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Force-System Resultants and Equilibrium
Published in Richard C. Dorf, The Engineering Handbook, 2018
Structural stability is the ability of a structural system to maintain its geometric integrity under compressive force or stress. When a structure is subjected to high compressive force/stress, it has a tendency to lose its stiffness and deflect in a direction perpendicular to the direction of the applied stress. When this occurs, the ability of the structure to carry the applied load will be compromised. For instance, a slender column buckles (i.e., becomes unstable under a compressive force) when the applied load reaches a critical value. If buckling occurs in the elastic range, this critical load can be computed as an eigenvalue problem [Chen and Lui, 1987] using the differential equation EId4vdx4+Pd2vdx2=0
Geometric stability of stationary Euler flows
Published in Geophysical & Astrophysical Fluid Dynamics, 2020
A more direct approach to trajectory stability arises from dynamical system theory where the Lagrangian dynamics of trajectory in phase space is described by structural stability (Peixoto 1962). This topological concept, when applied to divergence-free vector fields in physical space, suggests that all stationary solutions of the two-dimensional Navier–Stokes equations are structurally stable (Ma and Wang 1999). Such generic structural stability clearly disconnects from the prevalent hydrodynamic instability, which is not surprising because singular-point distribution rather than streamline geometry determines topological equivalence and most Eulerian dynamical properties are not retained in topological equivalence (Ghil et al.2001). It makes us wonder if there exists a nonlinear geometric stability that addresses fluid trajectory in physical space and meanwhile holds dynamical relevance.
Sediment removal efficiency estimation criteria for modern day desilting basins
Published in ISH Journal of Hydraulic Engineering, 2019
Satyajeet Sinha, Amar Pal Singh
It was observed that in comparison to formula derived for wide desilting basins, the formula consist of hydraulic radius parameter, cross-sectional and plan area suggested for modified shaped desilting basins gives more comparable results with model study output. Similarly in comparison to formula derived for unlined desilting basins, the formula consist of friction factor parameter for lined desilting basins will give more comparable results with model study output. The desilting basins considered in case studies are of free flow type, lined and the width changes from top to bottom to increase structural stability. Hence, the formula applicable for unlined desiling basins and wide channels cannot be used. Instead of that the modified formulae with friction factor, hydraulic radius parameter, cross-sectional and plan area as suggested in the paper can be used.
Structural stability without coercivity
Published in Optimization, 2022
Laura Poggiolini, Gianna Stefani
In order to prove our structural stability result, we take advantage of the Hamiltonian flow associated to singular extremals of the first kind. Indeed, differentiating twice the equality , SGLC allows to define in a neighbourhood of the range of the singular arc of the feedback control of singular extremals of the first kind Associated to this control we can consider the feedback Hamiltonian of singular extremals of the first kind which satisfies the following properties