The problem to identify pre-buckling states for thin-walled shell corresponds to the problem to identify pre-bifurcation solutions (the inverse bifurcation problem) for von Karman equations that govern the structure. Typical solution sequences similar to those of post-bifurcation solutions observed along the bifurcation paths of the nonlinear boundary problem for von Karman equations are extracted to serve as precursors of bifurcation (tools to solve the problem). The method allows one to divide all operations required to solve the problem under study into two non-equal parts. The most time-consuming part (to trace bifurcation paths and cluster the respective solution) is performed off-line, while the part of the algorithm that is carried out on-line (the identification algorithm) requires a relatively small number of arithmetic operations. This allows development of the efficient system of rapid identification of pre-buckling states.
The present paper presents the complete bifurcation structure of nonlinear boundary problem of thin-walled systems for cylindrical panel subjected to uniform external pressure. We examine various boundary conditions on straight edges (free, simply supported, rigidly clamped edges, edges with prescribed fixed joint conditions); curvilinear edges are simply supported. To construct solutions of the boundary problem in question and to trace equilibrium paths, we employ the non-linear extended Kantorovich method in conjunction with a conventional path-tracing technique. The structure has bifurcation paths associated with symmetric, skew-symmetric, asymmetric, and snap-through deformed shapes that provides a basis for analysis of the worst shape imperfections.
The complete bifurcation structure for cylindrical panel under uniform pressure.
That is a sound basis to determine the worst shape imperfection.
The extended Kantorovich method to construct the complete bifurcation structures.