Previous |  Up |  Next


numerical analysis; weak solution; boundary value problem; shallow shell; variational problem; finite elements
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 $Q(\Omega)$.
[1] S. Agmon: Lectures on elliptic boundary value problems. New York, 1965. MR 0178246 | Zbl 0142.37401
[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. MR 0252844
[3] J. Haslinger: Sur la solution d'un probleme de la plaque. Apl. mat. 19 (1974), No 5, 316-326. MR 0369902 | Zbl 0324.73049
[4] J. L. Lions E. Magenes: Problems aux limites non homogenes et applications. Volume I. Paris 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).
[6] A. G. Nazarov: Some contact problems of the theory of shells. (in Russian), DAN Arm. SSR, Vol. 9, No. 2, 1948.
[7] A. G. Nazarov: Foundations of the theory and the method of computing shallow shells. (in Russian), Moscow, 1966.
[8] J. Nečas: Les méthodes directes en theorie des équations elliptiques. Academia, Praha, 1967. MR 0227584
[9] J. T. Oden J. N. Ready: Variational methods in theoretical mechanics. Springer Verlag, 1976. MR 0478957
[10] G. N. Sawin N. P. Fleischman: Plates and shells with stiffening ribs. (in Russian). Kiev, 1964.
[11] P. Seide: Small elastic deformations of thin shells. Noordhoff International Publishing Leyden, 1975. MR 0403382 | Zbl 0313.73070
[12] G. Strang Y. Fix: An analysis of the finite element method. Prentice Hall Inc., 1973. MR 0443377
Partner of
EuDML logo