Nosníky na pružném podkladu řešené pomocí modifikované Bettiho věty

Beams on Elastic Foundation Using Modified Bettis Theorem

journal article in Web of Science

en

In this paper, the restricted form of the principle of quasi work – the so-called modified Bettis Theorem – is used for developing an alternative analytical solution of beams on an elastic foundation. A brief review of this principle is provided along with the reminder of the classical Winklers model. A methodology is based on the calculation of the deflection of beam on an elastic foundation from the deflection of a reference beam which is topologically equivalent. Fundamental formulae for the reference beam on an elastic foundation are derived and thoroughly discussed. Applying the modified Bettis theorem, these formulae can be used for analysis of any arbitrary topologically equivalent beam on an elastic foundation. The applicability of this methodology is proved and a detailed guidance for its use is provided as well. The methodology is illustrated by three representative examples. The beam on an elastic foundation is a structure which is often used in many areas of technical practice including civil engineering, aerospace engineering etc; thus, the presented alternative way of its analytical solution might be found helpful, mainly for quick calculation and for its simple algorithmization.

Článek se zabývá principem kvazi práce tzv. modifikovaného Bettiho teorému. Uveden je stručný přehled tohoto principu spolu s Winklerovým modelem. Metodika je založena na výpočtu průhybu nosníku na pružném podkladu z průhybu referenčního nosníku, který je topologicky ekvivalentní.

In this paper, the restricted form of the principle of quasi work – the so-called modified Bettis Theorem – is used for developing an alternative analytical solution of beams on an elastic foundation. A brief review of this principle is provided along with the reminder of the classical Winklers model. A methodology is based on the calculation of the deflection of beam on an elastic foundation from the deflection of a reference beam which is topologically equivalent. Fundamental formulae for the reference beam on an elastic foundation are derived and thoroughly discussed. Applying the modified Bettis theorem, these formulae can be used for analysis of any arbitrary topologically equivalent beam on an elastic foundation. The applicability of this methodology is proved and a detailed guidance for its use is provided as well. The methodology is illustrated by three representative examples. The beam on an elastic foundation is a structure which is often used in many areas of technical practice including civil engineering, aerospace engineering etc; thus, the presented alternative way of its analytical solution might be found helpful, mainly for quick calculation and for its simple algorithmization.

Prut na pružném podkladu; modifikovaný Bettiho teorém; princip kvazi prací; Winklerův model

Beam on elastic foundation; modified Bettis Theorem; Principle of quasi work; Winklers model

2014

01.11.2014

ELSEVIER

THE BOULEVARD, LANGFORD LANE, KIDLINGTON, OXFORD OX5 1GB, ENGLAND

0020-7403

88

2014

17–24

8