Yi. Chen et Hk. Stolarski, EXTRAPOLATED FIELDS IN THE FORMULATION OF THE ASSUMED STRAIN ELEMENTSPART-II - 3-DIMENSIONAL PROBLEMS, Computer methods in applied mechanics and engineering, 154(1-2), 1998, pp. 1-29
Assumed strain eight-node hexahedral elements with significantly exten
ded range of applicability are presented. These elements are formulate
d using only standard translational displacements at each of their eig
ht nodes and provide accurate solutions for a variety of benchmark pro
blems such as spacial beams, plates, shells as well as general three-d
imensional elasticity problems. The elements with such characteristics
are particularly useful to model problems of complex geometry, where
different regions of the domain might impose entirely different modeli
ng requirements. The formulation starts with introduction of a paralle
lepiped domain associated with the given eight-node hexahedral element
. Then, the assumed strain field is constructed for that associated pa
rallelepiped domain. It is done by identification of various modes of
its deformation and by proper modification of the strain field in the
constant and linear bending modes. Strain and displacement extrapolati
on from the associated parallelepiped to the original hexahedral domai
n is subsequently used to establish the assumed strain field for the g
iven element. Solutions to some popular benchmark problems demonstrate
that the proposed assumed strain hexahedral elements exhibit remarkab
ly high accuracy even when severely distorted and high aspect ratio me
shes are used. Another advantage of the present elements is that locki
ng for nearly incompressible materials is also mitigated. Unfortunatel
y, the elements pass the patch test only when their shapes are paralle
lopipeds.