Comparison among nonlinear optimization methods for the static equilibrium analysis of multibody systems with rigid and elastic elements

摘要

The present paper describes a set of procedures for the solution of the nonlinear static-equilibrium problem in complex multibody mechanical systems, including rigid and elastic elements. The error function is a simple one based on the potential function, which includes rigid elements by means of nonlinear constraints. To this end Lagrange Multipliers, along with various versions of the Augmented Lagrange Multipliers (ALM) or Primal-Dual Method are used, comparisons are made between them. A Newton-Raphson second-order method is used in seeking function minima for equilibrium positions. This procedure is also directly useful for other mechanism position problems, such as initial position, finite displacements, and deformed position, as well as direct and inverse problems.