The large deflection method in the analysis of elasto-plastic instability of thin shells with initial imperfections

Abstract

The theory of the instability of thin elasto-plastic shells with initial imperfections is wrought with great difficulties in respect of the complexity of geometrical and physical nonlinearities. This paper proposes a general method for analyzing the instability of stiffened thin elasto-plastic shells, with initial imperfections, under hydrostatic pressure. The nonlinearity of the inelastic shell buckling problems is linearized by a series of anisotropic elastic shell buckling problems; the process of linearization, the computation of the bifurcation point and the limit load of the buckled shell are completed by a general computer programme. This method has been applied to various shell structure problems such as the general instability of ring-reinforced cylindrical shells; the local buckling of shell plates between stiffeners; the buckling of stiffened conical shells and stiffened cylindrical panels; and the buckling of cylindrical shells with nonhomogeneity in the ring-stiffeners and the shell-plates. Many experiments are made, and the analytical results are confirmed with the experimental data. This proposed computer programme has been used in various engineering structural designs, such as the design of pressure hulls of submarines and the design of deep living torpedo shells. The general idea of this theory and the computational method can also be used in the design of some aeronautical structures. Recently, this method has been successfully used to solve the nonlinear buckling problems of cylindrical shells of composite materials with initial imperfections. With these buckling problems, not only the geometrical nonlinearities of shells, but also the physical nonlinearities of the composite materials are considered. This theory and the large deflection method have been introduced and discussed in detail in the recently published book Theory of stability of elasto-plastic thin shells [1].