Detail publikačního výsledku

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

VALA, J.; NĚMEC, I.; VANĚČKOVÁ, A.

Originální název

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

Anglický název

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

Druh

Článek Scopus

Originální abstrakt

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.

Anglický abstrakt

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.

Klíčová slova

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

Klíčová slova v angličtině

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

Autoři

VALA, J.; NĚMEC, I.; VANĚČKOVÁ, A.

Rok RIV

2021

Vydáno

15.11.2021

Nakladatel

Elsevier

Místo

Amsterdam

ISSN

0378-4754

Periodikum

MATHEMATICS AND COMPUTERS IN SIMULATION

Svazek

189

Číslo

11

Stát

Nizozemsko

Strany od

36

Strany do

54

Strany počet

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"
}