Dynamic Response Optimization of Complex Multibody Systems in a Penalty Formulation Using Adjoint Sensitivity

Abstract

Multibody dynamics simulations are currently widely accepted as valuable means for dynamic performance analysis of mechanical systems. The evolution of theoretical and computational aspects of the multibody dynamics discipline make it conducive these days for other types of applications, in addition to pure simulations. One very important such application is design optimization. A very important first step towards design optimization is sensitivity analysis of multibody system dynamics. Dynamic sensitivities are often calculated by means of finite differences. Depending of the number of parameters involved, this procedure can be computationally expensive. Moreover, in many cases, the results suffer from low accuracy when real perturbations are used. The main contribution to the state-of-the-art brought by this study is the development of the adjoint sensitivity approach of multibody systems in the context of the penalty formulation. The theory developed is demonstrated on one academic case study, a five-bar mechanism, and on one real-life system, a 14-DOF vehicle model. The five-bar mechanism is used to illustrate the sensitivity approach derived in this paper. The full vehicle model is used to demonstrate the capability of the new approach developed to perform sensitivity analysis and gradient-based optimization for large and complex multibody systems with respect to multiple design parameters.

Toward the integration of lattice structure-based topology optimization and additive manufacturing for the design of turbomachinery components

“…10 Nevertheless, they have been regarded among ''the most challenging and promising methods in structural optimization.'' [11][12][13][14][15] In fact, TO is a method ''able to determine the best distribution of material once an optimization function is defined together with a set of constraints.'' It works starting from a solid block of material whose material is removed to minimize or maximize the optimization objective function (OF).…”

Direct sensitivity analysis of multibody systems with holonomic and nonholonomic constraints via an index-3 augmented Lagrangian formulation with projections

“…The formulation solves the problems mentioned before for index-3 and index-1 formulations and reduces the dynamics equations to a system of ordinary differential equations (ODE), instead of the original DAE. The sensitivity equations for this formulation are also available in [37,38,19] and they were even used for the dynamic optimization of a whole vehicle in [48]. Accordingly the penalty method is a good candidate for the optimization of industrial problems.…”

A frequency domain approach for parameter identification in multibody dynamics

“…Various applications of the adjoint method in multibody dynamics for optimal control problems and parameter identifications in time domain can be found in recent works, e.g., in [ 7 ]. Adjoint sensitivities have been used in a penalty formulation in time domain for a full vehicle model in [ 9 ].…”