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We consider a structural truss problem where all of the physical model parameters are uncertain: not just the material values and applied loads, but also the positions of the nodes are assumed to be inexact but bounded and are represented by intervals. Such uncertainty may typically arise from imprecision during the process of manufacturing or cons...
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... consider the simple mechanical truss structure comprising five nodes connected by six linear elements as depicted in Figure 1; the elements are numbered in circles and the coordinates of the nodes are also given. Two of the nodes, 1 and 2, are fixed; the other three are free-moving. A downward loading force of 50kN is separately applied to both nodes 4 and ...
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We consider a statically determinate structural truss problem where all of the physical model parameters are uncertain: not just the material values and applied loads, but also the positions of the nodes are assumed to be inexact but bounded and are represented by intervals. Such uncertainty may typically arise from imprecision during the process o...
Citations
... Engineering problems that involve such parametric linear systems may stem from structural mechanics, e.g., [3,4,21,26,29,38,42], the design of electrical circuits [5,6], resistive networks [13], and robust Monte Carlo simulation [17], to name but a few examples. The source of parametric uncertainty is often the lack of precise data which may result from a lack of knowledge due to, e.g., measurement imprecision or manufacturing imperfections, or an inherent variability in the parameters, e.g., physical constants are only known to within certain bounds. ...
... In this chapter, we demonstrated the advanced application of a general-purpose parametric method, combined with the Bernstein enclosure of polynomial ranges, to linear systems obtained by standard FEM analysis of mechanical structures, and illustrated the efficiency of the new parametric solver. Further applications, viz. to truss structures with uncertain node locations, can be found in [38]. ...
We give a short survey on methods for the enclosure of the solution set of a system of linear equations where the coefficients of the matrix and the right hand side depend on parameters varying within given intervals. Then we present a hybrid method for finding such an enclosure in the case that the dependency is polynomial or rational. A general-purpose parametric fixed-point iteration is combined with ef-ficient tools for range enclosure based on the Bernstein expansion of multivariate polynomials. We discuss applications of the general-purpose parametric method to linear systems obtained by standard finite element analysis of mechanical structures and illustrate the efficiency of the new parametric solver.
... A downward loading force of 50kN is separately applied to both nodes 4 and 5. This is adapted from the model in [6] by the addition of an extra element, making it no longer statically-determinate. The model parameters are given in Table 1. ...
A tight verified solution enclosure is obtained for the node displacements of a simple truss model, whose parameters, including the node locations, are uncertain. The solution is based on a monotonicity analysis of these interval parameters. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
