NONLINEAR MECHANICAL BEHAVIORS OF FGM BEAMS BASED ON THE PHYSICAL NEUTRAL SURFACE

The stretching-bending coupling in constitutive equations of a functionally graded materials (FGM) beam does not exist when the coordinate system is located at the physical neutral surface of the FGM beam, thus the governing equations and boundary conditions for the FGM beam can be simplified. Based on the non-linear first-order shear deformation beam theory (FBT), the basic equations of the FGM beam are derived using the physical neutral surface concept. The thermal post-buckling, thermal bending and vibration response of postbuckled or bended configurations of an FGM beam subjected to uniformly thermal loads are investigated. It was assumed that the properties of the functionally graded material vary continuously only with the thickness of the beam and their variation has a simple power law distribution with the volume fraction of the constituents. The shooting method is employed to numerically solve the resulting equations. Numerical results obtained herein showed that thermal loads can cause the post-buckling deformations in a clamped FGM beam, while more complex thermal bending deformations in a simple supported beam. And moreover, the dynamic behavior of a clamped FGM beam was also different from that of the simple supported beam. Transversely shear deformation played an important role in the mechanical behavior of the FGM beams.