Author/Authors :
George Z. Voyiadjis، نويسنده , , Pawel Woelke، نويسنده ,
Abstract :
A non-linear finite element analysis is presented, for the elasto-plastic behavior of thick shells and plates including the
effect of large rotations. The shell constitutive equations developed previously by the authors [Voyiadjis, G.Z., Woelke,
P., 2004. A refined theory for thick spherical shells. Int. J. Solids Struct. 41, 3747–3769] are adopted here as a base for the
formulation. A simple C0 quadrilateral, doubly curved shell element developed in the authors previous paper [Woelke,
P., Voyiadjis, G.Z., submitted for publication. Shell element based on the refined theory for thick spherical shells] is
extended here to account for geometric and material non-linearities. The small strain geometric non-linearities are taken
into account by means of the updated Lagrangian method. In the treatment of material non-linearities the authors adopt:
(i) a non-layered approach and a plastic node method [Ueda, Y., Yao, T., 1982. The plastic node method of plastic analysis.
Comput. Methods Appl. Mech. Eng. 34, 1089–1104], (ii) an Iliushin s yield function expressed in terms of stress
resultants and stress couples [Iliushin, A.A., 1956. Plastichnost . Gostekhizdat, Moscow], modified to investigate the
development of plastic deformations across the thickness, as well as the influence of the transverse shear forces on plastic
behaviour of plates and shells, (iii) isotropic and kinematic hardening rules with the latter derived on the basis of the
Armstrong and Frederick evolution equation of backstress [Armstrong, P.J., Frederick, C.O., 1966. A mathematical
representation of the multiaxial Bauschinger effect. (CEGB Report RD/B/N/731). Berkeley Laboratories. R&D
Department, California.], and reproducing the Bauschinger effect. By means of a quasi-conforming technique, shear
and membrane locking are prevented and the tangent stiffness matrix is given explicitly, i.e., no numerical integration
is employed. This makes the current formulation not only mathematically consistent and accurate for a variety of applications,
but also computationally extremely efficient and attractive.
Keywords :
thick plates and shells , elasto-plastic analysis , Kinematic hardening , large displacements