AN ASYMPTOTIC THEORY OF THIN HYPERELASTIC PLATES .1. GENERAL-THEORY


ERBAY H., SUHUBI E.

INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE, cilt.29, ss.447-466, 1991 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 29 Konu: 4
  • Basım Tarihi: 1991
  • Doi Numarası: 10.1016/0020-7225(91)90087-j
  • Dergi Adı: INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE
  • Sayfa Sayıları: ss.447-466

Özet

A large deflection theory of thin hyperelastic plates is developed using an asymptotic analysis of three-dimensional equations of nonlinear elasticity in the reference configuration. The domain occupied by a thin plate is first transformed into a domain of comparable dimensions and then the displacement and stress components are scaled as in the von Karman theory. The displacement vector and the stress tensor are expanded in terms of powers of an appropriate thickness parameter and a hierarchy of equilibrium equations and boundary conditions are derived following the usual procedure. In a similar fashion the hierarchy of constitutive equations is found for an arbitrary form of strain energy function. The theories corresponding to the lowest two order members in this hierarchy are studied in detail and the zeroth order theory is shown to correspond to the celebrated von Karman theory. Moreover, it is demonstrated that the effect of physical nonlinearity becomes significant in the first order approximation.