STATIC BENDING ANALYSIS OF AN ISOTROPIC CIRCULAR PLATE USING FINITE ELEMENT METHOD

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1 International Journal Modern Trends in Engineering and Research e-issn : , Date: April, 20 STATIC BENDING ANALYSIS OF AN ISOTROPIC CIRCULAR PLATE USING FINITE ELEMENT METHOD Pratik S. Gujar 1 and Sandeep S. Pendhari 2 1 Lecturer, Department Structural Engineering, V.J.T.I., Mumbai (M.S.)gujar.pratik@gmail.com 2 Associate Pr., Department Structural Engineering, V.J.T.I., Mumbai (M.S.)sspendhari@vjti.org.in Abstract- An attempt is made in this study to perform static bending analysis an isotropic circular plate using four noded shell 63 element which is based on Kirchhf s Plate Theory. Modelling and analysis an isotropic circular plate is done by FEA stware ANSYS APDL. In this work effect various types meshes on deflections and bending stresses in circular plate is investigated and finally convergence FEA results analytical solution is studied. The results are obtained for aspect ratio 10 and 20. Simply supported and clamped boundary conditions uniformly distributed load are considered for present study. Keywords-Isotropic circular plate; Finite element method; 4 noded shell 63 element; Multi zone ;. I. INTRODUCTION Finite element analysis is a numerical technique which is widely used for solving many engineering problems having complex geometries, boundary conditions and loads. From last few decades, the fast improvement in computer hardware technology has boosted this method. Now there are many popular finite element analysis stware packages available. ANSYS is one them. Finite element analysis stware ANSYS is capable to analyze a wide range different problems. In the recent few years, there is an enormous amount research work is going on the structural analysis including the flexural or buckling thin or thick beams and plates. Still this area is open for research both at fundamental and applied level. Vanam et al. [2] presented static analysis an isotropic rectangular plate using four noded quadrilateral element. The aim study was static bending analysis an isotropic rectangular plate various boundary conditions and various types load applications. Numerical analysis has been carried out by developing programming in mathematical stware MATLAB and analyzed by using finite element analysis stware ANSYS.Kavade et al. [3] studied circular plate a hole for various types meshes. The effect an initial stretching a rectangular plate a cylindrical hole on the stress and displacement distributions around the hole was studied. Boedo analyzed [4] pre-tensioned clamped circular plate axisymmetric load for two different elements shell 63 and shell 93 in ANSYS. Results obtained are compared analytical results.vrabie and Baetu [5] analyzed an isotropic reinforced concrete plate using shell 63 and shell 181 element. Also effort was made to analyze same problem in SAP2000. Relative error in displacement by both the element and stwares is compared to a 3-D analysis. The present work aims to study effect various types meshes on the flexural deformation an isotropic circular plate. The results obtained from FEA are compared analytical results and convergence criteria is All rights Reserved

2 II. FINITE ELEMENT ANALYSIS Static bending analysis simply supported and clamped circular plate subjected to uniformly distributed load is studied. Here effect various types meshes on flexural properties plate is studied along convergence FEA solution to analytical solution based on Kirchhf s Plate Theory. Following are the values which are assumed. Diameter plate = 200 mm Aspect ratio = 10 and 20 Poisson s ratio steel (µ) = 0.3 Young s modulus steel (E) = 200 GPa Distributed load = 275 kpa Three types meshes are considered in the present study. mesh triangular element, quadrilateral element and. Figure 1, 2 and 3shows various types meshes considered for present work. Number divisions are considered along the circumference as, 40, 80,120,0 and 200. To simulate simply supported boundary conditions the translational degrees freedoms are constrained and for fixed boundary conditions, all six degrees freedom are constrained. Figure 2: triangular element Figure 2: quadrilateralel All rights Reserved 493

3 Figure 3: III. RESULTS AND DISCUSSION An isotropic circular plate is analyzed in FEA stware ANSYS for various types meshes. Results are obtained using 4 noded shell 63 element and compared analytical results. Finally convergence maximum displacement and maximum bending stress analytical solution is studied. Table 1. S. S. plate UDL (Aspect ratio = 20) All rights Reserved 494

4 Table 2. Clamped plate UDL (aspect ratio = 20) Table 3. S. S. plate UDL (Aspect ratio = 10) All rights Reserved 495

5 Table 4. Clamped plate UDL (aspect ratio = 10) In case simply supported circular plate UDL for aspect ratio 20, maximum displacement converges to analytical solution is at 80 no. div. for multi zone while for free quadrilateral element and free triangular element, it converges at 0 and 200 no. div. respectively. Similarly max. stress converges to analytical solution at no. div. for multi zone while for free quadrilateral element and free triangular element, it converges at 40 no. div. respectively (Table 1).On the other hand, clamped plate UDL for aspect ratio 20, maximum displacement converges to analytical solution at no. div. for multi zone, while for both free quadrilateral element and free triangular element, it converges at 120 no. div. respectively. Similarly max. stress converges to analytical solution at no. div. for all type (Table 2). Similar behavior is observed for simply supported (Table 3)and clamped boundary condition(table 4) for aspect ratio 10. IV. CONCLUDING REMARK Static bending analysis an isotropic circular plate is carried out using shell 63 element. Effect various types meshes on deflections and bending stresses is investigated. shows good agreement results the analytical solution hence it is preferred over other types. On the other hand, while comparing the results obtained from free quadrilateral element and free triangular element, free quadrilateral element gives better results than that free triangular element. Hence quadrilateral element is preferred over triangular element. 4 noded shell 63 element gives very accurate results in comparison analytical results obtained from Kirchhf s Plate Theory. All rights Reserved 496

6 [1]. P. S. Gujar and K. B. Ladhane, Bending Analysis Simply Supported and Clamped Circular Plate, SSRG International Journal Civil Engineering, vol. 2, issue 5, pp.69-74, [2]. B. C. L. Vanam, M. Rajyalakshmi and R. Inala, Static Analysis An Isotropic Rectangular Plate using FEA, Journal Mechanical Engineering Research,vol. 4(4), pp.148-2, [3]. G. C. Mekalke, M. V. Kavadeand S. S. Deshpande, Analysis a Plate a Circular Hole by, IOSR Journal Mechanical and Civil Engineering (IOSR-JMCE), ISSN: , pp.25-30, [4]. S. Boedo, Evaluation and comparison plate finite elements in ANSYS, NAS World Congress 99, Newport Rhode island, USA,1999. [5]. M. Vrabie and S. Baetu, Comparative Analysis the Bending Theories for Isotropic Plates- Case Study, BuletinulInstitutuluiPolitehnic Din Iasi, Publicat de UniversitateaTehnica, Gheorghe Asachi din IasiTomul LIX (LXIII), All rights Reserved 497

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