The Individual Element Test: A Basis for Checking and Deriving Elements

This paper on "The Individual Element Test: A Basis for Checking and Deriving Elements" was presented at the International Conference on Quality Assurance and Standards in Finite Element Analysis - 22-25 May 1989, Stratford-upon-Avon, England.

Summary

The paper discusses the concept of acceptance tests for finite elements through establishing explicit requirements that the stiffness matrix must fulfil. This may be done through the "individual element test" which Is a set of linear constraints that an element must satisfy identically in order to converge. This concept has been extended to a non-traditional way of formulating finite elements, denoted the "free formulation". This method allows for using non conforming displacement functions as well as tuning of the energy of an element, and it forms the basis for new classes of elements. The paper gives examples of such elements for membranes, plates, shells and solids.