# 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 (1978)

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

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topBock, 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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- J. L. Lions E. Magenes, Problems aux limites non homogenes et applications, Volume I. Paris 1968. (1968)
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- A. G. Nazarov, Some contact problems of the theory of shells, (in Russian), DAN Arm. SSR, Vol. 9, No. 2, 1948. (1948)
- A. G. Nazarov, Foundations of the theory and the method of computing shallow shells, (in Russian), Moscow, 1966. (1966)
- J. Nečas, Les méthodes directes en theorie des équations elliptiques, Academia, Praha, 1967. (1967) MR0227584
- J. T. Oden J. N. Ready, Variational methods in theoretical mechanics, Springer Verlag, 1976. (1976) MR0478957
- G. N. Sawin N. P. Fleischman, Plates and shells with stiffening ribs, (in Russian). Kiev, 1964. (1964)
- P. Seide, Small elastic deformations of thin shells, Noordhoff International Publishing Leyden, 1975. (1975) Zbl0313.73070MR0403382
- G. Strang Y. Fix, An analysis of the finite element method, Prentice Hall Inc., 1973. (1973) MR0443377

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