An adaptive singular ES-FEM for mechanics problems with singular field of arbitrary order

• An adaptive singular ES-FEM with singular fields of arbitrary order is proposed. • The formulation relies on an additional node on each edge of T3 elements connected to the singular point. • The shape functions (not the derivatives) are used to compute the stiffness matrix. • The performance of th...

Full description

Saved in:
Bibliographic Details
Published in:Computer methods in applied mechanics and engineering 2013-01, Vol.253, p.252-273
Main Authors: Nguyen-Xuan, H., Liu, G.R., Bordas, S., Natarajan, S., Rabczuk, T.
Format: Article
Language:English
Subjects:
Adaptive finite elements
Computer simulation
Crack propagation
Derivatives
Displacement
Mathematical analysis
Mathematical models
Singular ES-FEM
Singular stress fields
Singularity
Smoothed finite element method
Smoothing
Stiffness matrix
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:• An adaptive singular ES-FEM with singular fields of arbitrary order is proposed. • The formulation relies on an additional node on each edge of T3 elements connected to the singular point. • The shape functions (not the derivatives) are used to compute the stiffness matrix. • The performance of the method is improved by using an adaptive mesh technique. • Comparison is made with several other published methods and experiments. This paper presents a singular edge-based smoothed finite element method (sES-FEM) for mechanics problems with singular stress fields of arbitrary order. The sES-FEM uses a basic mesh of three-noded linear triangular (T3) elements and a special layer of five-noded singular triangular elements (sT5) connected to the singular-point of the stress field. The sT5 element has an additional node on each of the two edges connected to the singular-point. It allows us to represent simple and efficient enrichment with desired terms for the displacement field near the singular-point with the satisfaction of partition-of-unity property. The stiffness matrix of the discretized system is then obtained using the assumed displacement values (not the derivatives) over smoothing domains associated with the edges of elements. An adaptive procedure for the sES-FEM is proposed to enhance the quality of the solution with minimized number of nodes. Several numerical examples are provided to validate the reliability of the present sES-FEM method.
ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2012.07.017