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Article Dans Une Revue Mathematics and Computers in Simulation Année : 1998

Static equilibrium of hyperelastic thin shell: symbolic and numerical computation

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John Cagnol
Jean-Paul Marmorat

Résumé

We here examine the natural shapes of an hyperelastic thin shell called a Carpentier's joint, when the terminal position is known. More specifically we study a rectangular strip that is a flexible thin shell with a constant curvature in its width and a null curvature in its length, at its unconstrained state. We use the theory of large displacement and small strain for hyperelastic material. We first consider an appropriate parameterization of the joint. Then we compute the Green-St Venant strain tensor with a symbolic computation system and we generate the numerical code to compute the elastic energy. In particular, we make strong use of symbolic elements to resolve some problems with zero division. Numerical minimization of this energy is used to find the shape and a couple of simulation are presented.

Dates et versions

hal-00504833 , version 1 (21-07-2010)

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John Cagnol, Jean-Paul Marmorat. Static equilibrium of hyperelastic thin shell: symbolic and numerical computation. Mathematics and Computers in Simulation, 1998, 46 (2), pp.103-115. ⟨10.1016/S0378-4754(98)00072-X⟩. ⟨hal-00504833⟩
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