ANALOGOUS RELATIONSHIP BETWEEN THE STATIC SOLUTIONS OF FUNCTIONALLY GRADED BEAMS AND HOMOGENOUS BEAMS BASED ON THE FIRST-ORDER SHEAR DEFORMATION THEORY

Based on the first order shear deformation theory, linear transformative relation between the static bending solution of the functionally graded Timoshenko beams and the corresponding homogenous material beams were analyzed. Through comparing non-dimensional governing equations of functionally graded material beams and the corresponding homogenous beams, linearly dependant relation between their bending solutions was found. When the law of variation of the elastic modulus in the lateral direction is specified, the bending solution of the FGM Timoshenko beams can be linearly expressed by that of homogenous beams with the same geometry, the same loadings and the same constraints. Consequently, solutions of the bending problem of a non-homogenous Timoshenko beam can be reduced to that of a homogenous one and the calculation of the transition parameters, which simplifies the solution procedure.