The optimal control of flexible structures is an active area of research. The main body of work in this area is concerned with the control of time-dependent displacements and stresses, and assumes linear elastic conditions, namely linear elastic material behavior and small defor- tion. See, e. g. , [1]-[3], the collections of papers [4, 5], and references therein. On the other hand, in the present paper we consider the static optimal control of a structure made of a nonlinear elastic material and und- going large deformation. An important application is the suppression of static or quasi-static elastic deformation in flexible space structures such as parts of satellites by the use of control loads [6]. Solar rad- tion and radiation from other sources induce a temperature field in the structure, which in turn generates an elastic displacement field. The displacements must usually satisfy certain limitations dictated by the allowed working conditions of various orientation-sensitive instruments and antennas in the space vehicle. For example, a parabolic reflector may cease to be effective when undergoing large deflection. The elastic deformation can be reduced by use of control loads, which may be imp- mented via mechanically-based actuators or more modern piezoelectric devices. When the structure under consideration is made of a rubb- like material and is undergoing large deformation, nonlinear material and geometric effects must be taken into account in the analysis.

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Dedication. Publications by Avinoam Libai. Breathing Oscillations of Rotating Nonlinearly Elastic and Viscoelastic Rings; S.S. Antman. A Consistent Theory of, and a Variational Principle for, Thick Elastic Shells Undergoing Finite Rotations; S.N. Atluri, et al. On the Theory of Quasi-Shallow Shells; E.L. Axelrad. Experiments for Measuring Interface Fracture Properties; L. Banks-Sills. Some Refinements in Analysis of Thick-Walled Tubes in Axial Bending; C.W. Bert. Optimization of Panels with Riveted Z-Shaped Stiffeners via PANDA2; D. Bushnell. Nondestructive Testing of Thin-Walled Ceramic Matrix Composites with Matrix Cracks Using Thermography; L.W. Byrd, V. Birman. A Shell-Buckling Paradox Resolved; C.R. Calladine. Buckling Analysis of Composite Plates; R. Gilat, J. Aboudi. Static Optimal Control of the Large Deformation of a Hyperelastic Plate; D. Givoli, I. Patlashenko. Computer Simulation of Nonisothermal Elastoplastic Shell Responses; W.B. Krätzig, et al. On Application of the Exact Theory of Elastic Beams; P. Ladevèze, et al. Effects of Eccentric Stiffening on Static and Dynamic Nonlinear Response of Rectangular Panels Exposed to Thermomechanical Loading; L. Librescu, M.A. Souza. Bending and Twisting Effects in the Three-Dimensional Finite Deformation of an Inextensible Network; L. Luo, D.J. Steigman. Plastic Buckling of Rectangular Plates with Random Material Properties and Random Loading: A Demonstration of Probabilistic Structural Analysis; G. Maymon. On Using Rotations as Primary Variables in the Non-Linear Theory of Thin Irregular Shells; W. Pietraszkiewicz. On Shear Deformation Plate Solutions: Relationship to the Classical Solutions; J.N. Reddy, C.M. Wang. A Simple Derivation of Cosserat Theories of Shells, Rods and Points; M.B.Rubin. Structural Similitude and Scaling Laws for Plates and Shells: A Review; G.J. Simitses, et al. Reduction of the Linear Sanders-Koiter Equations for Fully Anisotropic Non-Circular Cylindrical Shells to Two Coupled Fourth-Order Equations; J.G. Simmonds. Large Deformation of a Pressurized Tube; C.R. Steele. On Lateral Buckling of End-Loaded Cantilevers with Transverse Shear Deformations; F.Y.M. Wan.