ANALYSIS OF DEFORMATION AND VON-MISES STRESS FOR THIN RECTANGULAR PLATES

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1 ANALYSIS OF DEFORMATION AND VON-MISES STRESS FOR THIN RECTANGULAR PLATES Ms.K.PADMAJA 1 1 Assistant Professor, Department of Mechanical Engineering, Dadi Institute of Engineering and Technology, Anakapalle Abstract- Now a day s sheet metals are very much in use due to less weight, noise reduction and heat dissipation hence theses are recommended in subsea over a sea depth of 2 to 3 km. So it is important to study the structural behavior about their design and structural analysis. An attempt to study the structural behavior about this for two different materials such as A 36 Mild steel and Al 5086.According to theory of plates the deflections are calculated. Finite Element Analysis is used to analyze the deformation behavior of plates. FEA is carried out using software ANSYS. Numerical and Analytical values are tabulated and hence found that Al 5086 is also preferable material as A36 Mild steel except cost. Keywords- Rectangular plate, deformation, Von-Mises stress, ANSYS workbench I. INTRODUCTION Subsea structures are being challenged to counteract the depletion of oil recourses with the new set of discoveries. As the encountered environmental loads are more severe in greater water depths, the geometric form of offshore platforms proposed for deep and ultra-deep waters needs special attention. Apart from being cost effective, the proposed geometric form shall also have better motion characteristics under the encountered forces arising from the rough sea. The materials used in the offshore face some problems such as corrosion and ability to weld under water. The fabrication and construction of structures used in the offshore, proper material selection needs to be carried out to achieve proper function and low cost. II. LITERATURES By receiving a number of surveys on plate failure the determination of the appropriate boundary condition of the appropriate boundary conditions for a two-dimensional theory of elastic flat plates (and shells) consistent with the expected order of accuracy theory is both critical and challenging [1]. The higher order accuracy offered by the governing differential equations of a higher order plate, may not be attained unless commensurate boundary conditions are developed and used for these equations [2]. Rectangular plate steel plates are widely used in various steel structures and steel industries. For a proper design of steel plate structures and efficient use of material, the behavior, strength, buckling and post-buckling characteristics of plates should be accurately determined [3]. The present study is to determine the exact characteristics equations for the case of S-C-S-F [4]. The two dimensional (2D) and three dimensional (3D) Finite Element Method(FEM) have been used to analysis the deformation behavior of perorated sheet during uniaxial tension [5]. The analysis is focused on early stage during which the highest hydrodynamic loads are generated. The liquid is assumed ideal and incompressible, gravity and surface tension effects are not taken into account. The flow generated by the impact is two dimensional and potential [6]. Aluminium alloy is relatively more expansive material then steel although its weight is one-third of steel. Thus use of steel as a structure adds additional weight by 60%. Mathematical equation was used to calculate the weight of the materials used to construct the deckhouse [7]. DOI: /IJMTER XYTR 123

