Article
Full entry |
PDF
(1.4 MB)
Feedback
PDF
(1.4 MB)
Feedback
Summary:
In this paper we prove the existence and the uniqueness of the weak solution of an orthotropic plate with stiffening ribs by methods of the abstract variational calculus. The solution of boundary value problem is obtained in the space $V(\Omega)\subset W_2^2(\Omega)$, where the bilinear form is $V(\Omega)$-elliptic. We introduce classical Galerkin's method for numerical solution Galerkin's approximation in space $V(\Omega)$ strongly converges to weak solution of boundary value problem in $V(\Omega)$.
References:
[1] S. Agmоn: Lectures on elliptic boundary value problems. New York, 1965. MR 0178246
[2] Hlaváček I., Nečas J.: On inequalities of Korn's Type I. boundary value problems for elliptic systems of partial differential equations. Arc. Rat. Mech. Annal. 36 (1970), 305-311. MR 0252844 | Zbl 0193.39001
[3] Lekhnitskij S. G.: Anisotropic Plates. (In Russian), Gos. isdatel'stvo, Moscow 1957.
[4] Lovíšek J.: Operator of thin plate reinforced with thin walid ribs. Aplikace matematiky, Vol. 18 (1973), No 5, 305-314. MR 0329400
[5] Lions J. L., Magenes E.: Problems aux limites non homogenes et applications. Volume I. Paris 1968.
[6] Nečas J.: Les méthodes directes en theorie des équations elliptiques. Academia, Praha 1967. MR 0227584
[7] Sarkisjan V. S.: Some problems of the theory of elasticity of an anisotropic solid. (in Russian), Yerevan 1970.
[8] Sawin G. N., Fleischman N. P.: Plates and Shells with Stiffening Ribs. (in Russian), Kiev, 1964.
Search
Partner of
