Jm. Pagalday et A. Avello, OPTIMIZATION OF MULTIBODY DYNAMICS USING OBJECT-ORIENTED PROGRAMMING AND A MIXED NUMERICAL-SYMBOLIC PENALTY FORMULATION, Mechanism and machine theory, 32(2), 1997, pp. 161-174
Multibody optimization is an increasingly important tool in mechanical
design that requires not only dynamic analysis but also computation o
f sensitivities. Sensitivities may be approximated by numerical differ
entiation in many optimization applications for which the calculation
of the objective function is not computationally demanding. However, i
n multibody optimization each evaluation of the objective function req
uires the integration of the equations of motion over the simulation p
eriod, which is usually time consuming. Therefore, exact calculation o
f sensitivities by direct differentiation is very convenient. In this
work, the constrained equations of motion are derived from a minimum p
rinciple using a penalty and augmented Lagrangian method. Then, sensit
ivities are evaluated symbolically with the aid of a symbolic manipula
tor tailored for multibody applications. Object oriented programming c
oncepts are used in the development of an optimization module that enh
ances the already existing multibody program COMPAMM. Two illustrative
examples are presented to assess the correctness of the proposed form
ulation. Copyright (C) 1996 Elsevier Science Ltd.