The Most Unfavorable Dynamiac Loads And Dynamiac Failure Analysis Of Single-Layer Spherical Shells

This paper mainly focuses on dynamic response analysis of single-layer spherical shells subjected to harmonic loads, step loads and earthquake excitation, thereafter some important conclusions are drawn, such as those about the most unfavorable loads, the collapse type and the failure mechanism.In this paper, four kinds of K8 single-layer spherical shells with spans of 40m and 50m, and rise-span ratios of 1/5 and 1/7 respectively are analyzed. The most unfavorable loads for the structures subjected to aforementioned loads are investigated, in which geometric non-linearity and material non-linearity are taken into account. Based on analysis of dynamic behavior of single-layer spherical shells subjected to harmonic loads with different frequencies and step loads with different duration, and under different site conditions and earthquake waves with different platform, the relationships between structural response and frequency characteristic, as well as the excitation duration are built up, by which the most unfavorable loads of single-layer spherical shells are obtained. Three detail conclusions are drawn as follows. (1) Under either horizontal or vertical harmonic loads, when the excitation frequency is closed to the natural frequency corresponding to the largest mode participation coefficient in the direction of the load, the structural response is the strongest, and the limit load is the lowest. (2) Under either horizontal or vertical step loads, when the duration is closed to the half natural period of the largest mode participation coefficient in the direction of the load, the dynamic structural response is the strongest, and the limit load is the lowest. (3) Under either horizontal or vertical earthquake excitation, if site predominant period Tg is closed to natural frequency Ti, the larger the mode participation coefficient is, the lower the limit acceleration is, and with the increase of platform duration of earthquake wave, the limit acceleration decreases in the same site condition.Based on analysis of structural response subjected to harmonic loads and step loads, two collapse types are summarized, which are named dynamic instability and strength failure. Through the analysis of structural stiffness matrix, the failure mechanism of single-layer spherical shells subjected to simple dynamic loads is analyzed and comparisons are made with dynamic failure and static failure. It seems that there is no clear relation between the amount of plastic members and collapse type, when the structure is subjected to harmonic loads; however, there are many notable signs to discriminate dynamic instability and strength failure, such as the increase of displacement, the increase of plastic members and the increase of plastic region during the failure course. Furthermore, it has no relation with collapse type whether the excitation frequency is in or out of resonant region. On the other hand, when the structure is subjected to step loads, the amount of plastic members is larger, the strength failure is easier to happen and the lowest limit load is generally relative to strength failure. The main reason of dynamic instability is that the structure has enough plastic hinges, which exhibits material non-linearity. But to the static instability, the axial force is the main reason, which exhibits geometric non-linearity instead.