OPTIMIZATION OF MULTIBODY DYNAMICS USING OBJECT-ORIENTED PROGRAMMING AND A MIXED NUMERICAL-SYMBOLIC PENALTY FORMULATION

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.