No abstract

In structural optimization, the level set method is known as a well-established approach for shape and topology optimization. However, special care must be taken, if the design domains are sparsely-filled and slender. Using steepest descent-type level set methods, slender structure topology optimizations tend to instabilities and loss of structural cohesion. A sole step size control or a selection of more complex initial designs only help occasionally to overcome these issues and do not describe a universal solution. In this paper, instead of updating the level set function by solving a Hamilton–Jacobi partial differential equation, an adapted algorithm for the update of the level set function is utilized, which allows an efficient and stable topology optimization of slender structures. Including different adaptations, this algorithm replaces unacceptable designs by modifying both the pseudo-time step size and the Lagrange multiplier. Besides, adjustments are incorporated in the normal velocity formulation to avoid instabilities and achieve a smoother optimization convergence. Furthermore, adding filtering-like adaptation terms to the update scheme, even in case of very slender structures, the algorithm is able to perform topology optimization with an appropriate convergence speed. This procedure is applied for compliance minimization problems of slender structures. The stability of the optimization process is shown by 2D numerical examples. The solid isotropic material with penalization (SIMP) method is used as an alternative approach to validate the result quality of the presented method. Finally, the simple extension to 3D optimization problems is addressed, and a 3D optimization example is briefly discussed.

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.

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.