Stress recovery and error estimation for the scaled boundary finite‐element method

By A. Deeks, J. Wolf. 2002

50 citations recorded by the source corpus.

The scaled boundary finite‐element method is a novel semi‐analytical technique, combining the advantages of the finite element and the boundary element methods with unique properties of its own. This paper develops a stress recovery procedure based on a modal interpretation of the scaled boundary finite‐element method solution process, using the superconvergent patch recovery technique. The recovered stresses are superconvergent, and are used to calculate a recovery‐type error estimator. A key feature of the procedure is the compatibility of the error estimator with the standard recovery‐type finite element estimator, allowing the scaled boundary finite‐element method to be compared directly with the finite element method for the first time. A plane strain problem for which an exact solution is available is presented, both to establish the accuracy of the proposed procedures, and to demonstrate the effectiveness of the scaled boundary finite‐element method. The scaled boundary finite‐element estimator is shown to predict the true error more closely than the equivalent finite element error estimator. Unlike their finite element counterparts, the stress recovery and error estimation techniques work well with unbounded domains and stress singularities. Copyright © 2002 John Wiley & Sons, Ltd.

Subfields: Computational Mechanics, Electrical and Electronic Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/c58b8ed0fd81aeec9a98e9aa1d5b2c383a1d578c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. Chongmin Song
2. Charles E. Augarde
3. T. Vu
4. A. Deeks
5. E. Ooi
6. Francis Tin-Loi
7. Zhenjun Yang

In Electrical and Electronic Engineering

1. Chongmin Song
2. Charles E. Augarde
3. A. Deeks
4. T. Vu
5. Francis Tin-Loi
6. E. Ooi

In Mechanics of Materials

1. Chongmin Song
2. T. Vu
3. A. Deeks
4. Charles E. Augarde
5. E. Ooi
6. Francis Tin-Loi
7. Sundararajan Natarajan
8. Zhenjun Yang

Citations in the corpus

• A p‐hierarchical adaptive procedure for the scaled boundary finite element method (2002, methodology): “first refinement p= [2; 2; 2; 2; 2; 2; 2; 2] is visually similar to the displacement field approximated for the last refinement p=[2; 2; 2; 2; 3; 4; 6; 6].”
• A super‐element for crack analysis in the time domain (2004, methodology): “Recently, stress recovery and error estimation techniques [24] and an h-hierarchical adaptive procedure [25] for the scaled boundary finite-element method are developed.”
• A matrix function solution for the scaled boundary finite-element equation in statics (2004, unknown): “[8].”
• A meshless local Petrov-Galerkin scaled boundary method (2005, methodology): “A virtual work derivation for elastostatics [4] increased the transparency of the method considerably, leading to the development of stress recovery and error estimation procedures [5], which in turn allowed adaptive procedures to be implemented [6].”