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 of sensitivities. Sensitivities may be approximated by numerical differentiation in many optimization applications for which the calculation of the objective function is not computationally demanding. However, in multibody optimization each evaluation of the objective function requires the integration of the equations of motion over the simulation period, which is usually time consuming. Therefore, exact calculation of sensitivities by direct differentiation is very convenient. In this work, the constrained equations of motion are derived from a minimum principle using a penalty and augmented Lagrangian method. Then, sensitivities are evaluated symbolically with the aid of a symbolic manipulator tailored for multibody applications. Object oriented programming concepts are used in the development of an optimization module that enhances the already existing multibody program COMPAMM. Two illustrative examples are presented to assess the correctness of the proposed formulation.