GREEN’S FUNCTION METHOD FOR STATIC AND DYNAMIC ANALYSIS OF FUNCTIONALLY GRADED BEAMS

The numerical analysis of static and dynamic problems of functionally graded material beams is usually conducted with the finite element method and suffers from the inherent deficiencies of the method. The governing equations for static analysis of functionally graded material beams are transformed to the forms for static analysis of isotropic material beams, and the Green’s functions corresponding to isotropic material beams are used for static analysis of functionally graded material beams. On this basis, the compliance matrix of a functionally graded material beam is further derived, and the equation of motion is established and solved for the dynamic problem of the functionally graded material beam. Numerical examples show that the proposed method can analyze the static and dynamic problems of functionally graded material beams with high efficiency and accuracy, indicating the feasibility of the present approach.