Geometrically Nonlinear Structural Analysis Using The Eight-Node Hexahedral Element With One-Point Quadrature And Hourglass Control.

Abstract

An eight-node hexahedral element with uniform reduced integration, which is free
of volumetric and shear locking and has no spurious singular modes, is implemented here for
geometrically nonlinear static structural analysis. In the element formulation, one-point
quadrature is used so that the element tangent stiffness matrix is given explicitly and
computational time is substantially reduced in the geometrically nonlinear analysis. In order
to avoid shear locking the generalized strain vector is written in a local corotational system
and certain non-constant terms in the shear strain components are omitted. The volumetric
locking is cured by setting the dilatational part of the normal strain components to be
constant. A corotational procedure is employed to obtain the deformation part of the
displacement increment in the corotational system and update element stresses and internal
force vectors. Numerical examples verify the computational efficiency and the potential of the
three-dimensional element in the analysis of shells, plates and beams undergoing large
displacements and rotations. Results are compared to those employing classical plate and
shell elements.