STATIC STABILITY RESEARCH ON SINGLE-LAYER SPHERICAL SHELLS BASED ON FORM VULNERABILITY THEORY

Classical form vulnerability theory, which is based on the initial well-formedness of a joint, cannot take such eternal factors as load and constraints into consideration. However, the static stability of single-layer spherical shells is closely related to those eternal factors. An improved analysis approach concerning the influences of loading condition, geometric non-linearity, and constraints was developed, in which the geometric stiffness matrix was introduced innovatively. On this basis, the difference of joint well-formedness caused by the introduction of geometric stiffness matrix was studied and the most unfavorable load distribution, as well as the corresponding buckling mechanism, of single-layer spherical shells were revealed. The most unfavorable load distribution always manifests a marked gradient of joint well-formedness together with the lowest stable capacity. For the domes, concentrated load on the vertex is seen as the most unfavorable load distribution, and moreover for joint instability, partial instability and general instability, all of which are related to the gradient of joint well-formedness. The joint instability appears in the domes if the well-formedness of the loading joint and its surrounding joints degenerated notably, corresponding to a concentrated loading mode; when the well-formedness of a joint cluster degraded obviously, the structure would behave in partially unstable fashion, corresponding to a half-span distributed loading mode; general instability would occur when the well-formedness of all joints degenerated to the same degree, corresponding to a full-span distributed loading mode.