Elastic foundation analysis of uniformly loaded functionally graded viscoelastic sandwich plates

Journal of Mechanics

Volumn 28, Issue 3, 2012, Pages 439-452

  Zenkour, A M ^a,b   Sobhy, M ^b  

^a KING ABDULAZIZ UNIVERSITY   (Saudi Arabia)

^b Kafrelsheikh University   (Egypt)

Author keywords

FG viscoelastic sandwich plate; Pasternak's foundations; Trigonometric plate theory; Uniform load

Indexed keywords

BENDING ANALYSIS; ELASTIC CORE; ELASTIC FOUNDATION; ELASTIC-VISCOELASTIC; EQUILIBRIUM EQUATION; FOUNDATION STIFFNESS; FUNCTIONALLY GRADED; GOVERNING EQUATIONS; LOADING TYPES; MATERIAL PROPERTY; PARAMETRIC STUDY; PASTERNAK; PLATE ASPECT RATIO; PLATE THEORIES; POWER LAW INDEX; POWER LAW VARIATION; SANDWICH PLATES; SHEAR DEFORMATION PLATE THEORIES; SIMPLY SUPPORTED; STATIC RESPONSE; TIME PARAMETER; UNIFORM LOADS;

ASPECT RATIO; BIOLOGICAL ORGANS; FUNCTIONALLY GRADED MATERIALS; INTERFACES (MATERIALS); LOADING;

VISCOELASTICITY;

EID: 84864935622     PISSN: 17277191     EISSN: 18118216     Source Type: Journal    
DOI: 10.1017/jmech.2012.53     Document Type: Article

References (37)

