Eight‐node hexahedral elements for gradient elasticity analysis

Abstract

AbstractComputational analysis of gradient elasticity often requires the trial solution to be C1 yet constructing C1 finite elements is not trivial. Further to the recent success of 4‐node quadrilateral and 4‐node tetrahedral elements which employ only displacement and displacement gradient as the nodal dofs, this paper develops 8‐node hexahedral elements for gradient elasticity analyses by the generalized discrete Kirchhoff and the relaxed hybrid‐stress methods. Both methods require a C0 displacement interpolation which is quadratic complete in the Cartesian coordinates. Starting from the 8‐node hexahedron with only displacement and displacement gradient as the nodal dofs, it is noted that another 6 mid‐face nodes and a condensable bubble node with displacement dofs are required for the quadratic completeness. The dofs of the mid‐face node are then constrained to those of the corner nodes defining the same element face. The C0 displacement of the resultant 8‐node hexahedron is quadratic complete only when all element faces are flat. Though the quadratic completeness of the two 8‐node elements has been partially compromised, the relaxed hybrid‐stress element model is marginally more accurate than the previously devised 4‐node tetrahedral elements.