Static and vibration analysis of functionally graded beams using refined shear deformation theory

Static and vibration analysis of functionally graded beams using refined shear deformation theory is presented. The developed theory, which does not require shear correction factor, accounts for shear deformation effect and coupling coming from the material anisotropy. Governing equations of motion are derived from the Hamilton's principle. The resulting coupling is referred to as triply coupled axial-flexural response. A two-noded Hermite-cubic element with five degree-of-freedom per node is developed to solve the problem. Numerical results are obtained for functionally graded beams with simply-supported, cantilever-free and clamped-clamped boundary conditions to investigate effects of the power-law exponent and modulus ratio on the displacements, natural frequencies and corresponding mode shapes.