By D. Durban, Dan Givoli, J.G. Simmonds
The optimum regulate of versatile constructions is an lively zone of study. the most physique of labor during this zone is anxious with the keep watch over 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. nonetheless, within the current paper we examine the static optimum keep an eye on of a constitution made from a nonlinear elastic fabric and und- going huge deformation. a big program is the suppression of static or quasi-static elastic deformation in versatile area constructions comparable to components of satellites via keep watch over 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 frequently fulfill definite boundaries dictated by way of the allowed operating stipulations of assorted orientation-sensitive tools and antennas within the house car. for instance, a parabolic reflector may possibly stop to be potent while present process huge deflection. The elastic deformation could be decreased through use of keep an eye on lots, that could be imp- mented through mechanically-based actuators or extra sleek piezoelectric units. whilst the constitution into consideration is made from a rubb- like fabric and is present process huge deformation, nonlinear fabric and geometric results has to be taken into consideration within the research.
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Extra info for Advances in the Mechanics of Plates and Shells: The Avinoam Libai Anniversary Volume
It is a theory specialized for the strongly variable stress states . 2) make it quite plain: the applicability of the theory of ‘quasishallow’ shells depends, not alone on the shell shape, however shallow it may be. An example. Donnell himself . Consider an infinitely long cylinder with closed circular cross section, buckling under radial pressure. , ) which is 33% above the correct p. l), this case is, out of reach of the theory. References 1 . : Das Gleichgewicht und die Bewegung einer unendlich dünnen, beliebig gekrümmten elastischen Schale.
This ‘skating on thin ice’  was, in actual fact, made possible by the concentration on a quite specific class of problems - those of buckling with small wave-length pattern. Such modes do, indeed, involve nearly exclusively displacements of the kind shown later to justify the strain-displacement relations employed by Donnell . - These modes encompass intensively varyable, predominantly normal, deflection and no large rotations. Libai in 1962  has opened the way to the consequent formulation of the Donnell-type theory.
The change of shell thickness is allowed in (G2) and (GM2). The kinematic assumption only is used in (G2), while both kinematic and stress states assumptions are used in (GM2). In the assumptions (GM1) and (GM2), we assume that t3 α = 0. This assumption does not indicate that the out-of-plane shearing stress resultants vanish. It will be shown later that the shearing stress resultants N α 3 do not vanish even if N 3 α = 0 holds. The time derivative of a3 corresponding each assumption is given by (39) (40) where W x I = RR t .