ANALOGOUS TRANSFORMATION OF STATIC AND DYNAMIC SOLUTIONS BETWEEN FUNCTIONALLY GRADED MATERIAL BEAMS AND UNIFORM BEAMS

Based on the theory of Euler-Bernoulli beams, the bending, buckling and freevibration of functionally graded material (FGM) beams were analyzed. Bycomparing the governing equations of functionally graded material beams anduniform beams, an analogous transform relation between the solution of FGM beamand that of uniform beam were obtained. If the material properties ofFGM beam can be expressed in power functions in the lateral direction,the transformationfactors between the solutions of the two kinds of beams were derived inanalytical forms, which reflect the non-uniform properties of thefunctionally graded material beams. Therefore, the solution of static and dynamicproblems of FGM beams can be transformed to that of a uniform beam andthe calculation of the transformation factors under the same loadings and boundaryconditions. This method can provide a simple and convenient approach inanalysis of non-uniform beams and find applications in engineering.