Design sensitivity analysis of rigid and flexible multibody systems

Formulations and numerical algorithms for design sensitivity analysis of rigid and flexible multibody systems are developed. Sensitivity equations are generated using the direct differentiation method. Differential-algebraic equations for dynamic and sensitivity analysis are solved using the state-space reduction method. The framework presented enables systematic and efficient implementation for large-scale multibody systems.; In order to overcome errors in sensitivity formulation using the simplifying assumption of centroidal body reference frames, a general formulation of the Newton-Euler equations of motion based on non-centroidal body reference frames, is developed for sensitivity analysis of rigid multibody systems. Algorithms based on explicit and implicit numerical integration formulas are presented to evaluate computational efficiency in application to large-scale stiff rigid multibody systems that have not heretofore been treated. Analytical derivatives of kinematic and kinetic terms with respect to design variables that are required by both explicit and implicit integration formulas in sensitivity analysis are developed and validated using finite differences. The influence of the number and type of design variables on computational cost is investigated.; Design sensitivity analysis of systems in which large displacement gross motion and small elastic deformation is addressed, a topic not previously treated in the literature. The modal flexibility method is used to characterize small elastic deformations, which reduces the number of dynamic degrees of freedom. Computational efficiency is achieved through decomposition of the mass matrix, Coriolis force, and applied force into time-dependent and time-independent parts. Analytical derivatives of kinematic and kinetic terms with respect to stale variables required by implicit numerical methods in dynamic analysis are developed. Analytical derivatives of kinematic and kinetic terms with respect to design variables for sensitivity analysis are developed. The accuracy of sensitivity equations is validated using finite differences. Computational efficiency of sensitivity analysis is examined through studying the influence of the number and type of design variables and the number of deformation modes on computational cost. Flexibility effects on sensitivity analysis relative to rigid body models are investigated. Behaviors of explicit and implicit numerical methods for flexible multibody systems are investigated.