Abstract
The buckling and post-buckling behaviour of slender structures is increasingly being harnessed for smart functionalities. Equally, the post-buckling regime of many traditional engineering structures is not being used for design and may therefore harbour latent load-bearing capacity for further structural efficiency. Both applications can benefit from a robust means of modifying and controlling the post-buckling behaviour for a specific purpose. To this end, we introduce a structural design paradigm termed modal nudging, which can be used to tailor the post-buckling response of slender engineering structures without any significant increase in mass. Modal nudging uses deformation modes of stable post-buckled equilibria to perturb the undeformed baseline geometry of the structure imperceptibly, thereby favouring the seeded post-buckling response over potential alternatives. The benefits of this technique are enhanced control over the post-buckling behaviour, such as modal differentiation for smart structures that use snap-buckling for shape adaptation, or alternatively, increased load-carrying capacity, increased compliance or a shift from imperfection sensitivity to imperfection insensitivity. Although these concepts are, in theory, of general applicability, we concentrate here on planar frame structures analysed using the nonlinear finite element method and numerical continuation procedures. Using these computational techniques, we show that planar frame structures may exhibit isolated regions of stable equilibria in otherwise unstable post-buckling regimes, or indeed stable equilibria entirely disconnected from the natural structural response. In both cases, the load-carrying capacity of these isolated stable equilibria is greater than the natural structural response of the frames. Using the concept of modal nudging it is possible to “nudge” the frames onto these equilibrium paths of greater load-carrying capacity. Due to the scale invariance of modal nudging, these findings may impact the design of structures from the micro- to the macro-scale.
Highlights
In structural mechanics, nonlinearities are often viewed as failure modes
We show that planar frame structures may exhibit isolated regions of stable equilibria in otherwise unstable post-buckling regimes, or stable equilibria entirely disconnected from the natural structural response
The combination of imperfection sensitivity and the stochastic nature of imperfections leads to uncertainty during design (Arbocz and Hol, 1995), which means that imperfection-sensitive structures, such as cylindrical shells under axial compression, are designed with empirically derived and often conservative knock-down factors (Jiménez et al, 2017)
Summary
Nonlinearities are often viewed as failure modes. In the case of material nonlinearity, where plastic deformations irreversibly change the constitutive behaviour of the material, avoiding nonlinearity is a good heuristic. The combination of imperfection sensitivity and the stochastic nature of imperfections leads to uncertainty during design (Arbocz and Hol, 1995), which means that imperfection-sensitive structures, such as cylindrical shells under axial compression, are designed with empirically derived and often conservative knock-down factors (Jiménez et al, 2017) In this vein, this paper explores the potential of controlling structural nonlinearities to tailor the post-buckling response of engineering structures for a specific purpose. The elastic post-buckling response in terms of initial and final stiffness can be tailored using modal superpositions of buckling modes seeded as initial imperfections (Hu and Burgueño, 2017) This approach is valuable for reducing the imperfection sensitivity of axially compressed cylindrical shells (Hu et al, 2014; Hu and Burgueño, 2015b).
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