Initial Shape Imperfections Research Articles

Theoretical and Experimental Buckling Loads of Imperfect Spherical Shell Segments

Buckling experiments with spherical shell segments subjected to three different axisymmetric loading conditions are described. Initial shape imperfections were measured so that the experimental results could be compared with theoretical predictions for imperfect shells. Relevant theoretical solutions including classical buckling and initial postbuckling are therefore reviewed. Due to the inherent irregular nature of the imperfections, a comparison is not straightforward. It was necessary to define the amplitude of an"equivalent" regular imperfection pattern. Because there is no rigorous justification for this approach, the experiments can neither verify nor invalidate the initial postbuckling theory, but there is no doubt that very important characteristics of the shells were predicted qualitatively correctly. According to classical linearized theory, the buckling stress should be approximately Independent of loading condition, but experiments as well as initial postbuckling analyses revealed that the critical principal stress for imperfect shellsmay well vary by a factor of 2 to 3 depending on the ratio between the principal stresses. Experimental results for a spherical shell subjected to an inward point-load were found to be in very good agreement with theoretical large-deflection analysis. Bifurcation from the axisymmetric condition associated with small loads was observed. As predicted by initial postbuckling theory, the bifurcations were found to be stable.

Technological characteristics and bearing capacity of waffle cylindrical shells

1. Significant scatter of the thicknesses of the linings and reinforcement are characteristic for real waffle shells fabricated by the method of mechanical milling. Since thickness differences significantly affect the weight, geometric, and stiffness parameters of the structure, it should be considered in computations, particularly during design. 2. Correct (governed by the level of production technology) selection of tolerances for dimensions is extremely important. In establishing and assigning tolerances for the production of waffle shells by the mechanical-milling method, the statistical characteristics of element thicknesses, which are presented in this study, can be used. 3. Relatively low stiffness of the reinforcement in waffle shells promotes their increased sensitivity to initial shape imperfections. Since the effect of flaws on shell stability should be considered in design, it is necessary to accumulate statistical data on the character and intensity of imperfections in real designs, and also to study their effect on bearing capacity. 4. A marked increase in the perturbation sensitivity of shells with decreasing relative rib stiffness suggests the expediency of establishing correlation relationships between thickness of reinforcement and the shell's sensitivity to its imperfection.