in a spherical vessel is defined by four geometric variables. [6]



Figure 3 Stress concentration factors (SCFs) for a nozzle in a spherical shell

Figure 4 SCF for a nozzle in a cylindrical shell.

These are the nozzle and sphere diameters d and D, and the corresponding thicknesses t and T. The stress

concentration factors can be expected to increase as the ratio d/D increases (keeping the same D/T, of

course). This is evident from Figure 4 However because of the thin-shell assumptions concerning the joining

of the nozzle and the sphere, the solutions can only be expected to describe the gross structural behavior.

The cylinder/cylinder geometry (for nozzles in cylindrical vessels) is much more difficult to analyze than

the nozzle sphere, which can be treated as an axisymmetric structure [7]. To obtain a suitable stress

concentration factor for a nozzle in a cylindrical vessel, an approximate axisymmetric model is sometimes

used. A popular approximation used is where the equivalent sphere has twice the diameter of the shell. The

general trend of the experimental results is shown in Figure, which is for a flush nozzle in a cylindrical shell.

3.4. Forces around Hole by Van Dyke, Lind, Savin, Mershone

In this van dyke, Lind, Savin, mershone gives the different formulas to estimated the SCF by considering

ratio of d/D, the result of a perturbation solution to Equation modified to include a circular hole covered by

a membrane, through terms of order (βpa2 ) is a stress concentration factor at the hole-shell boundary.[14]

Where,

β= 3(1-v2)/ 16R2T2 (5)

a) Van Dyke:

SCF (van dyke) = 3/2 + cos 2ϕ + П (βr2) (1+ 5/4 cos 2 ϕ) + (6)



For case of ϕ=0, equation becomes

SCF Van Dyke = 2.5 + (2.92 r2/RT) …… v = 0.3 (7)

Where r is opening size,

b) Savin’s formula for the same problem is

SCF= 2.5 + 2.3 (r2/RT) (8)

c) Lind’s Equation is

SCF= 1+ 4 βr (1+ (T/2R)) (9)

SCF= 1+2.585(r/ (RT) ½) (10)

d) Mershon obtained for the same problem

SCF= 2.5 + r/R (2R/T) ½ (11)

3.5. Peterson's Stress Concentration Factors

For single circular opening in the cylindrical shell Peterson’s SCF formula is used which said that for

pressure loading the analysis assumes that the force representing the total pressure corresponding to the area

of the opening is carried as a perpendicular shear force distributed around the edge of the hole. This is shown

in chart below. Results are given as a function of dimensionless parameter β: [13]

(12)

Where,

R is the mean radius of the shell, h is the shell thickness a is the radius of opening, ν is poisons ratio = 0.3

For membrane stresses:

0 ≤ β ≤ 2

Kt (β) = 2.5899+0.8002 β+4.0112 β2-1.8235 β3+0.3751 β4 (13)

2 ≤ β ≤ 4

Kt (β) = 8.3065-7.1716 β+6.70 β2-1.35 β3+0.1056 β4 (14)

3.6. Theoretical values for SCF analysis of a pressurized vessel–nozzle intersection: [11]

Prior to the availability of powerful numerical capabilities a number of simple formulas were developed for

the SCF in pressurized tees, based on theoretical or experimental considerations. Subsequently, some simple

formulas were developed based on statistical analysis of numerical results for tee joints determined using

the FEA. To find SCF in this type of the geometries the various authors gives different theoretical formula

which given below,

3.6.1 Lind, using the ‘area method’, developed the set of formulas given as:

s= d/ (2t) and S= D/2T (15)

SCF= max {Kt1, Kt2} (16)

3.6.2 Expressions for the SCF were given by Money

The experimental work done by Money on many tee joints. SCF formulas valid for r/R< 0.7, respectively,

are given by

SCF= 2.5 [(r/t) 2 × (T/R)] 0.2042 (17)



3.6.3 SCF Formula given by Decock

Based on results from experimental data, and presented a formula for the SCF in terms of non-dimensional

parameters as: [10]

(18)

3.6.4 SCF Formula given by Moffat:

Formula for the effective stress factor (ESF) based on a parametric analysis of tees using three-dimensional

FEA. The ESF is essentially equivalent to the SCF. The formula for the ESF is given by [9]

ESF=[a1+a2(d/D) + a3 (d/D)2 + a4 (d/D)3] + [a5 + a6(d/D) + a7(d/D)2+a8(d/D)3] (t/T) + [a9 + a10(d/D) +

a11(d/D)2 + a12(d/D)3] (D/T)p + [a13 + a14(d/D) + a15(d/D)2 + a16 (d/D)3] (t/T)(d/T)p (19)

Where p =1.2, and the constants a1–a16 are given by 2.5, 2.715, 8.125, -6.877, -0.5, -1.193, -5.416, 5.2,

0.0, 0.078, -0.195, 0.11, 0.0,-0.043, 0.152, -0.097.

