Constraint relationships in linear and nonlinear finite element analyses

Finite element analysis of engineering structures commonly requires the use of inter‐nodal displacement constraints. Current algorithms for this facility—elimination, Lagrange multipliers and penalty function methods—are briefly reviewed. An alternative approach is proposed which avoids some of the problems of these methods. This technique uses solution of the unconstrained stiffness equation with an extended number of right‐hand sides. The resulting solutions are then combined to satisfy the constraints. This method has application in the synthesis of sub‐structures with incompatible boundary variables. It is particularly efficient when the constraint affects many variables but the kinematics of the constraint can be expressed in terms of few independent variables, e.g. rigid body motion of part of the structure. In common with the Lagrange method, it produces data for use in a nonlinear analysis with constraints. The formulation of ‘rigid body’ constraints in geometric nonlinearity is detailed and demonstrated.