A novel continuum model for the reduction of numerical errors of finite-element analysis

作者：Mohammadi H^*; Bahramian F; Herzog W

来源：Proceedings of the Institution of Mechanical Engineers - Part C: Journal of Mechanical Engineering Science , 2011, 225(C4): 817-825.

DOI：10.1243/09544062JMES2319

• finite-element method
• finite-difference method
• least-square algorithm
• continuum model
• computational mechanics
• numerical scheme

The authors developed a novel numerical formulation that reduces the computational expense of solving linear and non-linear constitutive models. A finite-element constitutive law followed by a novel continuum model is discussed. The proposed approach is employed to reduce numerical errors obtained from the standard finite-element method. The continuum model is based on the Lagrange multipliers strategy along with the finite-difference method and a least-square algorithm. It is crucial to this approach that the components of either the strain or the stress tensor are known at the nodes of the finite-element mesh. The proposed model is independent of element topology which can be strongly and arbitrarily distorted.