4. CASE STUDY

In this case study we are going to find the effect of the various parameters changes on stress concentration

factor which lead to the maximum stress concentration. Design Specifications for comparative study of

different approaches are same as used by previous researcher for experimental study. Following fig5 shows

various dimensions used for analysis model.

Figure 5 Pressure vessel model used for analysis

Dimensions used for analysis are given in Table 4.1 below. Thickness of the shell as well as thickness

of the nozzle is different for each model from A1-A6 which helps to understand effect of opening ratio on

the stress concentration factor. Nozzle inside diameter was increased from 18mm-125mm as shown in Table

keeping shell inside diameter constant. Length of cylinder is 500mm.

Table 1 Dimensions used for comparison study

Sr.

No

Diameter

(D) mm

Nozzle

diameter

(d)

Shell

thickness

(T)

Nozzle

thickness

(t)

d/D

A1 200 18 5.5 6.26 0.09

A2 200 40 25 5 0.2

A3 200 50 12.12 6.9 0.25

A4 200 62 11.17 3.4 0.31

A5 200 100 18.18 9.09 0.5

A6 200 125 13.24 8.2 0.625



By using all formulae mentioned above stress concentrations are calculated for different models as shown

in following Tables 4.2 and 4.3. From two Tables it is observed that stress concentration increase with

increase in d/D ratio and other dimensions.

Table 2 SCF calculated by various Formulas and Experimental SCF

Table 3 SCF calculated by various Formulas

This all calculated values of SCF are compared with the experimental SCF values (graphs given in below)

taken from the previous work done by author M. Qadir, D. Redekop. This calculated value with specific case

study is then calculated by finite element analysis Using Ansys commercial code.

Figure.6 Comparison of Peterson’s with Experimental Figure 7 Comparison of Lind’s with Experimental

Peterson Lind Money Decok van

Dyke Savin Exp.

A1 3.00 2.71 3.32 2.68 2.93 2.83 2.55

A2 3.02 2.58 2.72 2.84 2.96 2.86 3.25

A3 3.64 3.19 3.51 3.38 4.00 3.68 3.4

A4 4.13 5.44 4.02 4.86 5.01 4.47 3.4

A5 4.79 3.48 3.10 3.34 6.51 5.66 4.23

A6 6.43 2.71 2.65 2.56 11.11 9.28 4.24

Lind Moffat

mershone somnath Roukars flat

plat

A1 1.99 3.22 3.04 2.5 3.07 3.31

A2 2.03 3.19 3.06 2.65 3.39 3.76

A3 2.85 3.68 3.51 2.75 3.52 3.98

A4 3.39 4.56 3.81 2.85 3.75 4.27

A5 4.03 3.8 4.15 2.9 4.83 5.28

A6 5.44 3.08 4.92 3 5.56 6.01



Figure 8 Comparison Money’s SCF with Experimental Figure 9 Comparison of SCF Van Dyke vs. Expri.

Figure 10 Comparison of Savin with Experimental Figure 11 Comparison of Decoke’s SCF with Experimental

Figure 12 Comparison of Lind’s 2 with Experimental SCF



Figure 13 Comparison of Licke and Penny’s with Experimental

Fig.14 Comparison of Mershone with Experimental Fig.15 Comparison of Roukars formula with Experimental

Figure 16 Comparison of Flat plate SCF with Experimental



5. FINITE ELEMENT ANALYSIS

The finite element analysis predicts the performance of the component in the service environment. This

permits the development of a predicted margin of safety, which is a quantitative measure of the component

acceptance criteria. Finite element method possesses the flexibility of discretizing problems with complex

geometries, or in which media is heterogeneous or anisotropic and it is capable of providing solutions

throughout the problem domain.

Structural analysis is choosing for the study of this problem. Structural analysis is probably the most

common application of the finite element method. The term structural (or structure) implies not only civil

engineering structures such as bridges and buildings, but also naval, aeronautical, and mechanical structures

such as ship hulls, aircraft bodies, and machine housings, as well as mechanical components such as pistons,

machine parts, and tools [5].

In the present study the effect of various configurations of nozzle with different diameter ratio and wall

thickness on the structural response is studied by utilizing the finite element method. Finite Element

Modeling (using ANSYS) is one of the most robust and widely used methods to virtually investigating the

faults occurring in real time problems which are in general difficult to witness. So that structural modeling

is done using ANSYS commercial code [8].

5.1. Model Building

Investigated problem is modeled as 3D problems due to shape of nozzle-vessel connection. Only quarter part

of pressure vessel is modeled for each model from A1 to A6 because it is possible to defined three symmetry

planes, (figure 17). FEM models are made based on the conditions stated in the problem description. A linear

elastic analysis was conducted throughout this study. The material properties used were: Young’s modulus

=210,000 MPa, Poisson’s ratio = 0.3.

