Structural Engineering and Mechanics

  • 제6권2호
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  • Pages.173-183
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  • 1998
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
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Finite element procedure of initial shape determination for hyperelasticity

  • Yamada, Takahiro (Department of Architecture, Faculty of Engineering, Science University of Tokyo)
  • 발행 : 1998.03.25
⟨ 이전 논문 다음 논문 ⟩

초록

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.

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참고문헌

  1. Govindjee, S. and Mihalic, P.A. (1995), "Computational methods for inverse finite elastostatics", UCB/SEMM-95/01.
  2. Kleiber, M. and Hisada, H. (Eds.) (1993), Design-Sensitivity Analysis, Atlanta Technology Publications.
  3. Shield, R.T. (1967), "Inversed deformation results in finite elasticity", Z. Angnew, Math, Phys., 18, 490-500. https://doi.org/10.1007/BF01601719
  4. Yamada, T. (1993), "A rezoning procedure for finite element analysis of incompressible hyperelasticity", Computing Systems in Engineering, 4, 59-68. https://doi.org/10.1016/0956-0521(93)90029-V
  5. Yamada, T. and Kikuchi, F. (1993), "An arbitarary Lagrangian-Eulerian finite element method for incompressible hyperelasticity", Computer Methods in Applied Mechamics Engineering, 102, 149-177. https://doi.org/10.1016/0045-7825(93)90106-8

피인용 문헌

  1. On a recursive formulation for solving inverse form finding problems in isotropic elastoplasticity vol.1, pp.1, 2014, https://doi.org/10.1186/2213-7467-1-10
  2. Finite element modelling of inverse design problems in large deformations anisotropic hyperelasticity vol.74, pp.6, 2008, https://doi.org/10.1002/nme.2193
  3. Pointwise Identification of Elastic Properties in Nonlinear Hyperelastic Membranes—Part I: Theoretical and Computational Developments vol.76, pp.6, 2009, https://doi.org/10.1115/1.3130805
  4. Inverse Shape Design of Deformable Structures and Deformable Wings vol.48, pp.1, 2011, https://doi.org/10.2514/1.C001007
  5. On referential and spatial formulations of inverse elastostatic analysis vol.310, 2016, https://doi.org/10.1016/j.cma.2016.06.020
  6. An iterative method for the inverse elasto-static problem vol.27, pp.8, 2011, https://doi.org/10.1016/j.jfluidstructs.2011.08.002
  7. Inverse finite element method for large-displacement beams vol.84, pp.10, 2010, https://doi.org/10.1002/nme.2935
  8. Inverse formulation for geometrically exact stress resultant shells vol.74, pp.8, 2008, https://doi.org/10.1002/nme.2215