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

✍ Scribed by Avilés, Rafael ;Ajuria, Goizalde ;Bilbao, Armando ;Vallejo, Javier

Publisher
John Wiley and Sons
Year
1998
Tongue
English
Weight
215 KB
Volume
14
Category
Article
ISSN
1069-8299

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✦ Synopsis

This paper presents four dierent 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 stiness, 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.

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✍ Jan L.M. Dillen 📂 Article 📅 1987 🏛 John Wiley and Sons 🌐 English ⚖ 453 KB 👁 1 views

It is shown how the Lagrange Multiplier method for constrained minimization can be implemented in a molecular mechanics program using the common approximations to the full-matrix Newton-Raphson minimization. The method reduces the number of cycles to achieve convergence, and also stabilizes the refi