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"
}