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The optimum regulate of versatile buildings is an energetic zone of analysis. the most physique of labor during this region is anxious with the keep watch over of time-dependent displacements and stresses, and assumes linear elastic stipulations, particularly linear elastic fabric habit and small defor- tion. See, e. g. , –, the collections of papers [4, 5], and references therein. however, within the current paper we think about the static optimum keep an eye on of a constitution made from a nonlinear elastic fabric and und- going huge deformation. a tremendous software is the suppression of static or quasi-static elastic deformation in versatile area constructions equivalent to elements of satellites by means of keep watch over a lot . sunlight 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 convinced obstacles dictated via the allowed operating stipulations of assorted orientation-sensitive tools and antennas within the area automobile. for instance, a parabolic reflector could stop to be potent while present process huge deflection. The elastic deformation should be diminished via use of keep watch over so much, that may be imp- mented through mechanically-based actuators or extra glossy piezoelectric units. while the constitution into account is made up of 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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The optimum regulate of versatile buildings is an energetic sector of analysis. the most physique of labor during this quarter is anxious 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.
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Additional info for Advances in the Mechanics of Plates and Shells: The Avinoam Libai Anniversary Volume
Kon. Ned. Ak. , B 73 , 460-478. 16. G. A. (1972) Nonlinear shell theory with finite rotation and stress-function vectors, J. Appl. , ASME, 3 9 , 1085-1090. 17. , Iura, M. N. (1999) Shell theories with drilling degrees of freedom and geometrical and material assumptions, Computer Modeling and Simulation in Engineering, 4(1), 42-49. 18. Washizu, K. , Pergamon Press. 19. C. , McGraw-Hill. L. , Woodside, CA 94062, USA Abstract – The theory of small-strain unrestricted deformation of thin elastic shells is specialized to the ‘Donnell-type’ theory of quasi-shallow shells, which owes its consequent - intrinsic and dual formulation to the idea first enunciated by Avinoam Libai.
A position of the a α inside the tangent plane of the deformed surface specifies a partition of the shear angle into the two angles between aα and a α *. 6) represented by a αβ ' = a β α '. This choice makes E αβ equal to the standard strain tensor (a αβ * – a αβ )/ 2 . However, the is different from the tensor , known as the “obvious choice” for the bending strain. 8). 3) requires derivatives of the local basis a α and curvature vectors k α , which have moved in the course of surface deformation.
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.