Relationship between bending solutions of FGM and homogenous circular cylindrical shells

摘要

Based on the Love's shell theory, relationship between bending solutions of functionally graded materials (FGM) and homogenous circular cylindrical shells was studied. By comparing the displacement-type governing equations for axially symmetrically bending of FGM and homogenous circular cylindrical shells, an analogous transform relation between the deflections of FGM circular cylindrical shell and those of homogenous one was obtained. By giving the material properties of FGM circular cylindrical shell changing as continuous functions in the thickness direction, the corresponding transition factor between the solutions of the two kind circular cylindrical shells were derived, which reflect the non-uniform properties of the functionally graded material circular cylindrical shell. Numerical example shows that the numerical solutions of the maximum of non-dimensional deflections are almost in agreement with the transformational solutions when n equals approximately 5, where n is the volume fraction index. As a result, solutions for axially symmetrically bending of a non-homogenous circular cylindrical shell can be reduced to that of a homogenous one and the calculation of the transformation factors.