On numerical solution of a variational inequality of the 4th order by finite element method

Jaroslav Haslinger

Aplikace matematiky (1978)

  • Volume: 23, Issue: 5, page 334-345
  • ISSN: 0862-7940

Abstract

top
The problem of a thin elastic plate, deflection of which is limited below by a rigid obstacle is solved. Using Ahlin's and Ari-Adini's elements on rectangles, the convergence is established and SOR method with constraints is proposed for numerical solution.

How to cite

top

Haslinger, Jaroslav. "On numerical solution of a variational inequality of the 4th order by finite element method." Aplikace matematiky 23.5 (1978): 334-345. <http://eudml.org/doc/15063>.

@article{Haslinger1978,
abstract = {The problem of a thin elastic plate, deflection of which is limited below by a rigid obstacle is solved. Using Ahlin's and Ari-Adini's elements on rectangles, the convergence is established and SOR method with constraints is proposed for numerical solution.},
author = {Haslinger, Jaroslav},
journal = {Aplikace matematiky},
keywords = {quadratic programming; elastic clamped plate; algorithm; energy functional; convergence; minimization problem; numerical solution; finite element method; Quadratic Programming; Elastic Clamped Plate; Algorithm; Energy Functional; Convergence; Minimization Problem; Numerical Solution; Finite Element Method},
language = {eng},
number = {5},
pages = {334-345},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On numerical solution of a variational inequality of the 4th order by finite element method},
url = {http://eudml.org/doc/15063},
volume = {23},
year = {1978},
}

TY - JOUR
AU - Haslinger, Jaroslav
TI - On numerical solution of a variational inequality of the 4th order by finite element method
JO - Aplikace matematiky
PY - 1978
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 23
IS - 5
SP - 334
EP - 345
AB - The problem of a thin elastic plate, deflection of which is limited below by a rigid obstacle is solved. Using Ahlin's and Ari-Adini's elements on rectangles, the convergence is established and SOR method with constraints is proposed for numerical solution.
LA - eng
KW - quadratic programming; elastic clamped plate; algorithm; energy functional; convergence; minimization problem; numerical solution; finite element method; Quadratic Programming; Elastic Clamped Plate; Algorithm; Energy Functional; Convergence; Minimization Problem; Numerical Solution; Finite Element Method
UR - http://eudml.org/doc/15063
ER -

References

top
  1. Cea J., Optimisation théorie et algorithmes, Dunod, Paris 1971. (1971) Zbl0211.17402MR0298892
  2. Ciarlet P. G., Conforming and nonconforming finite element methods for solving the plate problem, Conference on the numerical solution of differential equations, University of Dundee, July 1973, 03-06. (1973) MR0423832
  3. Ciarlet P. G., Raviart P. A., General Lagrange and Hermite interpolation in R n with applications to finite element methods, Arch. Rat. Anal. Vol. 46 (1972), 177- 199. (1972) Zbl0243.41004MR0336957
  4. Glowinski R., Analyse numerique d'inequations variationnelles d'ordre 4, (preprint of University Paris VI). 
  5. Jakovlev G. N., [unknown], Trans. Moscow Math. Soc. (1967), 227--313. (1967) 
  6. Janovský V., Procházka P., The nonconforming finite element method in the problem of clamped plate with ribs, Apl. Mat. 21 (1976), No 4, 273 - 289. (1976) MR0413548
  7. Glowinski R., Lions J. L., Trémolieres R., Analyse numérique des inéquations variationnelles, Dunod, Paris 1976. (1976) 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.