Constraint relation implementation for finite element analysis from an element basis

A procedure for implementing constraint relations among finite element nodal degrees of freedom is outlined. Rather than imposing the constraint relations on the global stiffness or mass matrix as the conventional approach, this procedure is based on the element formulation level in that the element matrices and vectors are properly converted to account for the effect of constraint relations before the global assemblage phase. Adjustment of the global matrix profile for constraint relations and matrix pivoting in equation solving are thus avoided, and the approach can be easily incorporated into existing program systems. In this paper, the theoretical treatment for the proposed procedure is given, and the software implementation aspects are also discussed.