Geometrically Nonlinear Analysis of Functionally Graded Beams Under Thermomechanical Loading

WANG Xue; ZHAO Weidong

doi:10.21656/1000-0887.390201

Volume 40 Issue 5

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WANG Xue, ZHAO Weidong. Geometrically Nonlinear Analysis of Functionally Graded Beams Under Thermomechanical Loading[J]. Applied Mathematics and Mechanics, 2019, 40(5): 508-517. doi: 10.21656/1000-0887.390201

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Geometrically Nonlinear Analysis of Functionally Graded Beams Under Thermomechanical Loading

doi: 10.21656/1000-0887.390201

School of Civil Engineering, Qinghai University, Xining 810016, P.R.China

Received Date: 2018-07-18
Rev Recd Date: 2018-10-03
Publish Date: 2019-05-01

Abstract

Abstract

Based on the classical beam theory, the geometric nonlinear governing equations for FGM beams under uniform temperature field and uniform transverse loading were derived according to the principle of virtual work and the variational method. In view of the immovably clamped boundary conditions, the 2-point boundary value problem was solved with the shooting method. For the zero uniform transverse loading, the thermal buckling critical temperature and equilibrium path of the FGM beam were investigated. The load-deflection curves of the FGM beam were given for the nonzero uniform temperature and the nonzero transverse uniform loading. The numerical results show that, the dimensional thermal buckling critical temperature of the beam decreases significantly and the post-buckling deformation increases significantly with the material volume fraction index increases, and the temperature variation has a heavy influence on the load-deflection curves. The bistable configurations and the switch of the FGM beam were found. The final equilibrium shape of the beam is not only related to the variable temperature and loading parameters, but also to the loading process.
- functionally graded beam,
- thermomechanical loading,
- load-deflection curve,
- bistable configuration,
- shooting method

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References(21)

References

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