Non-linear Static Modeling of Moderately Thick Functionally Graded Plate Using Dynamic Relaxation Method

Document Type : Persian

Authors

1 Assistant Professor, Shahid Beheshti University, Tehran, Iran.

2 PhD Student, Shahid Beheshti University, Tehran, Iran.

Abstract

In this paper, nonlinear static analysis of moderately thick plate made of functionally graded materials subjected to mechanical transverse loading is carried out using dynamic relaxation method. Mindlin first order shear deformation theory is employed to consider thick plate. Discretized equations are extracted for geometrically nonlinear behavior analysis.Loading Conditions and boundary conditions of the plate are uniformly distributed transverse load and simply supported at the four edges of the thick plate, respectively. In order to generalize the obtained results, the equations are solved by applying dynamic relaxation method based on central finite deference discretization in the non-dimensional form. The effects of problem parameters such as gradient constant of the functionally graded material and the side to thickness ratio of plate on the results are investigated. According to the obtained results, the need of including elastic large deflection and applying the theory which considers the effects of plate thickness on the plate bending response and also finally the need of employing dynamic relaxation solution method despite the non-linear terms resulted from large deflection of the functionally graded thick plate are discussed.

Keywords

References

[1] Koizumi M., The concept of FGM, Ceramic Transactions, Functionally Gradient. Materials, vol. 34, 1993, pp. 3-10.
[2] Aboudi J., Pindera M.J., Arnold S.M., Thermoelastic theory for the response of materials functionally graded in Two Directions, International Journal of Solid and Structures, vol. 33, 1996, pp. 931-966.
[3] Aboudi J., Pindera M.J., Arnold S.M., Elastic response of metal matrix composites with tailores microstructures to thermal gradient, International Journal of Solid and Structures, vol. 31, 1994, pp. 1393-1428.
[4] Aboudi J., Pindera M.J., Arnold S.M., Higher order theory for functionally graded materials, Composites Part B, vol. 30, 1999, pp. 777-832.
[5] Reddy J.N., Praveen G.N., Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates, , International Journal of Solid and Structures, vol. 35, 1998, pp. 4457-4476.
[6] Reddy J.N., Wang C.M., Kitipornchai S., Axisymmetric bending of functionally graded circular and annular plates, , European Journal of Mechanics A/Solids, vol. 18, 1999, pp. 185-199.
[7] Reddy J.N., Analysis of functionally graded plates, International Journal for Numerical Method in Engineering, vol. 47, 2000, pp. 663-684.
[8] Reddy J.N., Cheng Z.Q., Three-dimensional thermo-mechanical deformation of functionally graded rectangular plate, European Journal of Mechanics A/Solids, vol. 20, 2001, pp. 841-855.
[9] Cheng Z.Q., Batra R.C., Three-dimensional deformation of a functionally graded elliptic plate, Composite Part B, vol. 31, 2000, pp. 97-106.
[10] Cheng Z.Q., BatraR.C., Deflection relationships between the homogeneous Kirchhoff plate theory and different functionally graded plate theories, Archive of mechanics, vol. 52, 2000, pp. 143-158.
[11] Kashtalyan M., Three-dimensional elasticity solution for bending of functionally graded rectangular plates,European Journal of Mechanics A/Solids, vol. 23, 2004, pp. 853-864.
[12]  Woo J., Meguid S.A., Nonlinear analysis of functionally graded platesand shallow shells,International Journal of Solid and Structures, vol. 38, 2001, pp. 9-21.
[13] Yang J., Shen H.S., Non-linear analysis of functionally graded plates under transverse and in-plane loads, International Journal of Non-linear Mechanics, vol. 38, 2003, pp. 467-482.
[14]  Ghannad Pour S.A.M., Alinia M.M., Large deflection behavior of functionally graded plates under pressure loads, Composite Structures, 75, 2006, pp. 67-71.
[15]  Alibeigloo A., Exact solution for thermo-elastic response of functionally graded rectangular plates, Composite Structures, vol. 92, 2010, pp. 113-121.
[16] Kumar J.S., Reddy B.S., Reddy C.E., Nonlinear bending analysis of functionally graded plates using higher order theory, International Journal of Engineering Science and Technology, vol. 3, 2012, pp. 3010-3022.
[17] Otter J.R.H., Day A.S., Tidal flow computations, The Engineer, 209, 1960, pp. 177-182.
[18] DayA.S., An introduction to dynamic relaxation, The Engineer, vol. 19, 1965, pp. 218-221.
[19] Otter J.R.H., Computations for prestressed concrete reactor pressure vessels using dynamic relaxation, Nuclear Structural Engineering, vol. 1, 1965, pp. 61-75.
[20] Turvey G.J., Osman M.Y., Elastic large deflection analysis of isotropic rectangular Mindlin plates, International Journal of Mechanical sciences, vol. 32, 1990, pp. 315-328.
[21] Falahatgar S.R., Salehi M., Dynamic relaxation nonlinear viscoelastic analysis of annular sector composite plate, Journal of Composite Materials, vol. 43, 2009, pp. 257-275.
[22] Turvey G.J., Salehi M., DR large deflection analysis of sector plates, Computers and Structures, vol. 34, 1990, pp. 101-112.
