Euler–Bernoulli type beam theory for elastic bodies with nonlinear response in the small strain range

• Autorzy: Janečka A. , Průša V. , Rajagopal K. R.
• Języki publikacji: EN

Abstrakty

EN

The response of many new metallic alloys as well as ordinary materials such as concrete is elastic and nonlinear even in the small strain range. Thus, using the classical linearized theory to determine the response of bodies could lead to a miscalculation of the stresses corresponding to the given strains, even in the small strain regime. As stresses can determine the failure of structural members, such miscalculation could be critical. We investigate the quantitative impact of the material nonlinearity in the Euler–Bernoulli type beam theory. The governing equations for the deflection are found to be nonlinear integro-differential equations, and the equations are solved numerically using a variant of the spectral collocation method. The deflection and the spatial stress distribution in the beam have been computed for two sets of models, namely the standard linearized model and some recent nonlinear models used in the literature to fit experimental data. The predictions concerning the deflection and the spatial stress distribution based on the standard linearized model and the nonlinear models are considerably different.

Słowa kluczowe

EN

Euler-Bernoulli beam theory; nonlinear elasticity; small strain; implicit constitutive relations; spectral collocation method

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Archives of Mechanics
• Rocznik: 2016
• Tom: Vol. 68, nr 1
• Strony: 3--25
• Opis fizyczny: Bibliogr. 19 poz., fot., wykr.

Twórcy

autor

Janečka A.

• Faculty of Mathematics and Physics Charles University in Prague Sokolovská 83 Praha 8 – Karlín CZ 186 75, Czech Republic

autor

Průša V.

• Faculty of Mathematics and Physics Charles University in Prague Sokolovská 83 Praha 8 – Karlín CZ 186 75, Czech Republic

autor

Rajagopal K. R.

• Texas A&M University Department of Mechanical Engineering 3123 TAMU College Station TX 77843-3123, U.S.A.

Bibliografia

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Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.