On applications of generalized functions to calculations of beam design elements

Abstract eng:
The paper deals with the mathematical representation of discontinuities in loading and geometry of beams under the bending. A system of ordinary differential equations (SODE) that makes the classical model of the beam bending does not hold at points of a discontinuity of functions the shear force, the bending moment, the slope, and the deflection for their derivatives are not defined at points of jump discontinuities. To solve this problem we use the generalized functions (distributions) and we generalize the SODE of the beam bending so as to hold at loading and geometry discontinuity points. Further we show essential formulae for looking for solutions to the generalized SODE using the direct integration without employing the Laplace transform.

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