## On a stress resultant geometrically exact shell model. I: Formulation and optimal parametrization.(English)Zbl 0692.73062

The review of main ideas and advantages of the geometrically exact shell models is presented. It is intended to show that classical shell theory, phrased as one-director Cosserat surface, leads to an efficient numerical implementation which is suitable for large scale computation. The local balance laws, the local constitutive equation and the weak form of the momentum equations are precisely formulated but in a form suitable for numerical analysis and finite element implementation. Next, the basic kinematics of the model, including the precise definitions of the resultant linear, angular, and direction momentum is considered. Then local momentum balance equation in terms of resultant is introduced. The invariant constitutive equations in terms of stress resultants and conjugate strain measures are developed. Some directions of subsequent research (mainly concerned with numerical analysis within the framework of the finite element method) are briefly discussed.
Reviewer: A.Žilinskas

### MSC:

 74P99 Optimization problems in solid mechanics 74K15 Membranes 74S05 Finite element methods applied to problems in solid mechanics 74A20 Theory of constitutive functions in solid mechanics 74Axx Generalities, axiomatics, foundations of continuum mechanics of solids 74B20 Nonlinear elasticity
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