The sensitivity analysis of the dynamics of multibody systems is a topic that has been attracting the attention of several researchers for years, particularly due to its value in optimal control and design problems. D...
详细信息
The sensitivity analysis of the dynamics of multibody systems is a topic that has been attracting the attention of several researchers for years, particularly due to its value in optimal control and design problems. Depending on the dynamic formulation and the sensitivity method considered, different sets of sensitivity systems of equations would be reached involving diverse complexity levels. In this work, the analytical sensitivity analysis of the augmented Lagrangian index-3 formulation with velocity and acceleration projections (ALI3-P) is developed using the discrete adjoint variable method, considering a Newmark's family integrator for the numerical integration of the forward dynamics, adjoint sensitivity and gradient equations, and a penalty formulation for the initial acceleration problem. The accuracy and efficiency of the new sensitivity formulation are tested in a five-bar mechanism benchmark problem and in the multibody model of a real-life four-wheeled vehicle. The method has been implemented in the MBSLIM multibody library as two general sensitivity formulations over the already existing global and topological forward dynamics formulations in natural and joint coordinates respectively.
The design space of dynamic multibody systems (MBSs), particularly those with flexible components, is considerably large. Consequently, having a means to efficiently explore this space and find the optimum solution wi...
详细信息
The design space of dynamic multibody systems (MBSs), particularly those with flexible components, is considerably large. Consequently, having a means to efficiently explore this space and find the optimum solution within a feasible time-frame is crucial. It is well-known that for problems with several design variables, sensitivity analysis using the adjointvariablemethod extensively reduces the computational costs. This paper presents the novel extension of the discrete adjoint variable method to the design optimization of dynamic flexible MBSs. The extension involves deriving the adjoint equations directly from the discrete, rather than the continuous, equations of motion. This results in a system of algebraic equations that is computationally less demanding to solve compared to the system of differential algebraic equations produced by the continuous adjointvariablemethod. To describe the proposed method, it is integrated with a numerical time-stepping algorithm based on geometric variational integrators. The developed technique is then applied to the optimization of MBSs composed of springs, dampers, beams and rigid bodies, considering both geometrical (e.g., positions of joints) and non-geometrical (e.g., mechanical properties of components) design variables. To validate the developed methods and show their applicability, three numerical examples are provided. (C) 2018 Elsevier Ltd. All rights reserved.
暂无评论