Mat-1.3656 Seminar on
numerical analysis and computational science
Monday Jan 26, 2008, room
U322 at 14.15, Eirola & Stenberg
Antti Niemi, TKK
A bilinear shell element based on a refined shallow shell model
A four-node shell finite element of arbitrary quadrilateral shape
is developed and applied to the solution of static and vibration
problems. The
element incorporates five generalized degrees of freedom per node,
namely the
three displacements of the curved middle surface and the two rotations
of
its normal vector. The stiffness properties of the element are defined
using
isoparametric principles in a local coordinate system with axes
approximately
parallel to the edges of the element. A distinct feature of the present
formulation is the derivation of the geometric curvatures from the
interpolated normal
vector so as to enable explicit coupling between bending and stretching
in the
strain energy functional. In addition, the bending behavior of the
element
is improved with numerical modifications which include mixed
interpolation
of the membrane and transverse shear strains. The numerical experiments
show that the element is able to compete in accuracy with the highly
reputable
bilinear elements of the commercial codes ABAQUS and ADINA.