2 International Journal of Modern Trends in Engineering and Research (IJMTER) In case of complex and big construction systems subjected to the arbitrary loads, including complex boundary conditions, solving of differential equations by analytical methods is almost impossible. Then the solution is application of numerical methods [8]. III. MATERIAL SELECTION The demand in the offshore support vessel (OSV) market in Asia Pacific will continue to grow, driven by deepwater exploration and production activities. The Offshore Support Vessels undertake production support, diving support, supply duties for personnel and materials, anchor handling, towing, mooring, rig moving, emergency response or rescue and fire fighting operations. Various approaches have been utilized including lighter weight materials for equipments and deckhouse structure of OSV Comparison Mild Steel to Aluminium alloy The steel used in ship construction was mild steel with % carbon content. Beside that the use of high tensile steel in bottom and deck can reduce weight by 5-7%. The most commonly used aluminium alloys for marine applications were 5000 and 6000 series, which have magnesium as their primary alloying element [10, 11]. The 5000 series alloys have generally shown to have excellent resistance to corrosion; there was concern that material is becoming sensitized over time to intergranular corrosion and stress-corrosion cracking, particularly when subjected to higher service temperatures on exposed decks [10]. Besides that, most aluminium alloys require low maintenance because of their good corrosion resistance. Therefore, aluminium is an excellent candidate for all applications where the benefit of freedom from initial protection and maintenance yields a commercial benefit. Aluminium is lighter than mild steel (approximate weight: Aluminium ton/m³, Mild steel 7.84 ton/m³) and with an Aluminium structure it has been suggested that up to 60 per cent of the weight of a steel structure may be saved H32 Aluminum sheet / plate Alloy 5086 aluminium plates have even higher strength than 5052 or 5083 and its mechanical properties vary significantly with hardening and temperature. It is not strengthened by heat treatment; Instead, it becomes stronger due to strain hardening or cold working of the material. This alloy can be readily welded, retaining most of its mechanical strength. The good results with welding and good corrosion properties in seawater make Alloy 5086 extremely popular in marine applications. Alloy 5086 plate due to its high strength factor can be used in shipyard, tank cars, welded and superstructures and patrol and work boat hulls and armor plate etc Al5086 alloy is primarily alloyed with magnesium. It is not strengthened by heat treatment, instead becoming stronger due to strain hardening, or cold mechanical working of the material. Since heat treatment doesn't strongly affect the strength, 5086 can be readily welded and retain most of its mechanical strength. The good weld ability and corrosion properties in seawater make 5086 extremely popular for vessel gangways, and boat/yacht hulls. IV. METHODOLOGY The analysis of thin plates with small deflection makes the following three assumptions when the deflection,, is small in comparison to the thickness of the plate: There is no deformation in the middle plane of the plate. This plane remains neutral during bending Points of the plate lying initially on a normal-to-the-middle plane of the plate remain on the normal-to-the-middle surface of the plate after bending The stresses in the direction transverse to the plate can be disregarded. These three assumptions for thin plate theory are based on Kirchhoff s Plate Theory [11]. Thin plate theory relies on different boundary conditions to constrain the plate. The three assumptions that are made for thin plates with small deflections mean that the material of the plate will not All rights Reserved 124

International Journal of Modern Trends in Engineering and Research (IJMTER) stretched. With these three assumptions and the boundary conditions, the deflection of the plate, can be calculated.

3 International Journal of Modern Trends in Engineering and Research (IJMTER) stretched. With these three assumptions and the boundary conditions, the deflection of the plate, can be calculated. The plate is said to be thin when ; Figure 1: Thin Rectangular plate Simply Supported Rectangular plates under Sinusoidal Load: Assume that the load is distributed over the surface of the plate is given by the expression Where represents the intensity of load at the centre of the plate. The differential equation for the deflection surface in this case becomes Deflection and bending moments become zero at all edges of simply supported rectangular plate. By applying the Boundary conditions to the above equation: (1) (2) for x = 0 and x = a (3) (4) for y = 0 and y = b ( ) At Where E = Young s Modulus t = Thickness of the plate Sides of plate = 2.5 m (N.m)...Equation (A) By applying loads on rectangular plate: At Maximum loading condition: Assume: Perforation of the plate with 13 holes of 200 mm diameter Intensity of loading on plate over a sea depth of 2.5 meters along with load on it = ( ) By solving Equation (A) the numerical values of deformation for different thickness can be calculated. some other 4.1 FE Model in ANSYS: The software ANSYS is a complex tool for computer aided engineering (CAE) and in its latest releases it enables whole range of analyses. The connection functionality with software All rights Reserved 125

International Journal of Modern Trends in Engineering and Research (IJMTER) Pro/Engineering, Catia or Parasolid makes from ANSYS a decent meshing tool used for various objects of interest.

