A mixed variational principle for finite element analysis

✍ Scribed by Michael L. Day; T. Y. Yang

• Publisher: John Wiley and Sons
• Year: 1982
• Tongue: English
• Weight: 770 KB
• Volume: 18
• Category: Article
• ISSN: 0029-5981
• DOI: 10.1002/nme.1620180808

✦ Synopsis

Abstract

A mixed variational principle is developed and utilized in a finite element formulation. The procedure is mixed in the sense that it is based upon a combination of modified potential and complementary energy principles. Compatibility and equilibrium are satisfied throughout the domain a priori, leaving only the boundary conditions to be satisfied by the variational principle. This leads to a finite element model capable of relaxing troublesome interelement continuity requirements. The nodal concept is also abandoned and, instead, generalized parameters serve as the degrees‐of‐freedom. This allows for easier construction of higher order elements with the displacements and stresses treated in the same manner. To illustrate these concepts, plane stress and plate bending analyses are presented.