By D. Durban, Dan Givoli, J.G. Simmonds
The optimum keep an eye on of versatile constructions is an energetic zone of analysis. the most physique of labor during this quarter is worried with the keep an eye on of time-dependent displacements and stresses, and assumes linear elastic stipulations, specifically linear elastic fabric habit and small defor- tion. See, e. g. , –, the collections of papers [4, 5], and references therein. nevertheless, within the current paper we ponder the static optimum regulate of a constitution made from a nonlinear elastic fabric and und- going huge deformation. an immense software is the suppression of static or quasi-static elastic deformation in versatile house buildings equivalent to components of satellites via keep an eye on rather a lot . sun rad- tion and radiation from different assets result in a temperature box within the constitution, which in flip generates an elastic displacement box. The displacements needs to often fulfill convinced barriers dictated by means of the allowed operating stipulations of assorted orientation-sensitive tools and antennas within the house car. for instance, a parabolic reflector may perhaps stop to be potent while present process huge deflection. The elastic deformation might be decreased by means of use of keep an eye on quite a bit, that may be imp- mented through mechanically-based actuators or extra smooth piezoelectric units. while the constitution into consideration is made up of a rubb- like fabric and is present process huge deformation, nonlinear fabric and geometric results has to be taken under consideration within the research.
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Extra info for Advances in the Mechanics of Plates and Shells: The Avinoam Libai Anniversary Volume
The AMB equations under each assumption are written as (52) 25 (53) (54) Note that a 3 = RA 3 in (G1) and (GM1) while a 3 The following points should be stressed herein: = z R A 3 in (G2) and (GM2). • The AMB equation (54) under (GM2) includes the underlined term such that a 3 x N. Since N = this term vanishes because of the definition of the cross product. As a result, the AMB equation under (GM2) is the same as that under (GM1). • The AMB equation under (G1) and (G2) does not indicate that N where 3α = N α3 • The AMB equation plays an important role in the mechanical power and the objectivity, which shall be discussed in detail, later in this paper.
Reine u. angew. Mathem. 78(1874), 136- 173. 2. : Spannungen in Kugelschalen. Festschrift H. Müller-Breslau. Leipzig, 1912. 3. : A new theory for the buckling of thin cylinders under axial compression and bending Trans. ASME, 56 (1934). 4. I. General theory of thin elastic shells. ) Prikl. Mat. Mekh. (PMM) 4 (1940), 7-34. 5. : A consistent first approximation in the general theory of thin elastic shells. Proc. , Delft. North-Holland, Amsterdam, 1960. 6. : On the nonlinear elastokinetics of shells and beams.
5. Variational Principle According to Atluri [1-4] and Suetake, Iura and Atluri , the generalized functional for the shell is given by (71) where denotes the Lagrange multiplier, the prescribed value at the boundary, and W0 and c 3 are given, under each assumption, by The variables subjected to variation in Eq. (71) are and a 3 . e. in Eq. (72) is given by Since a 3 is subjected to variation, the DMB equation is recovered as the Euler equation. 1. (52) and (55), respectively. In the case of (GM1), appears in the AMB and DMB equations which is not the case in Eqs.
Advances in the Mechanics of Plates and Shells: The Avinoam Libai Anniversary Volume by D. Durban, Dan Givoli, J.G. Simmonds