First-order shear deformation plate models for functionally graded materials
Source abstract
Abstract
In this paper, first-order shear deformation plate models for modelling structures made of functionally graded materials are proposed. Identification of transverse shear factors is investigated through these models by energy equivalence. The transverse shear stresses are derived from the expression of membrane stresses and equilibrium equations. Using the obtained transverse shear factor, a numerical analysis is performed on the examples of a simply supported square plate and of a cylindrical bending sandwich plate clamped at both ends. The material properties are assumed to be isotropic at each point and vary through the thickness according to a power law distribution. The numerical results of the static analysis are compared to available solutions from previous studies.
Source: openaire · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Composite Structure Analysis and Optimization · Structural Analysis and Optimization · Vibration and Dynamic Analysis
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (40)
Show source-provided references
1. Berthelot · 1992
2. Un nouveau modèle de plaque multicouche épaisse
3. Exact correspondence between eigenvalues of membranes and functionally graded simply supported polygonal plates10.1006/jsvi.1999.2525 ↗
4. Three-dimensional thermoelastic deformations of functionally graded elliptic plates
5. Mechanical behavior of functionally graded material plates under transverse load – Part I: Analysis10.1016/j.ijsolstr.2005.04.011 ↗
6. Mechanical behavior of functionally graded material plates under transverse load – Part II: Numerical results10.1016/j.ijsolstr.2005.04.010 ↗
7. Three-dimensional analysis of an all-round clamped plate made of functionally graded materials10.1007/s00707-005-0270-y ↗
8. Micromechanical modelling of functionally graded materials10.1016/S0927-0256(98)00044-5 ↗
9. A review of refined shear deformation theories of isotropic and anisotropic laminated plates10.1177/073168402128988481 ↗
10. Shear correction factors in Timoshenko’s beam theory for arbitrary shaped cross-sections10.1007/s004660100239 ↗
11. Shear coefficients for Timoshenko beam theory10.1115/1.1349417 ↗
12. Active control of FGM plates with integrated piezoelectric sensors and actuators10.1016/S0020-7683(00)00050-0 ↗
13. FGM Activities in Japan10.1016/S1359-8368(96)00016-9 ↗
14. A postprocessing approach to determine transverse stresses in geometrically nonlinear composite and sandwich structures10.1177/002199803038111 ↗
15. Finite elements for functionally graded Reissner–Mindlin plates10.1016/j.cma.2003.09.014 ↗
16. Influence of rotary inertia and shear on flexural motion of isotropic elastic plates10.1115/1.4010217 ↗
17. Nonlinear transient thermoelastic analysis of functionally graded ceramic–metal plates10.1016/S0020-7683(97)00253-9 ↗
18. Static analysis of functionally graded elastic anisotropic plates using a discrete layer approach10.1016/j.compositesb.2005.05.009 ↗
19. The effect of transverse shear deformation on the bending of elastic plates10.1115/1.4009435 ↗
20. Reddy · 1999
21. Reddy · 1997
22. Analysis of functionally graded materials10.1002/(SICI)1097-0207(20000110/30)47:1/3<663::AID-NME787>3.0.CO;2-8 ↗
23. A new beam finite element for the analysis of functionally graded materials10.1016/S0020-7403(03)00058-4 ↗
24. Efficient linear transverse normal stress analysis of layered composite plates10.1016/S0045-7949(98)00097-2 ↗
25. Improved transverse shear stresses in composite finite elements based on first order shear deformation theory10.1002/(SICI)1097-0207(19970115)40:1<51::AID-NME49>3.0.CO;2-3 ↗
26. Analysis of sandwich beams with functionally graded core
27. Shear correction factors for plates and shells10.1002/nme.1620330712 ↗
28. Predictor–corrector procedures for analysis of laminated plates using standard Mindlin finite element models10.1016/S0263-8223(00)00095-7 ↗
29. Timoshenko · 1959
30. Nguyen TK, Sab K. and Bonnet G., A Reissner–Mindlin model for functionally graded materials. In: Proc of 3th European conf on Computational Mechanics, Lisbon, 6-2006.
31. Exact solution for thermoelastic deformations of functionally graded thick rectangular plates10.2514/2.1805 ↗
32. A model for thick laminates and sandwich plates10.1016/j.compscitech.2004.09.014 ↗
33. Generalized shear deformation theory for bending analysis of functionally graded materials10.1016/j.apm.2005.03.009 ↗
34. Buckling of fiber-reinforced viscoelastic composite plates using various plate theories10.1023/B:ENGI.0000042123.94111.35 ↗
35. Thermal effects on bending response of fiber-reinforced viscoelastic composite plates using a sinusoidal shear deformation theory10.1007/s00707-004-0145-7 ↗
36. Analytical solution for bending of cross-ply laminated plates under thermo-mechanical loading10.1016/j.compstruct.2003.11.012 ↗
37. A comprehensive analysis of functionally graded sandwich plates: Part 1 – Deflection and stresses10.1016/j.ijsolstr.2005.02.015 ↗
38. A comprehensive analysis of functionally graded sandwich plates: Part 2 - Buckling and free vibration10.1016/j.ijsolstr.2005.02.016 ↗
39. Derivation of effective elastic properties of two-phase materials using Voronoi cell finite element method10.1016/S0921-5093(98)00647-9 ↗
40. The superconvergent patch recovery and a posteriori error estimates Part 1: The recovery technique10.1002/nme.1620330702 ↗