Analytical Stability Considerations in Lightweight Design
Lightweight structures are thin walled and/or slender; hence, they are prone to the occurrence of structural instabilities under various loading conditions. In this chapter analytical equations for estimating the critical loads of some important structures, such as beams, plates, and cylindrical shells, are presented. All equations discussed are based on a static stability criterion and limited to linear elastic material behavior.
Stability Criteria and Post-buckling Behavior
Depending on the stiffness of the structure and the loading conditions, different forms for the loss of structural stability can be observed involving bifurcation of equilibria, snap-through, snapback, and flutter instabilities. Reaching the plastic limit load can also be considered as an occurrence of a structural instability but is not further discussed within this chapter.
- Donnell L (1932) A new theory of buckling of thin cylinders under axial pressure. ASME Trans 56: 795–806Google Scholar
- Lee S, Manuel F, Rossow E (1968) Large deflections and stability of elastic frames. J Eng Mech Div 94:521–548Google Scholar
- Rammerstorfer F, Daxner T (2009) Berechnungs und Designkonzepte für den Leichtbau. In: Degischer H, Lüftl S (eds) Leichtbau – Prinzipien, Werkstoffauswahl und Fertigungsvarianten. Wiley-VCH, Weinheim, pp 14–43, Copyright Wiley-VCH Verlag GmbH & Co. KGaA. (Figures partially reproduced with permission.)Google Scholar