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Structural Engineering and Mechanics
  Volume 6, Number 2, March 1998 , pages 173-183

Finite element procedure of initial shape determination for hyperelasticity
Yamada T

    In the shape design of flexible structures. it is useful to predict the initial shape from the desirable large deformed shapes under some loading conditions. In this paper, we present a numerical procedure of an initial shape determination problem for hyperelastic materials which enables us to calculate an initial shape corresponding to the prescribed deformed shape and boundary condition. The present procedure is based on an Arbitrary Lagrangian-Eulerian (ALE) finite element method for hyperelasticity, in which arbitrary change of shapes in both the initial and deformed states can be treated by considering the variation of geometric mappings in the equilibrium equation. Then the determination problem of the initial shape can be formulated as a nonlinear problem to solve the unknown initial shape for the specified deformed shape that satisfies the equilibrium equation. The present approach can be implemented easily to the finite element method by employing the isoparametric hypothesis. Some basic numerical results are also given to characterize the present procedure.

Key Words
    initial shape determination, incompressible hyperelasticity, arbitrary Lagrangian-Eulerian, finite element method
Yamada T, Sci Univ Tokyo, Fac Engn, Dept Architecture, Shinjuku Ku, 1-3 Kagurazaka, Tokyo 162, Japan
Sci Univ Tokyo, Fac Engn, Dept Architecture, Shinjuku Ku, Tokyo 162, Japan

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