On application of generalized functions to calculations of thin-walled beams

Abstract eng:
This article presents Ph.D. thesis dealing with applications of generalized functions (distributions) to analytical calculations of thin-walled beams with discontinuities in loading, supports, mid-line contour geometry and due to internal hinges or couplings. Three mathematical models of thin-walled beams have been generalized here using the distributional derivative in order to hold true also at points of discontinuity of unknown quantities. The first model is for thin-walled prismatic beam bending that covers the effect of shear lag based on the first approximation of mid-sUljace shear strain. The second one is for restrained torsion of open cross-section thin-walled prismatic bars. The third one is for coupled bending and torsion of open cross-section thin-walled prismatic beams that covers the effect of restrained wmping using plane approximation of bending warping and sectorial approximation of mid-line contour warping.

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