journal article·2013-06

Nonlinear bending analysis of FGM beams based on physical neutral surface and high order shear deformation theory

Da-Guang Zhang

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Abstract

Model of the FGM beams is first put forward by using on physical neutral surface and high-order shear deformation theory. Nonlinear von Karman strain–displacement relationships are adopted, and material properties are assumed to be temperature dependent and vary along the thickness. It is worth noting that physical neutral surface will be changed with temperature. Therefore, the displacements have special forms, there are no stretching–bending couplings in constitutive equations, and governing equations have the simple forms, so the solution procedure is similar as homogeneous isotropic beams. The validity of physical neutral surface higher-order shear deformation beam theory can be confirmed by comparison with related researchers’ results. Nonlinear bending approximate solutions are given out using Ritz method. Physical neutral surface theory has many merits in the engineering application due to its easiness and simplicity.
Source: openaire · Quality: candidate unverified · Source record ↗

Research context

OpenAlex topics: Composite Structure Analysis and Optimization · Structural Analysis and Optimization · Nonlocal and gradient elasticity in micro/nano structures

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

References (36)

Show source-provided references
1. An elasticity solution for functionally graded beams10.1016/S0266-3538(01)00007-0 ↗
2. Elasticity solution for stresses in a sandwich beam with functionally graded core10.2514/2.6853 ↗
3. Analytical solution of a cantilever functionally graded beam10.1016/j.compscitech.2006.08.023 ↗
4. Elasticity solutions for plane anisotropic functionally graded beams10.1016/j.ijsolstr.2006.04.026 ↗
5. Two-dimensional elasticity solutions for functionally graded beams resting on elastic foundations10.1016/j.compstruct.2007.07.004 ↗
6. Exact solution of the bending vibration problem of FGM beams with variation of material properties10.1016/j.engstruct.2010.02.010 ↗
7. Modal analysis of the FGM-beams with continuous transversal symmetric and longitudinal variation of material properties with effect of large axial force10.1016/j.engstruct.2011.09.022 ↗
8. Analytical solution for functionally graded anisotropic cantilever beam under thermal and uniformly distributed load10.1631/jzus.2007.A1351 ↗
9. Carrera · 2011
10. Analysis of FGM beams by means of classical and advanced theories10.1080/15376494.2010.518930 ↗
11. Hierarchical theories for the free vibration analysis of functionally graded beams10.1016/j.compstruct.2011.07.016 ↗
12. A thermo-mechanical analysis of functionally graded beams via hierarchical modeling10.1016/j.compstruct.2012.08.013 ↗
13. Bending and free vibration of functionally graded beams using various higher-order shear deformation beam theories10.1016/j.ijmecsci.2012.05.014 ↗
14. Static analysis of functionally graded beams using higher order shear deformation theory10.1016/j.apm.2007.09.015 ↗
15. A unified approach for analyzing static and dynamic behaviors of functionally graded Timoshenko and Euler–Bernoulli beams10.1016/j.jsv.2008.04.056 ↗
16. Bending and free vibration response of layered functionally graded beams: a theoretical model and its experimental validation10.1016/j.compstruct.2007.01.019 ↗
17. A new beam finite element for the analysis of functionally graded materials10.1016/S0020-7403(03)00058-4 ↗
18. A spectrally formulated finite element for wave propagation analysis in functionally graded beams10.1016/S0020-7683(03)00029-5 ↗
19. Free vibration characteristics of a functionally graded beam by finite element method10.1016/j.apm.2010.07.006 ↗
20. Free vibration and buckling analyses of functionally graded beams with edge cracks10.1016/j.compstruct.2007.03.006 ↗
21. Nonlinear free vibration of functionally graded carbon nanotube-reinforced composite beams10.1016/j.compstruct.2009.09.024 ↗
22. Non-linear vibration analysis of a functionally graded Timoshenko beam under action of a moving harmonic load10.1016/j.compstruct.2010.02.008 ↗
23. Nonlinear free vibration and post-buckling analysis of functionally graded beams on nonlinear elastic foundation10.1016/j.euromechsol.2011.01.005 ↗
24. Thermo-mechanical buckling and nonlinear free vibration analysis of functionally graded beams on nonlinear elastic foundation10.1016/j.compositesb.2011.08.041 ↗
25. A further discussion of nonlinear mechanical behavior for FGM beams under in-plane thermal loading10.1016/j.compstruct.2010.07.011 ↗
26. Exact solutions for nonlinear static responses of a shear deformable FGM beam under an in-plane thermal loading10.1016/j.euromechsol.2011.06.016 ↗
27. Thermal post-buckling of functionally graded material Timoshenko beams10.1007/s10483-006-0611-y ↗
28. Geometric nonlinear analyses of functionally graded beams using a tailored Lagrangian formulation10.1016/j.mechrescom.2011.07.006 ↗
29. Large deflection of functionally graded cantilever flexible beam with geometric nonlinearity: analytical and numerical approaches
30. Large deflection of flexible tapered functionally graded beam10.1007/s10409-011-0476-2 ↗
31. Functionally graded plates behave like homogeneous plates10.1016/j.compositesb.2007.02.026 ↗
32. A theoretical analysis of FGM thin plates based on physical neutral surface10.1016/j.commatsci.2008.05.016 ↗
33. A higher order beam finite element for bending and vibration problems10.1016/0022-460X(88)90244-1 ↗
34. Touloukian · 1967
35. Thermoelastical analysis of functionally graded cylinders and plates10.1080/01495739808956165 ↗
36. A novel technique for nonlinear analysis of beams on two-parameter elastic foundations10.1142/S0219455411004440 ↗