Figure 17 Quarter Mesh model of pressure vessel

An important aspect contributing to the accuracy of the finite element technique is the selection of the

right type of element. The element type selected for finite element analysis of pressure vessel is brick

SOLID45 (8noded). SOLID45 is used for the 3-D modeling of solid structures. The element is defined by

eight nodes having three degrees of freedom at each node: translations in the nodal x, y, and z directions.

The element has plasticity, creep, swelling, stress stiffening, large deflection, and large strain capabilities.

Efficient use of the finite element method is achieved by using an optimum size of mesh with proper

degrees of freedom at the nodes, depending upon the behavior of the structural response under consideration.



It is desirable to have a finer mesh for accuracy [5]. For meshing the model we have used mesh size that is

e-size as 5 as shown in Figure 17.

The boundary conditions applied such as nodes in the support area is fixed in one side & other is fixed

in Y-direction so that the rolling support is create in X-direction and internal pressure of 1.2Mpa is applied

to the vessel and the analysis is performed to see the stresses in nozzle.

5.2 FEA Calculated Results

The calculated VonMises results for A1-A6 from the finite element analysis are summarized in table 4. From

this results the SCF values are calculated by basic formula for each model (A1-A6) then these results were

compared with the experimental values. The plot of SCF by FEA and SCF by experimental values is plotted

with d/D opening ratio. The other dimensions like diameter of the shell is different for each model and

thickness is also get changes for both shell and nozzle. The effect of this all parameter is also get influence

the stress concentration around the opening, so in present case we also get the effect of other parameters on

each model of opening in pressure vessel.

Table 4 FEA Results VonMises stress and SCF

σ (Mpa)

Nominal

t T

Mm

d/D σmax

FEA

SCF

FEA

SCF

Expri.

A1 21.81 6.25 5.5 0.09 46.57 2.13 2.55

A2 4.8 5 25 0.20 18.54 3.86 3.25

A3 9.90 6.9 12.12 0.25 35.79 3.61 3.40

A4 10.74 3.4 11.17 0.31 48.90 4.55 3.40

A5 6.60 9.09 18.18 0.50 40.21 6.09 4.23

A6 9.049 8.2 13.26 0.62 66.65 7.36 4.24

Figure 18 Comparison of FEA results And Experimental SCF



5.3 FEA Analysis Results

Figure 19 Equivalent stress in Model A1 Figure 20 Equivalent stress in Model A2





6. DISCUSSION

In the study of estimating the stress concentration factor (SCF),the results of finite element analysis is given

in above table 4.2 with experimental results of previously work done and the graph SCF Vs d/D is plot to

compare both FEA and Experimental results on the basis of SCF. It has been seen that our FEA results are

significantly matches with the experimental results but some of the points is get very higher results as

compared to experimental results. Results for model A1-A4 get nearer to the comparative values.

It is seen that the thickness of the each model is different so that the results coming is also random. At

some point it is very high or very low, from d/D ratio of 0.09-0.31 the results were in similar fashion. The

pressure applied to each model is constant 1.2Mpa perhaps due to different shell diameter and thickness the

nominal stress value is changes so there is change in applied load inside the shell.

The results of FEA is lower for A3 having the nozzle diameter greater than A2, one of the cause for this

is the thickness of the nozzle i.e. 6.9mm greater than A2 5mm, But when opening size is increase the

thickness effect get reduce and SCF for the model A5 and A6 is higher than previous four models.

Here we discuss the various theoretical approaches for the SCF calculations, the result calculated from

this various formulas where compared with the experimental readings (graph given in appendix A). Some

of the approaches are base on theoretical work and some on experimental work, when the comparison is

made for SCF then it notice that the theoretical formulas can give quick predictions of the SCF values. In

developing these formulas each corresponding author used a limited range for the geometric parameters,

over which good results may be expected. For the present models, Money, Moffat, Savin, Mershone,

Peterson’s correlation equations, respectively, gave the most satisfactory results. The formulas given by

Lind, Decock, and Roukars generally gave conservative results. The formula gave by van Dyke and flat plate

showed results which were significantly conservative on the average, and which also showed a greater

fluctuation than the other formulas.

7. CONCLUSION

The current study is dealing with the SCF estimation by various approaches and to confirm SCF results

which are taken from previous work of authors, and to indicate the relative accuracy of various approaches

and theories. At the intersection of nozzle and cylinder/shell the observations was the systematic rise in the

SCF value with an increase in the diameter ratio d/D, for a specified vessel diameter-thickness ratio D/T. It

was also observed that for a specified d/D ratio, the SCF value increases.

