A highly efficient enhanced assumed strain physically stabilized hexahedral element

A method which combines the incompatible modes method with the physical stabilization method is developed to provide a highly e cient formulation for the single point eight-node hexahedral element. The resulting element is compared to well-known enhanced elements in standard benchmark type problems. It is seen that this single-point element is nearly as coarse mesh accurate as the fully integrated EAS elements. A key feature is the novel enhanced strain elds which do not require any matrix inversions to solve for the internal element degrees of freedom. This, combined with the reduction of hourglass stresses to four hourglass forces, produces an element that is only 6.5 per cent slower than the perturbation stabilized single-point brick element commonly used in many explicit nite element codes