4 International Journal of Modern Trends in Engineering and Research (IJMTER) Pro/Engineering, Catia or Parasolid makes from ANSYS a decent meshing tool used for various objects of interest. In this case the work process in ANSYS begins with an important of the geometry from CATIA software. Then material properties are defined followed by meshing. After that static structural analysis is conducted to obtain stress history. Figure 2: Fine Meshing of Rectangular plate The deformation of a simply supported plate with a uniformly distributed load on its surface is calculated. The analysis creates a finite element model using ANSYS to determine the maximum deformation of the A36 Mild steel and Al ANSYS allows for many different types of analyses. The analysis completed for this project utilized shell elements for both an A36 Mild steel and Al 5086 plate configurations. The overall size of each model in ANSYS can be reduced due to the symmetry of the plate and the symmetry of the boundary conditions. The finite element model can be solved after the boundary conditions and uniform pressure is applied. Boundary conditions applied to plate are S-C-S-C (Simply supported Clamped - Simply supported Clamped). The second part of the analysis uses thin plate theory equations solved to determine the accuracy of the ANSYS results. To calculate the deformation of the simply supported rectangular plate the Navier Solution outlined by Timoshenko in Theory of Plates and Shells can be applied Analysis of A36 Mild steel as Rectangular plate: In ANSYS pre-processing process, physical parameters are taken for simulation and then by importing the model meshing is generated. Loads and Boundary conditions are applied for analysis. Table1: Physical parameters used in simulation for A36 Mild steel Properties Metric Tensile Strength, Ultimate MPa Tensile Strength, Yield 250 MPa Compressive Strength, Yield 152 MPa Modulus of Elasticity 200 GPa Bulk Modulus(typical for steel) 140 GPa Poisson s ratio 0.26 Shear Modulus 79.3 GPa Density 7.85 g/cm 3 The deformation and Equivalent Von-Mises stress of A36 Mild Steel are observed in ANSYS post processor All rights Reserved 126

International Journal of Modern Trends in Engineering and Research (IJMTER) Figure 3: Deformation of A36 Mild Steel Figure 4: Equivalent Von-Mises stresses of A36 Mild Steel Comparing Numerical and

63 20 146560 4.68 5.00 25 286250 2.39 2.71 30 494640 1.38 1.49 35 785470 0.87 0.98 40 1172480 0.58 0.63 4.3. Analysis of Al 5086 as Rectangular plate: Table 3: Physical parameters used in simulation

5 International Journal of Modern Trends in Engineering and Research (IJMTER) Figure 3: Deformation of A36 Mild Steel Figure 4: Equivalent Von-Mises stresses of A36 Mild Steel Comparing Numerical and Analytical values of deformation for A36 Mild steel Plate: t Table 2: Deformation of A36 Mild steel D (in N.m) Numerical value (ANSYS) Analytical Value Analysis of Al 5086 as Rectangular plate: Table 3: Physical parameters used in simulation for Al 5086 Properties Al 5086 Alloy Tensile Strength, Ultimate 310 MPa Tensile Strength, Yield 276 MPa Modulus of Elasticity 68.9 GPa Poisson s ratio 0.33 Shear Modulus 27 GPa Density 2700 kg/m 3 Coefficient of thermal expansion Shear Strength Similarly by applying uniform loads on the Al 5086 alloy /ºC up to C 190 All rights Reserved 127

Deformation in mm International Journal of Modern Trends in Engineering and Research (IJMTER) Figure 5: Deformations of Al 5086 alloy Figure 6: Equivalent Von-Mises stresses of Al 5086 alloy

39 15 22410 30.63 36.68 20 53120 12.9 13.86 25 103750 6.62 7.58 30 179280 3.8 4.05 35 284690 2.41 2.66 40 424960 1.61 1.79 V.

