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

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

The optimum regulate of versatile constructions is an lively zone of analysis. the most physique of labor during this region is worried with the regulate 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 of the static optimum regulate of a constitution made up of 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 buildings corresponding to components of satellites by way of keep watch over a lot [6]. sunlight rad- tion and radiation from different resources set off a temperature box within the constitution, which in flip generates an elastic displacement box. The displacements needs to often fulfill convinced obstacles dictated via the allowed operating stipulations of assorted orientation-sensitive tools and antennas within the house automobile. for instance, a parabolic reflector may perhaps stop to be powerful whilst present process huge deflection. The elastic deformation should be diminished by way of use of keep watch over so much, that may be imp- mented through mechanically-based actuators or extra glossy piezoelectric units. whilst 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 under consideration within the research.

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Extra resources for Advances in the Mechanics of Plates and Shells: The Avinoam Libai Anniversary Volume

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Since the constitutive equations and the compatibility equations are the same as those of Eq. (72), we show the balance equations and the boundary conditions as follows: Constitutive Equations + Compatibility equations (74) Note that, in the case of Hu-Washizu type functional, the moment equilibrium equation is recovered in place of the AMB and DMB equations. With the help of Legendre transformation, we may have the complementary function defined by (75) (76) Substituting Eq. (75) or Eq. (76) into Eq.

11] J. Mawhin and M. Willem, Critical Point Theory and Hamiltonian Systems, Springer-Verlag, 1989. [12] P. J. Rabier and J. T. Oden, Bifurcation in Rotating Bodies, Masson, 1989. [13] N. Rouche, P. Habets, and M. Laloy, Stability Theory by Liapunov’s Direct Method, Springer-Verlag, 1977. [14] G. M. Zaslavskii, Physics of Chaos in Hamiltonian Systems, World Scientific, 1998. SUETAKE*** * UCLA, 7704 Boelter Hall, Los Angeles, CA 90095-1600, USA. ** Tokyo Denki University, Hatoyama, Hiki, Saitama, Japan.

Seidman, Quasilinear hyperbolic-parabolic equations of one-dimensional viscoelasticity, J. Diff. Eqs. 1 2 3 (1995), 132–185. [5] H. Dankowicz, Chaotic Dynamics in Hamiltonian Systems, World Scientific, 1997. 16 [6] I. Ekeland, Convexity Methods in Hamiltonian Mechanics, Springer, 1990. [7] J. K. Hale, Ordinary Differential Equations, Wiley Interscience, 1969. [8] R. , Birkhäuser, 1992. [9] A. Libai and J. G. Simmonds, The Nonlinear Theory of Elastic Shells, 2nd edn. Cambridge Univ. Press, 1998.

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