Lagrange multipliers and the primal-dual method in the non-linear static equilibrium of multibody systems

Abstract

This paper presents four different approaches to the solution of the non-linear static-equilibrium problem in complex linkages, including rigid and elastic elements. The error function is based on the potential of the system, and includes rigid elements by means of non-linear constraints. To this end use is made of Lagrange multipliers, along with the primal–dual method, penalty functions and weighted stiffness, comparisons being made between them. A Newton–Raphson method is used in seeking function minima for equilibrium positions. This procedure is also directly applicable to the other linkage and multibody position problems. © 1998 John Wiley & Sons, Ltd.