ON APPLICATIONS OF GENERALIZED FUNCTIONS TO CALCULATION OF THIN-WALLED BEAM DESIGN ELEMENTS SUBJECT TO NON-UNIFORM TORSION

Abstract eng:
Vlasov's mathematical model of the restrained torsion of a prismatic thin-walled open-section beam contains derivatives of unknown functions which are the torque, the bimoment, the twist, and the rotation of cross sections. But these derivatives are not defined at such points between ends of a beam where a concentrated torsional load or a concentrated bimoment load or an internal support or an internal coupling is located. In order that the Vlasov's mathematical model of thin-walled open-section elastic beam subjected to torsion allowing for constrained warping may hold true also at the points of discontinuity mentioned, which are common in calculating experience, we have used the distributional derivatives for the unknown quantities, and developed generalized mathematical model in the form of a system of ordinary differential equations (SODE). In order to solve this generalized model we use the Laplace transform, and find the general solution which is the generalization of the initial parameters' method since it covers also bars with internal couplings.

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