By D. Durban, Dan Givoli, J.G. Simmonds
The optimum keep an eye on of versatile buildings is an energetic zone of study. the most physique of labor during this sector is anxious with the regulate 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 reflect on the static optimum keep watch over of a constitution made from a nonlinear elastic fabric and und- going huge deformation. a big software is the suppression of static or quasi-static elastic deformation in versatile house constructions similar to elements of satellites by means of keep watch over quite a bit . sun rad- tion and radiation from different assets set off a temperature box within the constitution, which in flip generates an elastic displacement box. The displacements needs to frequently fulfill definite obstacles dictated by way of the allowed operating stipulations of varied orientation-sensitive tools and antennas within the house automobile. for instance, a parabolic reflector might stop to be potent while present process huge deflection. The elastic deformation will be diminished by means of use of keep watch over lots, that could be imp- mented through mechanically-based actuators or extra smooth piezoelectric units. while the constitution into account is made from a rubb- like fabric and is present process huge deformation, nonlinear fabric and geometric results needs to be taken into consideration within the research.
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Extra resources for Advances in the Mechanics of Plates and Shells: The Avinoam Libai Anniversary Volume
But, ordinarily, the undeformable local basis a α , a β proves preferable. , a αβ . The strain of the surface will be characterized by vectors Eα , ρ α and K α . These are defined as the difference between the a α*, b α * and k α* of the current shape, and the respective vectors a α , b α and k α (which are recalled to be the initial a α , b α and k α , moved with the tangent plane, but not otherwise changed by the deformation). 8) The components Eαβ represent the extension and the shear strain.
N. (1980) On some new general and complementary energy theorems for the rate problems in finite strain, classical elastoplasticity, Journal of Structural Mechanics, 8 (1), 61-92. 3. N. (1983) Alternate stress and conjugate strain measures, and mixed variational formulations involving rigid rotations, for computational analysis of finitely deformed solids, with application to plates and shell - I Theory, Computers and Structures, 18 , 93-116. 32 4. N. and Cazzani, A. (1995) Rotations in computational solid mechanics, Archives of Computational Methods in Engineering, 2(1), 49-138.
Despite its illegitimate part, the theory did not incur any widely perceived grave errors in applications. 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.
Advances in the Mechanics of Plates and Shells: The Avinoam Libai Anniversary Volume by D. Durban, Dan Givoli, J.G. Simmonds