Shape Measuring Criteria And The Establishment Of Benchmark Tests For Single Membrane 

Elements

This is the summary report on the project initiated by NAFEMS  to produce a set of single element benchmark tests and also to define a set of suitable shape parameters in order to be able to assess the performance of membrane finite elements.

It is important at this stage to distinguish between two sources of error in results produced by a finite element within its basic formulation to model a particular stress field. If the polynomial order of the stress field is greater than that contained within the element formulation, the stresses sampled will almost certainly be in error. This can only be checked at the post-processing stage in analysis. The second source of error, and the one which is of primary interest here, is the degradation in element performance as the shape is distorted from square in the mesh description. This source of error can be flagged before results are produced and is therefore a pre-processing function.

Stage 1 of the project was concerned with a review of existing work on the subject of shape sensitivity studies related to Finite Element analysis, and also the definition of the shape parameter tests to be used to assess the sensitivity of single elements to shape distortion.

Shape 2 involved implementing the definitions from stage 1 and running well over one thousand individual analyses t investigate the trends associated with distorting elements in pre-defined ways.

In Stage 3 the results produced were critically assessed and benchmarks defined to illustrate the sensitivity of elements to shape distortions. Recommendations were also made on suitable shape parameters that directly influence the accuracy of results produced.