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

English Title

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

Type

journal article - other

Language

en

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.

English 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;

Released

18.05.2020

Publisher

Elsevier

Location

Amsterdam

ISBN

0378-4754

Periodical

Mathematics and Computers in Simulation

Year of study

7777

Number

1

State

NL

Pages from

7777-1

Pages to

7777-19

Pages count

19

URL

Documents

BibTex


@article{BUT167866,
  author="Jiří {Vala} and Ivan {Němec} and Adéla {Vaněčková}",
  title="Exact solution of a thick beam on Pasternak subsoil in finite element calculations",
  annote="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.",
  address="Elsevier",
  chapter="167866",
  doi="10.1016/j.matcom.2020.05.017",
  howpublished="print",
  institution="Elsevier",
  number="1",
  volume="7777",
  year="2020",
  month="may",
  pages="7777-1--7777-19",
  publisher="Elsevier",
  type="journal article - other"
}