Search results for "generalized functions"
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Simplified Formulation of Solution for Beams on Winkler Foundation allowing Discontinuities due to Loads and Constraints
2009
The paper discusses material for a course in Structural Mechanics addressed to second-Year Civil Engineering students. The response of beams on a Winkler foundation characterized by discontinuities in both the displacements (deflections and/or slopes) and forces (internal forces and/or loads) is studied. In particular, a simplified formulation for the solution of the discontinuous differential equation governing this problem is given. In some cases, the formulation is able to give the exact solution in a closed form. This is made possible through the use of the generalized functions, such as the well-known Unit Step Function and the Dirac delta function. The cases of discontinuities due to …
MR3428804 Reviewed Benci, Vieri(I-PISA); Luperi Baglini, Lorenzo(A-WIENM) Generalized functions beyond distributions. (English, Arabic summary) Arab.…
2016
Generalized functions are here intended to mean a particular class V˜(Ω) of ultrafunctions, i.e. functions defined on a non-Archimedean field that extends a class V(Ω) of L2(Ω)-integrable continuous functions. The particular class of ultrafunctions is selected by some desiderata to obtain the properties sufficient for applications to PDE. One of these is to maintain the locality property of a local operator defined on V(Ω) when it is extended to V˜(Ω). This fact is related to the possibility of defining a sort of orthogonality between "Delta ultrafunctions''. The results are applied to the definition of the derivative operator, the definite integral and to associate an ultrafunction to ever…