Topology Optimization of Flexible Multibody Systems

Project Description

The field of lightweight structural design has been the focus of many researches as the reduction of mass results in energy efficiency and cost reduction. It is specially important in design of active multibody dynamic systems where energy consumption is often a crucial parameter. However, reduction of mass in elastic multibody systems reduces the stiffness of flexible parts which increases undesired deformations in the dynamic system. These deformations are a point of concern specially in high speed and high precision machines. Therefore, it is necessary to use optimization methods to reduce the mass in a dynamic system without impairing its performance.

Topology optimization method is a powerful tool for designing lightweight structures. This method tries to find the best distribution of material in a fixed design space. Therewith, this method allows for any formation of material inside the specified domain. So far, it has been mostly applied for static applications. In dynamic application it has been mostly used to influence the structure's eigenfrequencies. In contrast, in this project, topology optimization problem for flexible multibody systems are developed. These are based on transient simulation of the flexible multibody systems [1]. The necessary steps in the topology optimization of flexible multibody systems are shown below.

Optimization Process

The solution of the optimization problem is complex and is usually carried out with the help of iterative optimization algorithms. In each iteration step, a finite element model of the flexible body is first built. For this finite element model, model reduction methods are then used to determine the smallest possible set of global shape functions that can be used to approximate the deformation behavior of the flexible body with sufficient accuracy. Due to the smaller number of degrees of freedom, the multibody simulation is fast and efficient. A scalar quality criterion is calculated from the results of the multibody simulation and a sensitivity analysis is performed. Using the quality criterion and the gradient, the optimization algorithm finally determines an improved design and the next iteration begins.


For the parameterization of flexible bodies, the SIMP approach or level set methods are available. Both approaches aim to distribute a given amount of material in a defined reference area in such a way that the resulting structure resists the applied loads in the best possible way. Up to now, these approaches have mainly been used in structural analysis or to influence the natural frequencies of components. In contrast, the goal of this research project is to apply the methods to systems in which the loads depend on both time and the structure of the body itself.

Application Example

An application example, which is often used to test the methods employed, is the topology optimization of a lightweight robot [3,4]. The optimization goal is to reduce the trajectory error, which results from the structural elasticities, as much as possible. Further application examples are the topology optimization of wheel suspension components in automotive engineering or the optimal design of thrust crank drives.

Serial manipulator

Selected Publications

  1. Moghadasi, A. Contributions to topology optimization in flexible multibody dynamics. PhD Thesis, Hamburg University of Technology, MuM Notes in Mechanics and Dynamics, 2019.

  2. Held, A. On structural optimization of flexible multibody systems. PhD Thesis, University of Stuttgart, Shaker Verlag, Aachen, 2014.

  3. Seifried, R.; Held, A.: Optimal Design of Lightweight Machines using Flexible Multibody System Dynamics. Proceedings of the ASME 2012 International Design Engineering Technical Conferences (IDETC/CIE 2012), August 12-15, 2012, Chicago, IL, USA, paper ID DETC2012-70972.

  4. Held, A.; Seifried, R.: Topology Optimization of Members of Elastic Multibody Systems. PAMM Proceedings in Applied Mathematics and Mechanics, Vol. 12, 2012, pp. 67-68, [DOI:10.1002/pamm.201210025].



The project is funded by the German Research Foundation (DFG).