Development of robust finite elements for general purpose structural analysis

Abstract

The finite element method emerged out of the old work and energy methods and matrix structural analysis to become a numerical procedure to solve practical stress analysis problems in solid and structural mechanics. With the impetus given by the rapid development of computer technology, it became the most overwhelmingly popular analysis and design computational tool for a very wide spectrum of engineering science, e.g. fluid mechanics, heat transfer and electro-magnetics. Today, there are very powerful general-purpose software codes that make analyses and design tasks that were once considered to be intractable, routinely simple. Many of these are closely held proprietary codes owned and used in-house by large engineering firms or sold or licensed and supported by specialist companies. (Recent estimates indicate that the market for these codes has reached a turnover of a billion dollars and that industries and institutions spend several tens of billions of dollars in running such codes.) These codes are rarely given out in source code. In order to have an in-house code that could be continuously up-graded and enhanced, NAL initiated some work to develop a medium-sized general purpose code (about 20,000 lines of FORTRAN code) for the analysis of laminated composite structures (FEPACS - finite element package for analysis of composite structures), recognising the importance that laminated composites were assuming in aerospace structural technology. Several key elements commonly found in general purpose packages (GPP) used by the aerospace, automobile and mechanical engineering industries were identified. These were re-designed incorporating anisotropic composite capabilities and validated. Many hurdles were faced during this task and required an examination of the basic issues at a paradigmatic level. Concepts such as consistency and variational correctness were introduced and studied critically. These guidelines played a critical role in developing robust versions of the elements and are briefly covered in this review. The paradigms also helped to identify procedures to performa priori error estimates for the quality of approximation and this allowed the elements being developed to be critically validated. The article concludes with a summary of what has been achieved and also suggests areas where the concepts can be applied fruitfully in the study of the displacement type finite element method.