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Supercloseness of Orthogonal Projections onto Nearby Finite Element Spaces
We derive upper bounds on the difference between the orthogonal projections
of a smooth function onto two finite element spaces that are nearby, in the
sense that the support of every shape function belonging to one but not both of
the spaces is contained in a common region whose measure tends to zero under
mesh refinement. The bounds apply, in particular, to the setting in which the
two finite element spaces consist of continuous functions that are elementwise
polynomials over shape-regular, quasi-uniform meshes that coincide except on a
region of measure , where is a nonnegative scalar and
is the mesh spacing. The projector may be, for example, the orthogonal
projector with respect to the - or -inner product. In these and other
circumstances, the bounds are superconvergent under a few mild regularity
assumptions. That is, under mesh refinement, the two projections differ in norm
by an amount that decays to zero at a faster rate than the amounts by which
each projection differs from . We present numerical examples to illustrate
these superconvergent estimates and verify the necessity of the regularity
assumptions on
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Dynamic Behavior of Precast Concrete Beam-Column Sub-Assemblages with High Performance Connections Subjected to Sudden Column Removal Scenario
Unbonded posttensioned precast concrete (UPPC) structure has shown its excellent aseismic performance in laboratory tests and earthquake investigation. However, the progressive collapse behavior of UPPC subjected to column removal scenario is still unclear. To fill this knowledge gap, two 1/2 scaled UPPC beam-column sub-assemblages were tested under a penultimate column removal scenario. The dynamic test results indicated that UPPC sub-assemblages have desirable load redistribution capacity to mitigate progressive collapse. The failure modes of the sub-assemblages observed in dynamic test were quite similar to that in static counterparts
Comparison of several system identification methods for flexible structures
In the last few years various methods of identifying structural dynamics models from modal testing data have appeared. A comparison is presented of four of these algorithms: the Eigensystem Realization Algorithm (ERA), the modified version ERA/DC where DC indicated that it makes use of data correlation, the Q-Markov Cover algorithm, and an algorithm due to Moonen, DeMoor, Vandenberghe, and Vandewalle. The comparison is made using a five mode computer module of the 20 meter Mini-Mast truss structure at NASA Langley Research Center, and various noise levels are superimposed to produced simulated data. The results show that for the example considered ERA/DC generally gives the best results; that ERA/DC is always at least as good as ERA which is shown to be a special case of ERA/DC; that Q-Markov requires the use of significantly more data than ERA/DC to produce comparable results; and that is some situations Q-Markov cannot produce comparable results
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