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    Influence of Weighted Gradients in Topology Optimization of Flexible Multibody Systems
    (Springer, 2024-01-05)
    Azari Nejat, Ali
    ;
    Held, Alexander
    ;
    Seifried, Robert
    This paper deals with a level set-based topology optimization of flexible bodies within flexible multibody systems. The required gradient is provided by an adjoint sensitivity analysis. In this work, a modified Solid Isotropic Material with Penalization (SIMP) method is applied, which helps to avoid numerical issues connected to spurious modes in dynamic problems. Nevertheless, the included parametrization factors lead to a weighted gradient. To test the validity of corresponding optimization results, differently weighted gradients are then used within the topology optimization of a flexible piston rod in a slider-crank mechanism. The obtained results show, among others, the range of appropriate weightings in the studied example.
    Publicationtype: Conference Paper
      67
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    A fully coupled level set-based topology optimization of flexible components in multibody systems
    (2023-07)
    Azari Nejat, Ali
    ;
    Held, Alexander
    ;
    Seifried, Robert
    A fully coupled level set-based topology optimization of flexible components in multibody systems is considered. Thereby, using the floating frame of reference approach, the flexible components are efficiently modeled and incorporated in multibody systems. An adjoint sensitivity analysis is utilized to obtain the gradient of the objective function with respect to a set of density-like design variables assigned to elements included in the underlying finite element model. The utilized adjoint sensitivity analysis provides a gradient, which is within numerical limits exact. In this process, the parametrization of material properties of finite elements has a significant influence on the calculated gradient, in particular for poorly filled elements. These influences are studied in detail. As an application example, the compliance minimization problem of a flexible piston rod in a transient slider-crank mechanism is considered. For this model, the influence of different parametrization methods on the obtained gradient is discussed, and a gradient strategy is proposed to overcome numerical issues included in different parametrization laws. Using this gradient strategy within a level set-based algorithm, a topology optimization of the flexible piston rod is performed. The corresponding results are then compared with optimization results provided by the method of moving asymptotes (MMA). Moreover, the computational effort of the sensitivity analysis is high and scales with the number of design variables. In this work, a gradient approximation is introduced using radial basis functions (RBFs). This helps to develop an appropriate gradient for a level set-based topology optimization of the flexible components in multibody systems, where the RBF-based design space reduction decreases the computational effort of the utilized sensitivity analysis. Finally, the efficiency gain obtained by the introduced design space reduction is demonstrated by optimization examples.
    Publicationtype: Journal Article
    Scopus© Citations 3  51  210
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    A comparison of a level set method and the method of moving asymptotes for the topology optimization of flexible components in multibody systems
    (Wiley-VCH, 2023-03-24)
    Azari Nejat, Ali
    ;
    Held, Alexander
    ;
    Seifried, Robert
    The gradient-based topology optimization of flexible multibody systems is considered, where the floating frame of reference method is utilized to model the flexible components with an appropriate efficiency. Thereby, the quality of the optimization results depends, among others, on the chosen gradient calculation strategy and the applied optimization algorithm. Here, both a fully-coupled time-continuous adjoint sensitivity analysis and a weakly-coupled equivalent static load method are tested for gradient calculation. Moreover, both the method of moving asymptotes and a level set method are taken to solve the optimization problem. Different combinations of the mentioned gradient strategies and optimization algorithms are applied for the topology optimization of a flexible piston rod in a slider-crank mechanism. The corresponding results and comparisons shall be used as quality benchmarks for further studies. © 2023 The Authors. Proceedings in Applied Mathematics & Mechanics published by Wiley-VCH Gmb
    Publicationtype: Conference Paper
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    Scopus© Citations 4  221  792
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    An efficient adjoint sensitivity analysis of flexible multibody systems for a level‐set‐based topology optimization
    (Wiley-VCH, 2021-01-25)
    Azari Nejat, Ali
    ;
    Held, Alexander
    ;
    Seifried, Robert
    For large-scale topology optimization of flexible multibody systems, only little results exist. This is due to the complexity of the modeling of the flexible bodies and the big effort to provide exact gradients. The considered flexible multibody systems can undergo both large nonlinear motions as well as small elastic deformations. Here, the flexible components are modeled by the floating frame of reference approach. For gradient calculation, the fully coupled adjoint sensitivity analysis is used, which is a semi-analytical approach based on variational calculus. The computational effort strongly corresponds to the number of design variables. In this work, a design space reduction using radial basis functions is performed and the gradient of flexible components is constructed based on its exact value on a subset of selected design elements. In order to show the substantial gain in computation time, the exact and approximated gradient of a flexible crank in a slider-crank mechanism are computed and applied for a level-set-based topology optimization.
    Publicationtype: Conference Paper
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    Adjoint sensitivity analysis of flexible multibody systems in differential-algebraic form
    (2020-02)
    Azari Nejat, Ali
    ;
    Moghadasi, Ali
    ;
    Held, Alexander
    In the analysis and optimization of flexible multibody systems, an efficient sensitivity analysis can be performed using the adjoint variable method. Thereby, the procedure strongly depends on the equations of motion, which can be formulated either by minimal or by redundant coordinates yielding in turn a system of ordinary or differential-algebraic equations. In the current work, redundant coordinates are used to set an adjoint system for the sensitivity analysis of flexible multibody systems with kinematic loops, which are modeled using the floating frame of reference formulation. The procedure is tested by computing the structural gradient for the flexible crank of a slider-crank mechanism and compared with a reference procedure, where the adjoint system is formulated using minimal coordinates.
    Publicationtype: Journal Article
      106
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