Publication detail

Exact solution of a thick beam on Pasternak subsoil in finite element calculations

VALA, J. NĚMEC, I. VANĚČKOVÁ, A.

Original Title

Exact solution of a thick beam on Pasternak subsoil in finite element calculations

Type

journal article in Scopus

Language

English

Original Abstract

Advanced numerical analysis of structures forces the massive implementation of numerical algorithms, relying on certain convergence of sequences of discrete finite element and similar approximations in spaces of integrable functions, conceding non-physical discontinuities and imperfectness to all numerical results. This is demonstrated on a model example of a thick elastic beam on the 2-parametric Pasternak subsoil. A potential remedy, discussed in this paper, comes from the implementation of available knowledge of analytical solutions in standard variational formulations. The resulting sparse system of linear algebraic equations can be derived without any numerical differentiation; the numerical quadrature is limited to some integrals of explicitly known (MAPLE-generated) functions. Potential generalizations, including selected nonlinear problems, are sketched.

Keywords

Timoshenko beam; Pasternak foundation; Analytical solutions of ordinary differential equations; Finite element method;

Authors

VALA, J.; NĚMEC, I.; VANĚČKOVÁ, A.

Released

15. 11. 2021

Publisher

Elsevier

Location

Amsterdam

ISBN

0378-4754

Periodical

Mathematics and Computers in Simulation

Year of study

189

Number

11

State

Kingdom of the Netherlands

Pages from

36

Pages to

54

Pages count

19

URL

https://www.sciencedirect.com/science/article/pii/S0378475420301762?via%3Dihub

BibTex

@article{BUT167866,
  author="Jiří {Vala} and Ivan {Němec} and Adéla {Gálová}",
  title="Exact solution of a thick beam on Pasternak subsoil in finite element calculations",
  journal="Mathematics and Computers in Simulation",
  year="2021",
  volume="189",
  number="11",
  pages="36--54",
  doi="10.1016/j.matcom.2020.05.017",
  issn="0378-4754",
  url="https://www.sciencedirect.com/science/article/pii/S0378475420301762?via%3Dihub"
}