Time evolutional analysis of nonlinear structures

Imperfection sensitivity due to coupled local instability: a non‐convex QP solution algorithm

“…This approach, which we call simplified analysis, has been outlined in a previous paper [10], but not as an effective fully automatic technique for imperfection sensitivity analysis, because of the lack of a general procedure providing all the local minimizers for condition (15), even simplified in form (19) by the assumption of local buckling modes (16). Numerical procedures only exist (e.g.…”

“…This assumption (see Reference [9]) can be formally implemented as an energy decoupling condition: (16) and, due to Equation (7), implies…”

A strategy to identify exciting forces acting on structures

“…Practically, when the external force is general the evaluation of the response requires a timestepping scheme such as those proposed in References [28,29]. Alternatively, the response of a single-degree-of-freedom system can be tackled in the frequency domain by using the Fourier transform of unit impulse response function:…”

Finite element asymptotic analysis of slender elastic structures: A simple approach

“…It is worth noting that this work finds its natural collocation within a series of studies published in References 9,[10][11][12][13][14][15][16][17], and that with respect to References 10 and 18 it represents only an occasion for commenting on some critical concept more fully. But, after the publication of Reference 17, where the numerical accuracy of the method was theoretically stated, it is the authors' belief that this algorithm is to be presented again, with the main task of showing the factual simplicity of its FEM implementation.…”

“…We name it the fundamental path u' [A] and suppose it to be regular in A. Moreover, we can suppose that its tangent at the bifurcation point is (&tic, &): that is equivalent to saying that, for (8), j = 0 is a solution of (9), and consequently @:'C:7jc = 0 (10) Therefore, the tangent to the second equilibrium path (ub[ <I, ,Ib[<]), which we name bijiurcated, is defined by considering (9) and (10) and, apart from a scalar factor, by li, = I$, + zi , (11) According to K~i t e r ,~ we call perfect those structures whose equilibrium paths bifurcate. It is worth noting that the hypothesis that the fundamental path u'[A] is an analytical function of 1 enables any critical configuration found on the fundamental path to be characterized as a bifurcation point.…”