Eine Plattform für die Wissenschaft: Bauingenieurwesen, Architektur und Urbanistik
Eine Plattform für die Wissenschaft: Bauingenieurwesen, Architektur und Urbanistik
Solved Problems
A number of solved problems are proposed in this chapter. They concern conservative systems undergoing buckling (like planar beams, open thin-walled beams, and plates), as well as nonconservative systems (like rigid rods or beams under follower forces, aeroelastic and parametrically excited systems). For each problem, some questions are posed in sequence, driving the reader in building up the answer. Then, the solution to the problem is illustrated, consisting of (a) a step-by-step formulation, up to obtaining the governing equations, and (b) a commented illustration of the results. In Sect. 14.2, the critical loads of columns under self-weight beams partially or totally supported by a Winkler soil and braced frames are computed, using exact Ritz and finite element (FE) solutions. In Sect. 14.3, the critical load of open thin-walled beams (TWB), under different constraint and loads (axial, bending, and transverse), is determined. In Sect. 14.4, the critical loads of free or elastically supported plates and of compressed tubes are evaluated. In Sect. 14.5, the dynamic bifurcations induced by follower forces in a triple pendulum, braced planar beams, and braced 3D foil beams are investigated. In Sect. 14.6, the galloping of base-isolated beams and suspension bridges is studied; moreover, a numerical investigation of two degrees of freedom (DOF) systems under aerodynamic loads is carried out. In Sect. 14.7, the Mathieu equation is studied, either by numerical integrations or infinite Hill determinant; moreover, some parametrically excited pendula are analyzed.
Solved Problems
A number of solved problems are proposed in this chapter. They concern conservative systems undergoing buckling (like planar beams, open thin-walled beams, and plates), as well as nonconservative systems (like rigid rods or beams under follower forces, aeroelastic and parametrically excited systems). For each problem, some questions are posed in sequence, driving the reader in building up the answer. Then, the solution to the problem is illustrated, consisting of (a) a step-by-step formulation, up to obtaining the governing equations, and (b) a commented illustration of the results. In Sect. 14.2, the critical loads of columns under self-weight beams partially or totally supported by a Winkler soil and braced frames are computed, using exact Ritz and finite element (FE) solutions. In Sect. 14.3, the critical load of open thin-walled beams (TWB), under different constraint and loads (axial, bending, and transverse), is determined. In Sect. 14.4, the critical loads of free or elastically supported plates and of compressed tubes are evaluated. In Sect. 14.5, the dynamic bifurcations induced by follower forces in a triple pendulum, braced planar beams, and braced 3D foil beams are investigated. In Sect. 14.6, the galloping of base-isolated beams and suspension bridges is studied; moreover, a numerical investigation of two degrees of freedom (DOF) systems under aerodynamic loads is carried out. In Sect. 14.7, the Mathieu equation is studied, either by numerical integrations or infinite Hill determinant; moreover, some parametrically excited pendula are analyzed.
Solved Problems
Luongo, Angelo (Autor:in) / Ferretti, Manuel (Autor:in) / Di Nino, Simona (Autor:in)
Stability and Bifurcation of Structures ; Kapitel: 14 ; 553-637
24.02.2012
85 pages
Aufsatz/Kapitel (Buch)
Elektronische Ressource
Englisch
Columns under self-weight , Elastically restrained beams , Critical loads of TWB other than simply supported , Stability domains of TWB , Elastically restrained plates , Local instability of plate assemblies , Triple pendulum under follower forces , Visco-elastically restrained beams under follower forces , Aeroelastic stability of beams , Two DOF aeroelastic instabilities , Numerical treatments for the Mathieu equation , Parametrically excited pendula Engineering , Mechanical Statics and Structures , Solid Mechanics , Mechanical Engineering , Structural Materials , Solid Construction , Building Construction and Design
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