On the existence of a weak solution of the boundary value problem for the equilibrium of a shallow shell reinforced with stiffening ribs

Igor Bock; Ján Lovíšek

Aplikace matematiky (1978)

  • Volume: 23, Issue: 2, page 132-149
  • ISSN: 0862-7940

Abstract

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The existence and the unicity of a weak solution of the boundary value problem for a shallow shell reinforced with stiffening ribs is proved by the direct variational method. The boundary value problem is solved in the space W ( Ω ) ⊂ H 0 1 ( Ω ) × H 0 1 ( Ω ) × H 0 2 ( Ω ) , on which the corresponding bilinear form is coercive. A finite element method for numerical solution is introduced. The approximate solutions converge to a weak solution in the space Q ( Ω ) .

How to cite

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Bock, Igor, and Lovíšek, Ján. "On the existence of a weak solution of the boundary value problem for the equilibrium of a shallow shell reinforced with stiffening ribs." Aplikace matematiky 23.2 (1978): 132-149. <http://eudml.org/doc/15043>.

@article{Bock1978,
abstract = {The existence and the unicity of a weak solution of the boundary value problem for a shallow shell reinforced with stiffening ribs is proved by the direct variational method. The boundary value problem is solved in the space $W(\Omega )\subset H^1_0(\Omega )\times H^1_0(\Omega ) \times H^2_0(\Omega )$, on which the corresponding bilinear form is coercive. A finite element method for numerical solution is introduced. The approximate solutions converge to a weak solution in the space $Q(\Omega )$.},
author = {Bock, Igor, Lovíšek, Ján},
journal = {Aplikace matematiky},
keywords = {numerical analysis; weak solution; boundary value problem; shallow shell; variational problem; finite elements; Numerical Analysis; Weak Solution; Boundary Value Problem; Shallow Shell; Variational Problem; Finite Elements},
language = {eng},
number = {2},
pages = {132-149},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the existence of a weak solution of the boundary value problem for the equilibrium of a shallow shell reinforced with stiffening ribs},
url = {http://eudml.org/doc/15043},
volume = {23},
year = {1978},
}

TY - JOUR
AU - Bock, Igor
AU - Lovíšek, Ján
TI - On the existence of a weak solution of the boundary value problem for the equilibrium of a shallow shell reinforced with stiffening ribs
JO - Aplikace matematiky
PY - 1978
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 23
IS - 2
SP - 132
EP - 149
AB - The existence and the unicity of a weak solution of the boundary value problem for a shallow shell reinforced with stiffening ribs is proved by the direct variational method. The boundary value problem is solved in the space $W(\Omega )\subset H^1_0(\Omega )\times H^1_0(\Omega ) \times H^2_0(\Omega )$, on which the corresponding bilinear form is coercive. A finite element method for numerical solution is introduced. The approximate solutions converge to a weak solution in the space $Q(\Omega )$.
LA - eng
KW - numerical analysis; weak solution; boundary value problem; shallow shell; variational problem; finite elements; Numerical Analysis; Weak Solution; Boundary Value Problem; Shallow Shell; Variational Problem; Finite Elements
UR - http://eudml.org/doc/15043
ER -

References

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  1. S. Agmon, Lectures on elliptic boundary value problems, New York, 1965. (1965) Zbl0142.37401MR0178246
  2. I. Hlaváček J. Nečas, On inequalities of Korn's Type I. in boundary value problems for elliptic systems of partial differential equations, Arch. Rat. Mech. Annal. 36(1970), 305-311. (1970) MR0252844
  3. J. Haslinger, Sur la solution d'un probleme de la plaque, Apl. mat. 19 (1974), No 5, 316-326. (1974) Zbl0324.73049MR0369902
  4. J. L. Lions E. Magenes, Problems aux limites non homogenes et applications, Volume I. Paris 1968. (1968) 
  5. J. Lovíšek, A weak solution of statically nonlinear problem for shallow shells considering the wind action, Scientific research, SVŠT Bratislava, 1975 (in Slovak). (1975) 
  6. A. G. Nazarov, Some contact problems of the theory of shells, (in Russian), DAN Arm. SSR, Vol. 9, No. 2, 1948. (1948) 
  7. A. G. Nazarov, Foundations of the theory and the method of computing shallow shells, (in Russian), Moscow, 1966. (1966) 
  8. J. Nečas, Les méthodes directes en theorie des équations elliptiques, Academia, Praha, 1967. (1967) MR0227584
  9. J. T. Oden J. N. Ready, Variational methods in theoretical mechanics, Springer Verlag, 1976. (1976) MR0478957
  10. G. N. Sawin N. P. Fleischman, Plates and shells with stiffening ribs, (in Russian). Kiev, 1964. (1964) 
  11. P. Seide, Small elastic deformations of thin shells, Noordhoff International Publishing Leyden, 1975. (1975) Zbl0313.73070MR0403382
  12. G. Strang Y. Fix, An analysis of the finite element method, Prentice Hall Inc., 1973. (1973) MR0443377

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