Geometrically non-linear lattice model of a cantilever beam

Authors

  • Дмитро Миколайович Колесник Zaporizhzhya State Engineering Academy Lenin Av. 226, Zaporizhzhya, Ukraine,69006, Ukraine
  • Олександр Дмитрович Шамровський Zaporizhzhya State Engineering Academy Lenin Av. 226, Zaporizhzhya, Ukraine,69006, Ukraine

DOI:

https://doi.org/10.15587/1729-4061.2013.14824

Keywords:

Cantilever beam, load distribution, large displacement, discrete model lattice model

Abstract

The article is devoted to the geometrically non-linear analysis of the bend of a cantilever beam under a uniformly distributed load. The objective of the article is to check out whether the developed discrete lattice model can be used for the calculation of large displacements in the problem of the bending of the cantilever beam under the uniformly distributed load. The proposed discrete model is a combination of many elements of the lattice consisting of four pairs of nodes connected by six elastic connections with two stiffness, the influence of each of which was determined by the type of deformation, which allows modeling the arbitrary Poisson's ratio. The calculation of the discrete model was carried out by the method of successive displacements. The paper considers two types of load of the cantilever: a load having a constant direction and a tracking load. For both cases, the tables with the results of the calculation by the method of successive displacements in a dimensionless form are presented. In addition, the graphs of dependence of the dimensionless displacements on the dimensionless load are presented and compared with the results of other authors. The comparison showed a high degree of accuracy of the calculation using the proposed discrete model. The results can be used for comparison with the results of other methods of solution of geometrically non-linear problems. In addition, the results provide an assumption about the effectiveness of the proposed discrete model for plane static geometrically non-linear problems of solid mechanics based on simplified beam theory

Author Biographies

Дмитро Миколайович Колесник, Zaporizhzhya State Engineering Academy Lenin Av. 226, Zaporizhzhya, Ukraine,69006

Assistant

Department of Higher and Applied Mathematics

Олександр Дмитрович Шамровський, Zaporizhzhya State Engineering Academy Lenin Av. 226, Zaporizhzhya, Ukraine,69006

Doctor of Technical Sciences, Professor

Department of Automated Systems Software

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Published

2013-06-20

How to Cite

Колесник, Д. М., & Шамровський, О. Д. (2013). Geometrically non-linear lattice model of a cantilever beam. Eastern-European Journal of Enterprise Technologies, 3(7(63), 48–51. https://doi.org/10.15587/1729-4061.2013.14824

Issue

Vol. 3 No. 7(63) (2013): Applied mechanics

Section

Applied mechanics

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Copyright (c) 2014 Дмитро Миколайович Колесник, Олександр Дмитрович Шамровський

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