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This and the next 2 images are from:
William Luiz Fernandes, Daniel Boy Vasconcellos and Marcelo Greco (Universidade Federal de Minas Gerais, Belo Horizonte, Minas Gerais, Brazil),
“Dynamic Instability in Shallow Arches under Transversal Forces and Plane Frames with Semirigid Connections”, Mathematical Problems in Engineering, Volume 2018, Article ID 1985907, 14 pages, https://doi.org/10.1155/2018/1985907
ABSTRACT: Structural engineering demands increasingly lighter systems, which can cause instability problems and compromise performance. A high slenderness index of a structural element makes it susceptible to instability. It is important to understand the problem, the limits of stability, and its postcritical behavior. An example that can occur in collapsed arches under a cross load is the dynamic snap-through behavior, where the structure in a given equilibrium condition jumps to a new remote equilibrium setting, causing usually sudden curvature. The semirigid connections are a source of physical nonlinearity and can influence the overall stability of the structural system, in addition to the distribution of stresses in the same system. Conventional approaches make use of static considerations. However, instability problems are inherently evolutionary processes, so a transient analysis is necessary for a complete description of structural behavior. The present work evaluates the geometrically nonlinear dynamic behavior of collapsed arches subjected to transverse force and plane frames with semirigid connections. The time domain responses, via Newmark's Method and positional formulation of the Finite Element Method, were obtained in terms of displacements, velocities, acceleration, and phase diagrams.
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