1. Reddy, J. N. and Cheng, Z. Q., "Three-Dimensional Thermomechanical Deformations of Functionally Graded Rectangular Plates," European Journal of Mechanics A/Solids, 20, pp. 841-855 (2001).
2. Reddy, J. N., "Analysis of Functionally Graded Plates," International Journal for Numerical Methods Engineering, 47, pp. 663-684 (2000).
3. Brischetto, S. and Carrera, E., "Advanced Mixed Theories for Bending Analysis of Functionally Graded Plates," Computers & Structures, 88, pp. 1474-1483 (2010).
4. Zenkour, A. M., "Generalized Shear Deformation Theory for Bending Analysis of Functionally Graded Plates," Applied Mathematical Modelling, 30, pp. 67-84 (2006).
5. Zenkour, A. M., "Benchmark Trigonometric and 3-D Elasticity Solutions for an Exponentially Graded Thick Rectangular Plate," Archives of Applied Mechanics, 77, pp. 197-214 (2007).
6. Zenkour, A. M., "On Vibration of Functionally Graded Plates According to a Refined Trigonometric Plate Theory," International Journal of Structural Stability and Dynamics, 5, pp. 279-297 (2005).
7. Yang, J. and Shen, H.-S., "Dynamic Response of Initially Stressed Functionally Graded Rectangular Thin Plates," Composite Structures, 54, pp. 497-508 (2001).
8. Yang, J. and Shen, H.-S., "Non-Linear Analysis of Functionally Graded Plates Under Transverse and In-Plane Loads," International Journal of Non-Linear Mechanics, 38, pp. 467-482 (2003).
9. Chakraborty, A., Gopalakrishnan, S. and Reddy, J. N., "A New Beam Finite Element for the Analysis of Functionally Graded Materials," International Journal of Mechanical Sciences, 45, pp. 519-539 (2003).
10. Sankar, B. V., "An Elasticity Solution for Functionally Graded Beams," Composites Science and Technology, 61, pp. 689-696 (2001).
11. Reddy, J. N., Wang, C. M. and Kitipornchai, S., "Axisymmetric Bending of Functionally Graded Circular and Annular Plates," European Journal of Mechanics A/Solids, 18, pp. 185-199 (1999).
12. Arciniega, R. A. and Reddy, J. N., "Large Deformation Analysis of Functionally Graded Shells," International Journal of Solids and Structures, 44, pp. 2036-2052 (2007).
13. Bekuit, J.-J. R. B., Oguamanam, D. C. D. and Damisa, O., "A Quasi-2D Finite Element Formulation for the Analysis of Sandwich Beams," Finite Elements in Analysis and Design, 43, pp. 1099-1107 (2007).
14. Chen, Y.-R. and Chen, L.-W., "Vibration and Stability of Rotating Polar Orthotropic Sandwich Annular Plates with a Viscoelastic Core Layer," Composite Structures, 78, pp. 45-57 (2007).
15. Hazard, L. and Bouillard, P., "Structural Dynamics of Viscoelastic Sandwich Plates by the Partition of Unity Finite Element Method," Computer Methods in Applied Mechanics and Engineering, 196, pp. 4101-4116 (2007).
16. Chen, Q. and Chan, Y. W., "Integral Finite Element Method for Dynamical Analysis of Elastic-Viscoelastic Composite Structures," Composite Structures, 74, pp. 51-64 (2000).
17. Koutsawa, Y., Haberman, M. R., Daya, E. M. and Cherkaoui, M., "Multiscale Design of a Rectangular Sandwich Plate with Viscoelastic Core and Supported at Extents by Viscoelastic Materials," International Journal of Mechanical Materials & Design, 5, pp. 29-44 (2009).
18. Zenkour, A. M., "A Comprehensive Analysis of Functionally Graded Sandwich Plates: Part 1-Deflection and Stresses," International Journal of Solids and Structures, 42, pp. 5224-5242 (2005).
19. Zenkour, A. M., "A Comprehensive Analysis of Functionally Graded Sandwich Plates: Part 2-Buckling and Free Vibration," International Journal of Solids and Structures, 42, pp. 5243-5258 (2005).
20. Zenkour, A. M. and Alghamdi, N. A., "Thermoelastic Bending Analysis of Functionally Graded Sandwich Plates," Journal of Materials Science, 43, pp. 2574-2589 (2008).
21. Shodja, H. M., Haftbaradaran, H. and Asghari, M., "A Thermoelasticity Solution of Sandwich Structures with Functionally Graded Coating," Composites Science and Technology, 67, pp. 1073-1080 (2007).
22. Zhao, J., Li, Y. and Ai, X., "Analysis of Transient Thermal Stress in Sandwich Plate with Functionally Graded Coatings," Thin Solid Films, 516, pp. 7581-7587 (2008).
23. Anderson, T. A., "A 3D Elasticity Solution for a Sandwich Composite with Functionally Graded Core Subjected to Transverse Loading by a Rigid Sphere," Composite Structures, 60, pp. 265-274 (2003).
24. Kashtalyan, M. and Menshykova, M., "Three-Dimensional Elasticity Solution for Sandwich Panels with a Functionally Graded Core," Composite Structures, 87, pp. 36-43 (2009).
25. Avramidis, I. E. and Morfidis, K., "Bending of Beams on Three-Parameter Elastic Foundation," International Journal of Solids and Structures, 43, pp. 357-375 (2006).
26. Abdalla, J. A. and Ibrahim, A. M., "Development of a Discrete Reissner-Mindlin Element on Winkler Foundation," Finite Elements in Analysis and Design, 42, pp. 740-748 (2006).
27. Ergüven, M. E. and Gedikli, A., "A Mixed Finite Element Formulation for Timoshenko Beam on Winkler Foundation," Computational Mechanical, 31, pp. 229-237 (2003).
28. Chucheepsakul, S. and Chinnaboon, B., "Plates on Two-Parameter Elastic Foundations with Nonlinear Boundary Conditions by the Boundary Element Method," Composite Structures, 81, pp. 2739-2748 (2003).
29. Sheng, C. X., "A Free Rectangular Plate on Elastic Foundation," Applied Mathematics and Mechanics, 13, pp. 977-982 (1992).
30. Zhou, D., Lo, S. H., Au, F. T. K. and Cheung, Y. K., "Three- Dimensional Free Vibration of Thick Circular Plates on Pasternak Foundation," Journal of Sound and Vibration, 292, pp. 726-741 (2006).
31. Huang, Z. Y., Lü, C. F. and Chen, W. Q., "Benchmark Solutions for Functionally Graded Thick Plates Resting on Winkler-Pasternak Elastic Foundations," Composite Structures, 85, pp. 95-104 (2008).
32. Malekzadeh, P., "Three-Dimensional Free Vibration Analysis of Thick Functionally Graded Plates on Elastic Foundations," Composite Structures, 89, pp. 367-373 (2009).
33. Illyushin, A. A. and Pobedrya, B. E., Foundation of Mathematical Theory of Thermo Viscoelasticity, Moscow, Nauka, in Russian (1970).
34. Allam, M. N. M. and Zenkour, A. M., "Bending Response of a Fiber-Reinforced Viscoelastic Arched Bridge Model," Applied Mathematical Modelling, 27, pp. 233-248 (2003).
35. Zenkour, A. M., "Buckling of Fiber-Reinforced Viscoelastic Composite Plates Using Various Plate Theories," Journal of Engineering Mathematics, 50, pp. 75-93 (2004).
36. Buczkowski, R. and Torbacki, W., "Finite Element Modeling of Thick Plates on Two-Parameter Elastic Foundation," International Journal for Numerical and Analytical Methods in Geomechanics, 25, pp. 1409-1427 (2001).
37. Timoshenko, S. P. and Woinowsky-Krieger, W., Theory of Plates and Shells, New-York, McGraw-Hill (1970).