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Euler–Bernoulli type beam theory for elastic bodies with nonlinear response in the small strain range
Type of publication: Article
Citation:
Publication status: Published
Journal: Archives of Mechanics
Volume: 68
Number: 1
Year: 2016
Pages: 3-25
URL: http://am.ippt.pan.pl/am/artic...
Abstract: 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 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 the 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.
Preprint project: MORE
Preprint year: 2016
Preprint number: 10
Preprint ID: MORE/2016/10
Keywords: Euler--Bernoulli beam theory, implicit constitutive relations, nonlinear elasticity, small strain, spectral collocation method
Authors Janečka, Adam
Průša, Vít
Rajagopal, K. R.
Added by: [VP]
Total mark: 0
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