Finite elements based on energy orthogonal functions

✍ Scribed by P. G. Bergan

• Publisher: John Wiley and Sons
• Year: 1980
• Tongue: English
• Weight: 731 KB
• Volume: 15
• Category: Article
• ISSN: 0029-5981
• DOI: 10.1002/nme.1620151009

✦ Synopsis

Abstract

It is shown how the convergence requirements for a finite element may be written as a set of linear constraints on the stiffness matrix. It is then attempted to construct a best possible stiffness matrix. The constraint equations restrict the way in which these stiffness terms may be chosen; however, there is normally still room for improving or optimizing an element. It is demonstrated how an element stiffness matrix may be found using rigid body, constant strain and higher order deformation modes. Further, it is shown how the constraint equations may be exploited in deriving an ‘energy orthogonality theorem’. This theorem opens the door to a whole new class of simple finite elements which automatically satisfy the convergence requirements. Examples of deriving plane stress and plate bending elements are given.