The FEA results were calculated with different model showed the good agreement with experimental

values. Most of the FEA results were match with experimental values. The Plots of SCF Vs d/D for all

methods where gives well comparison data of various values so, the accuracy of all formulas were studied

here for estimating SCF for openings in pressure vessels.

REFERENCES

[1] Durelii A. J., Parks V. J. (1973). Stresses in a pressurized ribbed cylindrical shell with a reinforced hole,

The Journal of Strain Analysis for Engineering Design, Vol. 8, pp-140-150.

[2] Bildy Les M. (2000). A Proposed Method for Finding Stress and Allowable Pressure in Cylinders with

Radial Nozzles, Codeware.

[3] Makulsawatudom p., Mackenzie D. (2004). Stress concentration at crossholes in thick cylindrical vessels,

The Journal of Strain Analysis for Engineering Design, Vol. 39, pp 471-481.

[4] Liu You-Hong. (2004). Limit pressure and design criterion of cylindrical pressure vessels with nozzles,

International Journal of Pressure Vessels and Piping, vol. 81, pp 619–624.

[5] Alashti R. A., Rahimi G. H. (2008). Parametric Study of Plastic Load of Cylindrical Shells with Opening

Subject to Combined Loading, Journal of Aeronautical society, Vol. 5, No.2, pp 91-98.

[6] Chattopadhyay S. (2005). Pressure vessel design and practice. CRC press publication.



[7] Carter W.J. (1999). Openings & Reinforcements, CASTI Guidebook to ASME Section VIII Div. 1 –

Pressure Vessels – 2nd Edition.

[8] Whitesides R. W. Openings in ASME code pressure vessels, www.PDHcenter.com, sited on

28thJune2011.

[9] Moffat D. G. (1991). Effective stress factors for piping branch junctions due to internal pressure and

external moment loads. J Strain Analysis; Vol.26: pp 84–101.

[10] Decock J. (1995). Reinforcement method of openings in cylindrical pressure vessels subjected to internal

pressure Centre de Recherché Scientifiques Techniques de L’Industrie des Fabrications Metalliques.

[11] Qadir M., Redekop D. (2009). SCF analysis of a pressurized vessel–nozzle intersection with wall thinning

damage, International Journal of Pressure Vessels and Piping 86, pp 541–549.

[12] Qayssar Saeed Masikh, Dr. Mohammad Tariq and Er. Prabhat Kumar Sinha, Analysis 0f A Thin and Thick

Walled Pressure Vessel For Different Materials. International Journal of Mechanical Engineering and

Technology (IJMET), 5(10), 2014, pp.9-19

[13] Pallavi J.Pudke, Dr. S.B. Rane and Mr. Yashwant T. Naik, Design and Analysis of Saddle Support: A

Case Study In Vessel Design and Consulting Industry. International Journal of Mechanical Engineering

and Technology (IJMET), 4(5), 2013, pp.139-149

[14] I.M.Jamadar, S.M.Patil, S.S.Chavan, G.B.Pawar and G.N.Rakate, Thickness Optimization of Inclined

Pressure Vessel Using Non Linear Finite Element Analysis Using Design by Analysis Approach.

International Journal of Mechanical Engineering and Technology (IJMET), 3(3), 2012, pp.682–689

[15] Laham S. (1990). Stress Intensity Factor and Limit Load Handbook, Engineering division, Issue 2.

[16] Pilkey W. (2009). Peterson’s stress concentration factor, Jone wile and son’s publication. pp 176-339.

[17] Ramsey. (1975). stress concentration factors for circular, reinforced penetration in pressurized cylindrical

shells, Ph.D. Thesis.

AUTHORS' BIOGRAPHIES

Mr. AVINASH KHARAT

Assistant Professor, Mechanical Department,

Bharati Vidyapeeth’s, College of Engineering,

Kolhapur ME(CAD/CAM/CAE) From KIT, Kolhapur

Mr. SUYAH B.KAMBLE

Assistant Professor, Mechanical Department, Bharati Vidyapeeth’s,

College of Engineering, Kolhapur

M.Tech (PROD) from VJTI, Mumbai

Mr. INDRAJEET D.BURASE

Assistant Professor, Mechanical Department,

Bharati Vidyapeeth’s, College of Engineering, Kolhapur

M.Tech (CAD/CAM/CAE) From RIT. Islampur

Mr. AMOL V. PATIL

Assistant Professor, Mechanical Department, Bharati Vidyapeeth’s,

college of Engineering, Kolhapur

ME(Mech. Machine Design) From FAMT Ratanagiri

http://www.pdhcenter.com/

Date post:	12-Feb-2018
Category:	Documents
Upload:	hoangdien
View:	213 times
Download:	1 times

COMPARATIVE STUDY OF DIFFERENT APPROACHES · PDF fileTo obtain a suitable stress concentration...

Documents