6 Deformation in mm International Journal of Modern Trends in Engineering and Research (IJMTER) Figure 5: Deformations of Al 5086 alloy Figure 6: Equivalent Von-Mises stresses of Al 5086 alloy Comparing Numerical and Analytical values of deformation for Al 5086 Plate: t Table 4: Deformation of Al 5086 alloy D(in N.m) Numerical value (ANSYS) Analytical Value V. RESULTS AND DISCUSSIONS The stress history obtained for A36 Mild steel and Al 5086 are within the tensile yield strength value and the thickness of plate at 40 mm having less deformation. From the base plate thickness calculation we can observe that the deformation of both A36 Mild steel and Al 5086 at 40 mm thickness is negligible and the stresses generated are 12.5 MPa for A36 Mild steel and MPa for Al 5086 very less when compared with yield tensile strength 250 MPa and 276 MPa respectively. This graph concludes that as the thickness increases the Flexural rigidity of plate (D) increases which are in the denominator of deformation formulae so the deformation decreases gradually A36 Mildsteel Al Figure 7: Deformation Vs Thickness for Analytical All rights Reserved 128

7 Deformation in mm International Journal of Modern Trends in Engineering and Research (IJMTER) A36 Mild steel Al Figure 8: Deformation Vs Thickness for Numerical values VI. CONCLUSION The deformation and stresses generated were observed for two different types of material such as A36 Mild steel and Al 5086.According to properties of Al 5086 is best to use as a plate having high strength over a sea depth of 2-3 km and going to with stand loads similar to A36 Mild steel where the deformation is negligible. Aluminium alloy has excellent strength to weight ratio making it ideal for use in situations where high strength and low weight are required. The use of the Aluminium alloy was higher initial cost, this have been estimated at 8 to 10 times the price of the steel on a tonnage basic. Besides that, most aluminum alloys require low maintenance because of their good corrosion resistance. Therefore, aluminum is an excellent candidate for all applications where the benefit of freedom from initial protection and maintenance yields a commercial benefit. It concludes that if initial cost is neglected Al alloy with 5000 and 6000 series materials can have similar features like A36 Mild steel. REFERANCES [1] Frederic Y.M. Wan. Department of Mathematics, University of California Irvine, Irvine, CA , USA. Stress Boundary Conditions for Plate Bending International Journal of Solids and Structures 40 (2003) [2] Gregory, R.D., Wan, F.Y.M., 1985a. On plate theories and Saint-Venant s Principle. Int. J. Solids Struct. 21, [3] S.A. Sadrnejad, A. Saedi Daryan and M. Ziaei Vibration Equations Of Thick Rectangular Plates Using Midlin Plate Theory [4] Gorman, D.J., Free vibration analysis of Mindlin plates with uniform elastic edge support by the superposition method. J. Sound Vibrat., 207: DOI: /jsvi [5] Seunng Luhl Baik, Kyn Hwan Oh and Dong Nyung Lee Analysis of the Deformation of A Perforated Sheet under A Uniaxial Tension [6] A. A. Korobkin and A. Iafrati, Hydrodynamic Loads on Flat Plate Entering Water [7] Muzathik A.M, Ferry M, Chan M.Y, Samo K.B and Noor C.W.M Comparison of Aluminium Alloy and Steel Materials as Deckhouses for Offshore Support Vessels [8] Analysis of rectangular thin plates by using finite difference method Journal of Novel Applied Sciences [9] Sielski, R A The history of Aluminium as a deckhouse material, Journal article; Paper presented at ASNE Day. [10] Stephen. F. Polard. Boatbuilding with aluminium International Marine Camden, Marine, page 22.Capalex Advantages of aluminium. Capital Aluminium Extrusions Ltd. [11] Stephen P. Timoshenko and James M. Gere, Theory of Elastic All rights Reserved 129

Analysis of Plates by using ANSYS

Analysis of Plates by using ANSYS N.V.Divya 1, Syed Rizwan 2 P.G. Student, Department of Structural (Civil) Engineering, Chiranjeevi Reddy Institute of Engg & Tech, Anantapuramu, Andhra Pradesh, India