EXTRAPOLATED FIELDS IN THE FORMULATION OF THE ASSUMED STRAIN ELEMENTSPART-II - 3-DIMENSIONAL PROBLEMS

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.