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Application of the generalized nonlinear constitutive law in 2D shear flexible beam structures


[ 1 ] Instytut Analizy Konstrukcji, Wydział Inżynierii Lądowej i Transportu, Politechnika Poznańska | [ P ] employee

Scientific discipline (Law 2.0)

[2.6] Civil engineering and transport

Year of publication


Published in

Archives of Civil Engineering

Journal year: 2021 | Journal volume: vol. 67 | Journal number: no. 3

Article type

scientific article

Publication language


  • generalized nonlinear constitutive law
  • finite element analysis
  • nonlinear materials
  • composite structures
  • Timoshenko beam element

EN The paper presents a modified finite element method for nonlinear analysis of 2D beam structures. To take into account the influence of the shear flexibility, a Timoshenko beam element was adopted. The algorithm proposed enables using complex material laws without the need of implementing advanced constitutive models in finite element routines. The method is easy to implement in commonly available CAE software for linear analysis of beam structures. It allows to extend the functionality of these programs with material nonlinearities. By using the structure deformations, computed from the nodal displacements, and the presented here generalized nonlinear constitutive law, it is possible to iteratively reduce the bending, tensile and shear stiffnesses of the structures. By applying a beam model with a multi layered cross-section and generalized stresses and strains to obtain a representative constitutive law, it is easy to model not only the complex multi-material cross-sections, but also the advanced nonlinear constitutive laws (e.g. material softening in tension). The proposed method was implemented in the MATLAB environment, its performance was shown on the several numerical examples. The cross-sections such us a steel I-beam and a steel I-beam with a concrete encasement for different slenderness ratios were considered here. To verify the accuracy of the computations, all results are compared with the ones received from a commercial CAE software. The comparison reveals a good correlation between the reference model and the method proposed.

Pages (from - to)

157 - 176




License type

CC BY-NC-ND (attribution - noncommercial - no derivatives)

Open Access Mode

open journal

Open Access Text Version

final published version

Full text of article

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Ministry points / journal


Ministry points / journal in years 2017-2021


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