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Computational Science, Engineering & Technology Series
ISSN 17593158 CSETS: 35
COMPUTATIONAL METHODS FOR ENGINEERING TECHNOLOGY Edited by: B.H.V. Topping and P. Iványi
Chapter 10
On the Distributional Approach in Some Problems of Structural Mechanics A. Baratta
Department of Structures for Engineering and Architecture, University of Naples Federico II, Napoli, Italia A. Baratta, "On the Distributional Approach
in Some Problems of Structural Mechanics", in B.H.V. Topping and P. Iványi, (Editor), "Computational Methods for Engineering Technology", SaxeCoburg Publications, Stirlingshire, UK, Chapter 10, pp 255289, 2014. doi:10.4203/csets.35.10
Keywords: structural mechanics, nonregular functions, distributions,
discontinuities, unilateral behaviour, impulsive dynamics.
Abstract
Very often, in structural mechanics, problems are faced where the solution is ruled
by differential equations where some nonregular data have to be inserted. In an
elementary context, this is the case, for instance, of the elastic deflection of a beam
under the action of a lumped load, or of the dynamics of an elastic oscillator acted
on by an impulse. In all these cases, and in many others, solutions are not regular,
neither continuous nor derivable, and solutions, or some higher degree derivatives of
the solution, are not functions. By contrast, in these cases, both solutions and/or data
can be placed in a distributional environment, where compact formulations can be
adopted by using a distributional formalism, and problems deriving from nonregularity
of the objectives of the problem can be simply overcome. In this paper,
some examples are presented showing how to manage the distributional approach
and how to interpret the mathematical results in a highly expressive fashion, where
the technical or practical counterpart of "distributional objects" can be recognized as
having a well defined mechanical meaning.
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