Shape Control for Experimental Continuation

An experimental method has been developed to locate unstable equilibria of nonlinear structures quasi-statically. The technique involves loading a structure by application of either a force or a displacement at a main actuation point, while simultaneously controlling the overall shape using additional probe points. The method is applied to a shallow arch, and unstable segments of its equilibrium path are identified experimentally for the first time. Shape control is a fundamental building block for the experimental---as opposed to numerical---continuation of nonlinear structures, which will significantly expand our ability to measure their mechanical response.Comment: Updated Figure 6 experimental results with correct calibration factor for linear transducer. Updated Figure 6 finite element results with correct load multiplier for half-model. Updated paper text to reflect these changes. 5 pages, 6 figure

Three-dimensional Ion Distribution in a Filtered Vacuum Arc Discharge

Three-dimensional measurements of the ion flux along the filter of a magnetically filtered d-c vacuum arc are presented. The device includes a metallic plasma-generating chamber with cooper electrodes coupled to a substrate chamber through a quarter-torus magnetic filter. The filtering magnetic field was high enough to magnetize the electrons but not the ions. The ion current distribution was studied using a multi-element Cu probes, placed at three different positions along the filter. The ion saturation current of each probe was measured by biasing the probe at -70V with respect the grounded anode. Preliminary results of the three dimensional ion flux distribution and the floating potential of the plasma as functions of the bias filter voltage and magnetic field intensity are reported. © 2006 American Institute of Physics.Fil:Kelly, H. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.Fil:Marquez, A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.Fil:Pirrera, M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina

Exploring the design space of nonlinear shallow arches with generalised path-following

The classic snap-through problem of shallow arches is revisited using the so-called generalised path-following technique. Classical buckling theory is a popular tool for designing structures prone to instabilities, albeit with limited applicability as it assumes a linear pre-buckling state. While incremental-iterative nonlinear finite element methods are more accurate, they are considered to be complex and costly for parametric studies. In this regard, a powerful approach for exploring the entire design space of nonlinear structures is the generalised path-following technique. Within this framework, a nonlinear finite element model is coupled with a numerical continuation solver to provide an accurate and robust way of evaluating multi-parametric structural problems. The capabilities of this technique are exemplified here by studying the effects of four different parameters on the structural behaviour of shallow arches, namely, mid span transverse loading, arch rise height, distribution of cross-sectional area along the span, and total volume of the arch. In particular, the distribution of area has a pronounced effect on the nonlinear load-displacement response and can therefore be used effectively for elastic tailoring. Most importantly, we illustrate the risks entailed in optimising the shape of arches using linear assumptions, which arise because the design drivers influencing linear and nonlinear designs are in fact topologically opposed

Morphing shell structures:A generalised modelling approach

AbstractMorphing shells are nonlinear structures that have the ability to change shape and adopt multiple stable states. By exploiting the concept of morphing, designers may devise adaptable structures, capable of accommodating a wide range of service conditions, minimising design complexity and cost. At present, models predicting shell multistability are often characterised by a compromise between computational efficiency and result accuracy. This paper addresses the main challenges of describing the multistable behaviour of thin composite shells, such as bifurcation points and snap-through loads, through the development of an accurate and computationally efficient energy-based method. The membrane and the bending components of the total strain energy are decoupled by using the semi-inverse formulation of the constitutive equations. Transverse displacements are approximated by using Legendre polynomials and the membrane problem is solved in isolation by combining compatibility conditions and equilibrium equations. This approach provides the strain energy as a function of curvature only, which is of particular interest, as this decoupled representation facilitates efficient solution. The minima of the energy with respect to the curvature components give the multiple stable configurations of the shell. The accurate evaluation of the membrane energy is a key step in order to correctly capture the multiple configurations of the structure. Here, the membrane problem is solved by adopting the Differential Quadrature Method (DQM), which provides accurate results at a relatively small computational cost. The model is benchmarked against three exemplar case studies taken from the literature

Sensitivity of cross-sectional compliance to manufacturing tolerances for wind turbine blades

Wind-turbine blades are complex structures and, despite advancements in analysis techniques, differences persist between predictions of their elastic response and experimental results. This undermines confidence in the ability to reliably design and certify novel blade designs that include self-regulating features like bend-twist coupling To address these discrepancies, this study investigates the influence of manufacturing tolerances on the compliance properties of blade cross-sections, focusing specifically on a previously disregarded feature: the trailing edge bond-line. To conduct this investigation, the validated cross-sectional modelling tools BECAS and VABS are used to demonstrate that even small geometric variations can have significant influence on cross-sectional stiffness properties. The results are further examined and substantiated through the utilisation of 3D finite element models, adopting both shell and solid elements. We conclude that an accurate geometric representation of the cross-section is necessary to adequately capture the shear flow within it and assure accurate predictions on cross-sectional stiffness properties.</p

Generalised path-following for well-behaved nonlinear structures

Recent years have seen a research revival in structural stability analysis. This renewed interest stems from a paradigm shift regarding the role of buckling instabilities in engineering design—from detrimental sources of catastrophic failure to novel opportunities for functionality. Novel nonlinear structures take the form of optimised thin-walled structures that operate safely in the post-buckling regime; shape-morphing structures that exploit multi-stability to snap and pop between different configurations; and meta-materials that derive novel material properties from a cascade of choreographed instabilities. Hence, elastic instabilities are no longer considered as structural failures but rather exploited for repeatable well-behaved adaptations. In this article we focus on shape-morphing—a bio-inspired design strategy that intends to conform structures to different operating conditions. Computational tools that integrate easily with established methods used in industry, and that are capable of capturing the full phase diagram of compound instabilities and entangled post-buckling paths typical of these structures, are limited. Such a capability is crucial, however, as confidence in predictive tools can be key in enabling non-conventional designs. One potential candidate in this regard is generalised path-following, which combines the computational robustness of numerical continuation algorithms with the geometric versatility of the finite element method. In this paper we collate an array of successful computational tools introduced by other researchers, and introduce our own developments, to present a modelling framework fit for analysing and designing with well-behaved nonlinear structures in industry and academia. Particularly, we show that the full complexity of multi-snap events of morphing composite laminates is robustly captured by generalised path-following algorithms, and that the ability to determine loci of singular points with respect to a set of parameters is especially useful for tracing the boundaries of bistability in parameter space. Furthermore, we shed new insight into the mechanics of multi-stable laminates, showing that the multi-stability and snapping behaviour of these structures is much richer than previously assumed, featuring many unstable post-buckling branches and localised regions of stability