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Mechanics in Engineering ›› 2010, Vol. 32 ›› Issue (5): 45-49.doi: 10.6052/1000-0879-lxysj2010-031

• Application study • Previous Articles     Next Articles

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

  

  • Received:2010-01-21 Revised:2010-04-15 Online:2010-10-08 Published:2010-09-07

Abstract: Based on the theory of Euler-Bernoulli beams, the bending, buckling and free vibration of functionally graded material (FGM) beams were analyzed. By comparing the governing equations of functionally graded material beams and uniform beams, an analogous transform relation between the solution of FGM beam and that of uniform beam were obtained. If the material properties of FGM beam can be expressed in power functions in the lateral direction, the transformation factors between the solutions of the two kinds of beams were derived in analytical forms, which reflect the non-uniform properties of the functionally graded material beams. Therefore, the solution of static and dynamic problems of FGM beams can be transformed to that of a uniform beam and the calculation of the transformation factors under the same loadings and boundary conditions. This method can provide a simple and convenient approach in analysis of non-uniform beams and find applications in engineering.

Key words: functionally graded material beam, bending, buckling, free vibration, analogous transformation