Error Control in Finite Element Analysis Using the Hierarchical Modelling Process

This paper on "Error Control in Finite Element Analysis Using the Hierarchical Modelling Process" was presented at the 5th International Conference on Reliability of Finite Element Methods for Engineering Applications - 10-12 May 1995, Amsterdam, The Netherlands.

Summary

This paper describes a process of identification and control of errors that may be encountered when analysing a structure using the finite element method. This has been carried out by following a hierarchical modelling process which divides the analysis into clearly defined steps starting from the real world problem to the interpretation of the analysis results.
In each step of the modelling process, possible sources of error are identified and methods of controlling and quantifying such errors are investigated.
The concept of dividing the structure into features (components) during the modelling process is presented and its advantages in identifying and controlling analysis errors are explored.
To demonstrate the benefits of the hierarchical modelling process and the features/primitives concept, the vibration analysis of a relatively simple structure formed of beams and plates bolted and welded together is presented.
Although the detection and control of errors in the presented example were carried out by inspecting intermediate results obtained during the steps of the analysis, this procedure is intended for implementation in an automated process where mathematical assessment of intermediate and final results can be carried out. This automated process will be necessary when analysing complex structures having large numbers of possible error sources, where many tests and intermediate analyses may be required.
To help construct such an automated process, various methods of detecting and controlling errors are proposed. These methods can be utilised in a process of objective error control measures during the analysis.