A Novel Method for Numerical Analysis of 3D Nonlinear Thermo-Mechanical Bending of Annular and Circular Plates with Asymmetric Boundary Conditions Using SAPM

Subject Areas : Mechanical Engineering

A. R Golkarian ¹ ( Department of Mechanical Engineering, Science & Research Branch, Islamic Azad University, Tehran, Iran )
M Jabbarzadeh ² ( Department of Mechanical Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran )
Sh Dastjerdi ³ ( Department of Mechanical Engineering, Shahrood Branch, Islamic Azad University, Shahrood, Iran )

Received: 2019-03-30 Accepted : 2019-05-26 Published : 2019-09-30

Keywords: Annular plates, 3D elasticity, SAPM, Asymmetry, Nonlinear bending,

Abstract :

This study is the first report of numerical solution of nonlinear bending analysis for annular and circular plates based on 3D elasticity theory with asymmetric boundary conditions using semi-analytical polynomial method (SAPM). Orthotropic annular and circular plates are subjected to transverse loading and 3D bending analysis in the presence of symmetric and asymmetric boundary conditions is studied. For asymmetry cases, the plate boundaries are divided to two or three parts and various boundary conditions such as clamped, simply-supported and free edges are defined for each part. The asymmetry in one and two directions is studied. The influence of elastic foundations, mechanical and thermo-mechanical loadings are examined. Regarding this fact that no study has been done in the case of asymmetric boundary conditions, the obtained results are compared with FEM results by ABAQUS. The results show good agreement with the literatures and FEM results, which it shows that the presented method can use to analyze the 3D bending of plates under asymmetric conditions. Also, it is observed that 3D elasticity estimates some higher deflections than other theories. But, the obtained results by 3D elasticity theory and those obtained by FEM analysis in the case of asymmetric conditions are so close.

References:

[1] Kirchhoff G., 1850, Über das Gleichgwich und die Bewegung einer elastischen Scheibe, Journal für die Reine und Angewandte Mathematik 40: 51-88.
[2] Tsiatas G.C., 2009, A new Kirchhoff plate model based on a modified couple stress theory, International Journal of Solids and Structures 46(13): 2757-2564.
[3] Mindlin R.D., 1951, Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates, ASME Journal of Applied Mechanics 18: 31-38.
[4] Reissner E., 1945, The effect of transverse shear deformation on the bending of elastic plates, ASME Journal of Applied Mechanics 12: 68-77.
[5] Lou J., He L., Du J., 2015, A unified higher order plate theory for functionally graded microplates based on the modified couple stress theory, Composite Structures 133: 1036-1047.
[6] Reddy J.N., 1984, A simple higher-order theory for laminated composite plates, Journal of Applied Mechanics 51(4): 745-752.
[7] Touratier M., 1991, An efficient standard plate theory, International Journal of Engineering Science 29(8): 901-916.
[8] Soldatos K., 1992, A transverse shear deformation theory for homogeneous monoclinic plates, Acta Mechanica 94 (3): 195-220.
[9] Ferreira A.J.M., Roque C.M.C., Jorge R.M.N., 2005, Analysis of composite plates by trigonometric shear deformation theory and multiquadrics, Computers & Structures 83(27): 2225-2237.
[10] Karama M., Afaq K.S., Mistou S., 2003, Mechanical behavior of laminated composite beam by the new multi-layered laminated composite structures model with transverse shear stress continuity, International Journal of Solids and Structures 40(6): 1525-1546.
[11] Thai H-T., Vo T.P., 2013, A size-dependent functionally graded sinusoidal plate model based on a modified couple stress theory, Composite Structures 96: 376-383.
[12] Reddy J.N., Berry J., 2012, Nonlinear theories of axisymmetric bending of functionally graded circular plates with modified couple stress, Computers & Structures 94(12): 3664-3668.
[13] Reddy J.N., Romanoff J., Loya J.A., 2016, Nonlinear finite element analysis of functionally graded circular plates with modified couple stress theory, European Journal of Mechanics -A/Solids 56: 92-104.
[14] Dastjerdi S., Jabbarzadeh M., 2016, Nonlocal bending analysis of bilayer annular/circular nano plates based on first order shear deformation theory, Journal of Solid Mechanics 8: 645-661.
[15] Dastjerdi S., Jabbarzadeh M., 2016, Non-local thermo-elastic buckling analysis of multi- layer annular/circular nano-plates based on first and third order shear deformation theories using DQ method, Journal of Solid Mechanics 8: 859-874.
[16] Dastjerdi S., Abbasi M., Yazdanparast L., 2017, A new modified higher-order shear deformation theory for nonlinear analysis of macro- and nano-annular sector plates using the extended Kantorovich method in conjunction with SAPM, Acta Mechanica 228(10): 3381-3401.
[17] Yang B., Kitipornchai S., Yang Y.F., Yang J., 2017, 3D Thermo-mechanical bending solution of functionally graded graphene reinforced circular and annular plates, Applied Mathematical Modelling 49: 69-86.
[18] Tielking J.T., 1979, Asymmetric bending of annular plated, International Journal of Solids and Structures 16: 361-373.
[19] Pardoen G.C., 1975, Asymmetric bending of circular plates using the finite element method, Computers & Structures 5: 197-202.
[20] Al Jarbouh A., 2015, Mechanical modelling for the behavior of the metallic plate under the effect of bending loads, Energy Procedia 74: 1119-1132.
[21] Timoshenko S., Woinowsky-Krieger S., 1959, Theories of Plates and Shells, New York, McGraw-Book Company.
[22] Damkilde L.,Continuum Materials, Aalborg Universitet Esbjerg, IOP Publishing Homes Civil.
[23] Dastjerdi S., Jabbarzadeh M., 2017, Non-linear bending analysis of multi-layer orthotropic annular/circular graphene sheets embedded in elastic matrix in thermal environment based on non-local elasticity theory, Applied Mathematical Modelling 41: 83-101.
[24] Altekin M., Yu¨ kseler R.F., 2011,Proceedings of the World Congress on Engineering, London, U.K.
[25] Szilard R., 1974, Theory and Analysis of Plates, Engle wood Cliffs, Prentice-Hall Inc.
[26] Reddy J.N., Wang C.M., Kitipornchai S., 1999, Axisymmetric bending of functionally grade circular and annular plates, European Journal of Mechanics -A/Solids 18: 185-199.
[27] Golmakani M.E., 2013, Non-linear bending analysis of ring-stiffened functionally graded circular plates under mechanical and thermal loadings, International Journal of Mechanical Sciences 79: 130-142.
[28] Reddy J.N., Romanoff J., Loya J.A., 2016, Nonlinear finite element analysis of functionally graded circular plates with modified couple stress theory, European Journal of Mechanics -A/Solids 56: 92-104.
[29] Hosseini Kordkheili S.A., Moshrefzadeh-Sani H., 2013, Mechanical properties of double-layered graphene sheets, Computational Materials Science 69: 335-343.