Lagrange multipliers and the primal-dual method in the nonlinear static equilibrium of multibody systems. (English) Zbl 0913.73050
Summary: This paper presents four different approaches to the solution of the nonlinear 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 nonlinear constraints. To this end, we use Lagrange multipliers, along with the primal-dual method, penalty functions and weighted stiffness, and make comparisons between them. A Newton-Raphson method is employed for seeking function minima for equilibrium positions.
MSC:
| 74P99 | Optimization problems in solid mechanics |
| 74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |
| 70B15 | Kinematics of mechanisms and robots |
Keywords:
constrained optimization; complex linkages; elastic elements; error function; potential; rigid elements; penalty functions; weighted stiffness; Newton-Raphson methodReferences:
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