| 1. |
- Fan, Zhirui, et al.
(författare)
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Multiscale eigenfrequency optimization of multimaterial lattice structures based on the asymptotic homogenization method
- 2020
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Ingår i: Structural and Multidisciplinary Optimization. - : Springer Science and Business Media LLC. - 1615-147X .- 1615-1488. ; 61:3, s. 983-998
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Tidskriftsartikel (refereegranskat)abstract
- Ultralight lattice structures exhibit excellent mechanical performance and have been used widely. In structural design, the fundamental frequency is highly important. Therefore, a multiscale topology optimization method was utilized to optimize the fundamental frequency of multimaterial lattice structures in this study. Two types of optimization problems were studied, namely, maximizing the natural fundamental frequency with mass constraints and minimizing compliance with frequency constraints. The Heaviside-penalty-based discrete material optimization method was adopted for the optimal selection of candidate materials. The asymptotic homogenization method was used to evaluate the equivalent macroscale properties according to the microstructure of the lattice material. To enable gradient optimization, sensitivities were outlined in detail. A density filter with a volume-preserving Heaviside projection was used to eliminate the risk of a checkerboard pattern and reduce the number of gray elements. A polynomial penalization scheme was employed to eliminate localized spurious eigenmodes in the low-density region. Finally, several numerical examples were performed to validate the proposed method. These numerical examples resulted in novel microstructural configurations with remarkably improved vibration resistance.
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| 2. |
- Fan, Zhirui, et al.
(författare)
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Nonlinear stiffness optimization with prescribed deformed geometry and loads
- 2022
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Ingår i: Structural and Multidisciplinary Optimization. - : Springer Science and Business Media LLC. - 1615-147X .- 1615-1488. ; 65:2
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Tidskriftsartikel (refereegranskat)abstract
- Optimization based on traditional forward motion analysis to ensure a prescribed load distribution on a deformed geometry is challenging, since the load distribution is highly coupled to the deformed geometry, boundary conditions, and the optimized material layout. In contrast to traditional forward motion analysis, the deformed configuration is prescribed in the inverse motion analysis, and the undeformed configuration is the outcome of the analysis. Consequently, the inverse motion analysis is able to define an exact deformed geometry. In the present study, we make use of this key advantage to design structures with both an exact deformed geometry and a prescribed load distribution. The objective in the optimization is to minimize a general function of the nodal displacement vector. To formulate a well-posed optimization problem, the design is regularized using the partial differential equation filter and the sensitivity analysis is based on the adjoint method. The computational model is developed for neo-Hookean hyper-elasticity and the balance equations are discretized using the finite element method. The resulting nonlinear equations are solved using a conventional Newton–Raphson scheme. In the numerical examples, a cantilever beam with an embedded perfect circular shape is first considered. Next, a 2D gasket-like structure is designed, and finally, we consider a 3D structure with contact-like boundary conditions. In these examples, the prescribed deformed geometry is subject to a distributed external force. The examples show that the deformed geometry and load distribution can be exactly prescribed through stiffness optimization based on the inverse motion analysis.
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| 3. |
- Sui, Qianqian, et al.
(författare)
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Topology optimization of thermo-hyperelastic structures utilizing inverse motion based form finding
- 2023
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Ingår i: Engineering Optimization. - 0305-215X. ; 55:1, s. 110-124
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Tidskriftsartikel (refereegranskat)abstract
- The inverse motion concept is used to optimize thermo-hyperelastic structures using an exact description of the deformed geometry. This method prescribes the shape of the structure in the deformed state, and the optimization yields the shape of the undeformed configuration, i.e. the manufactured state. The kinematics of the thermoelastic model is defined through the multiplicative decomposition of the deformation gradient in combination with neo-Hookean hyperelasticity. To regularize the optimization problem and obtain distinct boundaries, the mathematical design field is thresholded using a smoothed Heaviside function and smeared using a partial differential equation. The sensitivity analyses of the objective function and constraints are both based on the adjoint method. The capabilities of the proposed approach are shown by numerical examples wherein the weight is minimized and the performance of multi-material compliant mechanisms is optimized.
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