New prismatic solid-shell element : Assumed strain formulation and hourglass mode analysis

Abstract

The formulation of a six-node solid-shell called SHB6, which is a linear, isoparametric element, is discussed. An eigenvalue analysis of the element stiffness matrix is first carried out. Several modifications are introduced into the formulation of the SHB6 element following the assumed strain method adopted by Belytschko and Bindeman. SHB6's coordinates and displacements are related to the nodal coordinates and displacements through the linear shape functions. Applying the simplified form of the Hu-Washizu nonlinear mixed variational principle, in which the assumed stress field is chosen to be orthogonal to the difference between the symmetric part of the displacement gradient and the assumed strain field, the formula is obtained. The newly developed SHB6 element was implemented into the finite element codes INCA and ASTER. It represents some improvement since it converges well and performs much better than the PRI6 six-node three-dimensional element in all of the benchmark problems tested.