Application of generalized constraints in the stiffness method of structural analysis.

The importance of correctly representing conditions in the finite element analysis of structures by the displacement or stiffness method is discussed. Methods of imposing simple nodal displacement constraints and calculating the associated reactions are reviewed. The concept of constraint coordinates is introduced in describing more complex constraining relationships among the displacements of the structure or among the forces acting on it. A generalized coordinate transformation procedure based on the coordinate concept is developed which is generally applicable to all conditions of linear, holonomic constraints. Several examples illustrating practical applications of the procedure are given. These include 1) inextensional analysis of a framed structure, 2) insertion of a pinned connection in a rigid frame, 3) rigid ring insert in shell structure, 4) free-free vibrations, and 5) static analysis of unsupported structure.