Linear transformation between the bending solutions of functionally graded and homogenous circular plats

Based on the first-order shear deformation theory (FSDT),linear transformation relationship between bending solutions of functionallygraded material (FGM) and homogenous circular plates was studied. Firstly,through theoretically analyzing and comparing the displacement-typegoverning equations for axially symmetrically bending of FGM and homogenouscircular plates based on the first-order shear deformation theory, linearlydependent relationship between the rotational angles of FGM circular plateand those of homogenous one was found. By giving the material properties ofFGM circular plates changing as continuous functions in the thicknessdirection, the corresponding transition factor between the solutions of thetwo kind plates were derived in analytical forms. Furthermore, a linearrelationship between the deflections of FGM circular plate based on FSDT andthose of homogenous one based on the classical plate theory were derived. Asa result, solutions for static bending based on the first-order sheardeformation plate theory of a non-homogenous circular plate can be reducedto that based on classical plate theory of a homogenous one and thecalculation of the transformation factors. This approach provides a simpleand facile procedure for solutions of the non-homogenous moderately thickFGM circular plates, which can be very easily and conveniently used inengineering. By using the above mentioned approach, analytical bendingsolutions of FGM circular plates with simply supported as well as clampedboundary conditions under uniformly distributed lateral force werepresented, which show a very good agreement with the results given by Reddy.