[23] Turvey G.J., Salehi M., Computer-generated elasto-plastic design data for pressure loaded circular plates, Computers and Structures, vol. 41, 1991, pp. 1329-1340.
[24] Salehi M., Shahidi A.G., Large deflection analysis of sector Mindlin plates, Computers and Structures, vol. 52, 1994, pp. 987-998.
[1] Koizumi M., The concept of FGM, Ceramic Transactions, Functionally Gradient. Materials, vol. 34, 1993, pp. 3-10.
[2] Aboudi J., Pindera M.J., Arnold S.M., Thermoelastic theory for the response of materials functionally graded in Two Directions, International Journal of Solid and Structures, vol. 33, 1996, pp. 931-966.
[3] Aboudi J., Pindera M.J., Arnold S.M., Elastic response of metal matrix composites with tailores microstructures to thermal gradient, International Journal of Solid and Structures, vol. 31, 1994, pp. 1393-1428.
[4] Aboudi J., Pindera M.J., Arnold S.M., Higher order theory for functionally graded materials, Composites Part B, vol. 30, 1999, pp. 777-832.
[5] Reddy J.N., Praveen G.N., Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates, , International Journal of Solid and Structures, vol. 35, 1998, pp. 4457-4476.
[6] Reddy J.N., Wang C.M., Kitipornchai S., Axisymmetric bending of functionally graded circular and annular plates, , European Journal of Mechanics A/Solids, vol. 18, 1999, pp. 185-199.
[7] Reddy J.N., Analysis of functionally graded plates, International Journal for Numerical Method in Engineering, vol. 47, 2000, pp. 663-684.
[8] Reddy J.N., Cheng Z.Q., Three-dimensional thermo-mechanical deformation of functionally graded rectangular plate, European Journal of Mechanics A/Solids, vol. 20, 2001, pp. 841-855.
[9] Cheng Z.Q., Batra R.C., Three-dimensional deformation of a functionally graded elliptic plate, Composite Part B, vol. 31, 2000, pp. 97-106.
[10] Cheng Z.Q., BatraR.C., Deflection relationships between the homogeneous Kirchhoff plate theory and different functionally graded plate theories, Archive of mechanics, vol. 52, 2000, pp. 143-158.
[11] Kashtalyan M., Three-dimensional elasticity solution for bending of functionally graded rectangular plates,European Journal of Mechanics A/Solids, vol. 23, 2004, pp. 853-864.
[12]  Woo J., Meguid S.A., Nonlinear analysis of functionally graded platesand shallow shells,International Journal of Solid and Structures, vol. 38, 2001, pp. 9-21.
[13] Yang J., Shen H.S., Non-linear analysis of functionally graded plates under transverse and in-plane loads, International Journal of Non-linear Mechanics, vol. 38, 2003, pp. 467-482.
[14]  Ghannad Pour S.A.M., Alinia M.M., Large deflection behavior of functionally graded plates under pressure loads, Composite Structures, 75, 2006, pp. 67-71.
[15]  Alibeigloo A., Exact solution for thermo-elastic response of functionally graded rectangular plates, Composite Structures, vol. 92, 2010, pp. 113-121.
[16] Kumar J.S., Reddy B.S., Reddy C.E., Nonlinear bending analysis of functionally graded plates using higher order theory, International Journal of Engineering Science and Technology, vol. 3, 2012, pp. 3010-3022.
[17] Otter J.R.H., Day A.S., Tidal flow computations, The Engineer, 209, 1960, pp. 177-182.
[18] DayA.S., An introduction to dynamic relaxation, The Engineer, vol. 19, 1965, pp. 218-221.
[19] Otter J.R.H., Computations for prestressed concrete reactor pressure vessels using dynamic relaxation, Nuclear Structural Engineering, vol. 1, 1965, pp. 61-75.
[20] Turvey G.J., Osman M.Y., Elastic large deflection analysis of isotropic rectangular Mindlin plates, International Journal of Mechanical sciences, vol. 32, 1990, pp. 315-328.
[21] Falahatgar S.R., Salehi M., Dynamic relaxation nonlinear viscoelastic analysis of annular sector composite plate, Journal of Composite Materials, vol. 43, 2009, pp. 257-275.
[22] Turvey G.J., Salehi M., DR large deflection analysis of sector plates, Computers and Structures, vol. 34, 1990, pp. 101-112.
[23] Turvey G.J., Salehi M., Computer-generated elasto-plastic design data for pressure loaded circular plates, Computers and Structures, vol. 41, 1991, pp. 1329-1340.
[24] Salehi M., Shahidi A.G., Large deflection analysis of sector Mindlin plates, Computers and Structures, vol. 52, 1994, pp. 987-998.
[25] Turvey G.J., SalehiM., Circular plates with one diametral stiffener-an elastic large deflection analysis, Computersand Structures, vol. 63, 1997, pp. 775-783.
[26] Golmakani E., KadkhodayanM., Nonlinear bending analysis of annular FGM plates using higher-order shear deformation plate Theories, Composite Structures, vol. 93, 2011, pp. 973-982.
[27] Delale F., Erdogan F., The crack problem for a nonhomogeneous plane, ASME Journal of Applied Mechanics, vol. 50, 1983, pp. 609-614.
[28] Reddy J.N., Mechanics of laminated Composite Plates and Shells Theory and Analysis, Second Edition, CRC Press, 2004, Boca Raton, FL.
[29] Chajes A., Principles of Structural Stability Theory, Prentice-Hall, 1974.
[30] Cassel A.C., Hobbs R.E., Numerical stability of dynamic relaxation analysis of non-linear structures, International Journal for Numerical Methods in Engineering, vol. 10, 1976. pp. 1407-1410.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering
Volume 8, Issue 1 - Serial Number 1
February 2015
Pages 13-37

Files

Share

How to cite

Statistics