Thermal post-buckling of functionally graded material timoshenko beams with surface-bonded piezoelectric layers
Received:March 24, 2009  Revised:June 08, 2010
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KeyWord:functionally graded material  Timoshenko beam  laminated piezoelectric beam  shoot method  thermal buckling  buckling voltage
苏厚德 兰州理工大学 理学院,兰州 ;甘肃蓝科石化高新装备股份有限公司,海洋装备部,兰州
李世荣 兰州理工大学 理学院,兰州 ;扬州大学 建筑科学与工程学院,扬州
高颖 兰州理工大学 理学院,兰州
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      Post-buckling of functionally graded material Timoshenko beams with surface-bonded piezoelectric layers subjected to temperature rise and electric field is studied. By accurately considering the axial extension and transverse shear deformation in the sense of theory of Timoshenko beam, geometrically nonlinear governing equations, for functionally graded beams subjected to thermo-electro-mechanical loadings were formulated. In the analysis, it was assumed that the material properties of the beam vary continuously as a power function of the thickness coordinate and that the piezoelectric layers are isotropic and homogenous. By using a shooting method, the obtained nonlinear boundary value problem was numerically solved and buckling and post-buckling response of the beams with the both ends fixed and subjected to transversely non-uniform heating and uniform electric field were presented. Characteristic curves of the post-buckling deformation of the beam varying with thermal load, the electrical load, and the power law index are plotted. Numerical results show that the tensional force produced in the piezoelectric layers by the voltage can efficiently increase the critical buckling temperature and defer the thermal post-buckling to occur. Due to being transversely non-uniform in the material properties, there exists tension-bending coupling effects in the beam even in uniform temperature rise in the thickness direction. However, for the piezoelectric-FGM beam with the two ends fixed the post-buckling is also bifurcation form under transversely non-uniform temperature rise.