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Advances in the Mechanics of Plates and Shells: The Avinoam by D. Durban, Dan Givoli, J.G. Simmonds

By D. Durban, Dan Givoli, J.G. Simmonds

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. , [1]–[3], 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 [6]. 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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Advances in the Mechanics of Plates and Shells: The Avinoam Libai Anniversary Volume

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. , [1]–[3], the collections of papers [4, 5], and references therein.

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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.

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