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COMPUTATIONAL METHODS FOR ENGINEERING TECHNOLOGY
Edited by: B.H.V. Topping and P. Iványi
On the Distributional Approach in Some Problems of Structural Mechanics
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", Saxe-Coburg Publications, Stirlingshire, UK, Chapter 10, pp 255-289, 2014. doi:10.4203/csets.35.10
Keywords: structural mechanics, non-regular functions, distributions, discontinuities, unilateral behaviour, impulsive dynamics.
Very often, in structural mechanics, problems are faced where the solution is ruled by differential equations where some non-regular 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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