Vol. 2, No. 7, 2007

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Nonlinear shell theory: a duality approach

Giovanni Romano, Carmen Sellitto and Raffaele Barretta

Vol. 2 (2007), No. 7, 1207–1230

The nonlinear kinematics of thin shells is developed in full generality according to a duality approach in which kinematics plays the basic role in the definition of the model. The Kirchhoff–Love shell model is the central issue and is discussed in detail but shear deformable and polar models are also considered and critically reviewed. The analysis is developed with a coordinate-free approach which provides a direct geometrical picture of the shell model. The finite and tangent Green strains of the foliated continuum are explicitly expressed in terms of middle surface kinematics. The new expressions contributed here do not require the splitting of the velocity into parallel and normal components to the middle surface, and provide a computationally convenient context. Finite strain measures for the shell and their tangent and secant rates are analyzed and consistency and nonredundancy properties are discussed. The relations between the finite Green strain, its tangent and secant rates and the corresponding shell strains, are provided. The differential and boundary equilibrium equations of the shell are given in variational terms, both in unsplit and split form. A new expression of the boundary equilibrium equations is contributed and its mechanical soundness with respect to the classical one is emphasized. Equilibrium in a reference placement for the shell model is briefly discussed.

strain measures, nonlinear shells, kinematics, equilibrium
Received: 6 December 2005
Accepted: 12 March 2007
Published: 1 September 2007
Giovanni Romano
University of Naples Federico II
Department of Structural Engineering
via Claudio 21
80125 Naples
Carmen Sellitto
Centro Italiano Ricerche Aerospaziali (CIRA)
LAMC (Computational Mechanics Laboratory)
via Maiorise
81043 Capua (CE)
Raffaele Barretta
University of Naples Federico II
Department of Structural Engineering
via Claudio 21
80125 Naples