Elastoplastic Stability Analyses For Ceramic/Metallic Functionally Graded Structures

In the last two decades, structural stabilities of plates and shells made of functionally graded materials(or FGM) have recieved intensive concern, however, the research focus is still on stability of their elastic structures. By setting FGM cylindrical shells and rings as the basic research objects, this thesis covers elastoplastic buckling, postbuckling and free vibration issues of these new classes of structures.Firstly, discussion is addressed for the research topics of this thesis according to the current research progress at home and aborad. Further, the incremental and the total theories of material elastoplasty are introduced. The possible anisotopic characteristics in elastoplastic deformation of materials help to formulate the buckling govering equations of anisotopic FGM cylindrical shells and plane-tress or plane-strain rings. Through eigenvalue analysis, the analytical solutions of elastoplastic buckling critical loads of structures are founded. Finally, a semi-analytic procedure is produced to calculate the critical loads. Meanwhile, researches are presented for elatic buckling and free vibration issues for FGM rings under the plane-stress or plane-strain state. During the analyses, effects of structural dimensional parameters, material inhomogeneous parameters, as well as the elastoplastic properties of materials on structural stabilities are discussed.From the present research, several conclusions can be drawn. The elastoplastic buckling critical loads of FGM cylindrical shells and rings are generally lower slightly than the corresponding elastic counterparts, which is aroused by material plastic flow. Structures with smaller radius-to-thickness ratio, larger contain of ceramic constituent or higer values of yield strength and strengthening modulus would enhance the elastoplastic buckling critical loads. The material flow district at buckling point of FGM cylindrical shells and rings would be enlarged as the structural thickness and the volum fraction of ceramic constituent increase, and thus structures tend to occur elastoplastic or even plastic buckling. In the case of hydrostatic loaded FGM rings, whether the material physic nonlinearity is include or not, the plane-strain solutions of structural buckling critical load are always higher than the plane-stress results. There are insensitive districts of the elastoplastic critical load versus the inhomogeneous parameter for FGM rings.