Static and Dynamic Stability Analysis of a Sigmoid Functionally Graded Timoshenko Beam

Thisarticle presents the evaluation of static and dynamic behavior of simply supported sigmoid functionally graded ordinary (SFGO) beam. A finite element method is used considering first order shear deformation for the analysis.The element chosen in the present case is different from the conventional elements in the sense that the shape functions of the element is obtained from the exact solution of the static part of the governing differential equation derived from Hamilton’s principle. Along with this the shape functions are dependent on length, material and cross-sectional properties ensuring better accuracy of the solution. The material properties are assumed to follow sigmoid distribution of power law. It is observed that an SFGO beam with lower power index is a batter beam as per as parametric instability is concerned. Key wordsDynamic Stability, sigmoid distribution, Power law, Static load factor, Dynamic load factor.