Shallow-dome structures and interaction between buckling and snap-through

Lightweight structures have the advantages of being ecological, virtuous, and beautiful to the eyes. The transparency and the fluent geometry that can be achieved with these structures, make them a reference point in modern structural engineering. Their design and production attain to many challenging fields in engineering such as the digital fabrication, the control and optimization theory, and the smart structures. However, their slenderness returns an high sensitivity to instability problems. Stability of equilibrium has a key role in structural engineering: the multiple nature and the vast set of influencing factors makes necessary a constant investigation and development of focused approaches. Above all, the sudden character that distinguish the instabilities requires a consistent effort to assure the safety of large and slender structures. Lastly, the interactive and dynamic essence of the instability demands a complex composition of solution schemes to treat it from a static point of view. Aim of this thesis is to study the interaction between the snap-through and the buckling and its effect on maximum load reduction, imperfection sensitivity, and especially on the variation in the structural behavior. Even if the dangerousness of the phenomenon is known, the problem requires a systematic treatment that concerns the study of the equilibrium paths. The path shape and characteristic provides crucial information about variation of inner forces regime, shallowness and slenderness effects, imperfections and connections influence. Hence, in the first part of the manuscript, a focused theoretical approach is devoted to the establish the describing and discriminating parameters. Additionally, a series of numerical simulations are presented to validate the formulations. Obtained results fulfill a first step in covering the gap between the physical knowledge of the problem and its actual scientific connotation. The results find an application in the stability of reticulated structures, commonly geometrically non-linear, but also a useful tool for the design and analysis of MEMS and micro-switchers. In this scale, the interaction phenomenon is too much often used for triggering a device without being completely grasped. The heinous data about mems collapse due to pull-in instability, about more than 40% of mems broke in this manner, is a reliable witness. In the structural engineering field, from the famous collapses of the 60's and 70's to the 2014 emblematic collapses of more than 100 reticulated domes in China caused by some exceptional snow storms. International organizations, such as the IASS, redacted new guideline for design, constructions and reliability of metal roofs, demonstrating a renewed interest in the interactive collapses. Among all, new methods for taking into account the imperfection sensitivity has been presented, based on probabilistic approaches. In the second part of the thesis, using the results obtained for a simple structures, the structural weaknesses and flaws are investigated. The results suggest that the methods adopted, commonly used for Fracture Mechanics, are useful for studying the local instability occurrence and consequences. For classical morphologies, such as diamatic and geodesic domes, the elastic local collapses of lateral and compressive buckling appears to be responsible for sharp load decreases. At the same time, for grid shells, the high stiffness connections required, proves to be a trigger to progressive and catastrophic collapses. Identification of snap-back phenomena in the equilibrium path of these structures are similar to the shell and cylinders collapses, where the intensity of flexural and axial regime of forces determines the catastrophic degree of the fail. The concept illustrated in this manuscript can be used for the safety assessment of lightweight structures and for optimization criteria for mems and micro-scale material structure.