Additional constraints may soften a non-conservative structural system: Buckling and vibration analysis

Mesoscopic Scale Instability in Particulate Materials

“…6 and 8). These findings are perfectly in accordance with the recent investigation on elastic structures (Ziegler column), in which it is shown that some loading conditions can destabilize an elastic structure, especially when kinematical constraints are prescribed (Challamel et al 2008;Nicot et al 2012a;Lerbet et al 2013).…”

“…Because relative motions can take place between the constitutive bodies, such nonconservative geometrical effects may occur. This result, well established in structural mechanics (Challamel et al 2008;Nicot et al 2012a, b;Lerbet et al 2013), is shown to also be valid in any granular material.…”

“…This paper will not come back on these basic aspects of instability in granular media. The loss of stability by divergence appears to be related to the loss of definite positiveness of the constitutive matrix (or equivalently of its symmetric part) for homogeneous elastoplastic problems and of the stiffness matrix for (1) elastic discrete systems (Challamel et al 2008;Nicot et al 2012a;Lerbet et al 2013) or (2) elastoplastic boundary value problems simulated by the Finite Element Method (Laouafa et al 2011).…”

On the stability of nonconservative continuous systems under kinematic constraints

“…www.zamm-journal.org (19) is equivalent to find a c ∈ V so that ∃w = 0 ⊥ a cà (P )(w) = λa c (22) with λ ∈ R.…”

“…Many research papers have recently described the instability issue of non conservative elastic systems with a new point of view (see for example [7,[21][22][23][24][25][26][27][28][29]). They mainly build a bridge between the so-called second order work criterion and the usual Lyapounov stability criterion.…”