Geometrically non-linear analysis in elastodynamics using the eight-node finite element with one-point quadrature and the generalized-alpha method

Abstract

A formulation for the geometrically non-linear dynamic analysis of elastic structures using the eight-node hexahedral element with one-point quadrature and the Generalized-α method is presented in this paper. It is well known that the Newmark’s method, whichis considered the most popular time-stepping scheme for structural dynamics, exhibits un-conditional stability in the case of linear systems. However, this characteristic is lost in thenon-linear regime owing to the lack of an energy balance within each time step of the integra-tion process. In order to obtain a numerical scheme with energy-conserving and controllablenumerical dissipation properties the Generalized-α method is implemented, where optimized time integration parameters are determined as functions ofthe spectral radius. The Finite Element Method (FEM) is employed in the present model for spatial discretizations using the eight-node hexahedral isoparametric element with uniform reduced integration. In order to avoid the excitation of spurious modes an efficient hourglass control technique is used sothat volumetric locking and shear locking are not observed. Some examples are analyzed in order to investigate the behaviour of the element formulation with one-point integration under highly non-linear conditions.