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A regularization scheme for explicit level-set XFEM topology optimization
Markus J. GEISS, Jorge L. BARRERA, Narasimha BODDETI, Kurt MAUTE
Front. Mech. Eng.. 2019, 14 (2): 153-170.
https://doi.org/10.1007/s11465-019-0533-2
Regularization of the level-set (LS) field is a critical part of LS-based topology optimization (TO) approaches. Traditionally this is achieved by advancing the LS field through the solution of a Hamilton-Jacobi equation combined with a reinitialization scheme. This approach, however, may limit the maximum step size and introduces discontinuities in the design process. Alternatively, energy functionals and intermediate LS value penalizations have been proposed. This paper introduces a novel LS regularization approach based on a signed distance field (SDF) which is applicable to explicit LS-based TO. The SDF is obtained using the heat method (HM) and is reconstructed for every design in the optimization process. The governing equations of the HM, as well as the ones describing the physical response of the system of interest, are discretized by the extended finite element method (XFEM). Numerical examples for problems modeled by linear elasticity, nonlinear hyperelasticity and the incompressible Navier-Stokes equations in two and three dimensions are presented to show the applicability of the proposed scheme to a broad range of design optimization problems.
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Concurrent optimization of structural topology and infill properties with a CBF-based level set method
Long JIANG, Yang GUO, Shikui CHEN, Peng WEI, Na LEI, Xianfeng David GU
Front. Mech. Eng.. 2019, 14 (2): 171-189.
https://doi.org/10.1007/s11465-019-0530-5
In this paper, a parametric level-set-based topology optimization framework is proposed to concurrently optimize the structural topology at the macroscale and the effective infill properties at the micro/meso scale. The concurrent optimization is achieved by a computational framework combining a new parametric level set approach with mathematical programming. Within the proposed framework, both the structural boundary evolution and the effective infill property optimization can be driven by mathematical programming, which is more advantageous compared with the conventional partial differential equation-driven level set approach. Moreover, the proposed approach will be more efficient in handling nonlinear problems with multiple constraints. Instead of using radial basis functions (RBF), in this paper, we propose to construct a new type of cardinal basis functions (CBF) for the level set function parameterization. The proposed CBF parameterization ensures an explicit impose of the lower and upper bounds of the design variables. This overcomes the intrinsic disadvantage of the conventional RBF-based parametric level set method, where the lower and upper bounds of the design variables oftentimes have to be set by trial and error. A variational distance regularization method is utilized in this research to regularize the level set function to be a desired distance-regularized shape. With the distance information embedded in the level set model, the wrapping boundary layer and the interior infill region can be naturally defined. The isotropic infill achieved via the mesoscale topology optimization is conformally fit into the wrapping boundary layer using the shape-preserving conformal mapping method, which leads to a hierarchical physical structure with optimized overall topology and effective infill properties. The proposed method is expected to provide a timely solution to the increasing demand for multiscale and multifunctional structure design.
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Topology optimization of piezoelectric bi-material actuators with velocity feedback control
Mariana MORETTI, Emílio C. N. SILVA
Front. Mech. Eng.. 2019, 14 (2): 190-200.
https://doi.org/10.1007/s11465-019-0537-y
In recent years, the new technologies and discoveries on manufacturing materials have encouraged researchers to investigate the appearance of material properties that are not naturally available. Materials featuring a specific stiffness, or structures that combine non-structural and structural functions are applied in the aerospace, electronics and medical industry fields. Particularly, structures designed for dynamic actuation with reduced vibration response are the focus of this work. The bi-material and multifunctional concepts are considered for the design of a controlled piezoelectric actuator with vibration suppression by means of the topology optimization method (TOM). The bi-material piezoelectric actuator (BPEA) has its metallic host layer designed by the TOM, which defines the structural function, and the electric function is given by two piezo-ceramic layers that act as a sensor and an actuator coupled with a constant gain active velocity feedback control (AVFC). The AVFC, provided by the piezoelectric layers, affects the structural damping of the system through the velocity state variables readings in time domain. The dynamic equation analyzed throughout the optimization procedure is fully elaborated and implemented. The dynamic response for the rectangular four-noded finite element analysis is obtained by the Newmark’s time-integration method, which is applied to the physical and the adjoint systems, given that the adjoint formulation is needed for the sensitivity analysis. A gradient-based optimization method is applied to minimize the displacement energy output measured at a predefined degree-of-freedom of the BPEA when a transient mechanical load is applied. Results are obtained for different control gain values to evaluate their influence on the final topology.
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Manufacturing cost constrained topology optimization for additive manufacturing
Jikai LIU, Qian CHEN, Xuan LIANG, Albert C. TO
Front. Mech. Eng.. 2019, 14 (2): 213-221.
https://doi.org/10.1007/s11465-019-0536-z
This paper presents a manufacturing cost constrained topology optimization algorithm considering the laser powder bed additive manufacturing process. Topology optimization for additive manufacturing was recently extensively studied, and many related topics have been addressed. However, metal additive manufacturing is an expensive process, and the high manufacturing cost severely hinders the widespread use of this technology. Therefore, the proposed algorithm in this research would provide an opportunity to balance the manufacturing cost while pursuing the superior structural performance through topology optimization. Technically, the additive manufacturing cost model for laser powder bed-based process is established in this paper and real data is collected to support this model. Then, this cost model is transformed into a level set function-based expression, which is integrated into the level set topology optimization problem as a constraint. Therefore, by properly developing the sensitivity result, the metallic additive manufacturing part can be optimized with strictly constrained manufacturing cost. Effectiveness of the proposed algorithm is proved by numerical design examples.
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Level set-based isogeometric topology optimization for maximizing fundamental eigenfrequency
Manman XU, Shuting WANG, Xianda XIE
Front. Mech. Eng.. 2019, 14 (2): 222-234.
https://doi.org/10.1007/s11465-019-0534-1
Maximizing the fundamental eigenfrequency is an efficient means for vibrating structures to avoid resonance and noises. In this study, we develop an isogeometric analysis (IGA)-based level set model for the formulation and solution of topology optimization in cases with maximum eigenfrequency. The proposed method is based on a combination of level set method and IGA technique, which uses the non-uniform rational B-spline (NURBS), description of geometry, to perform analysis. The same NURBS is used for geometry representation, but also for IGA-based dynamic analysis and parameterization of the level set surface, that is, the level set function. The method is applied to topology optimization problems of maximizing the fundamental eigenfrequency for a given amount of material. A modal track method, that monitors a single target eigenmode is employed to prevent the exchange of eigenmode order number in eigenfrequency optimization. The validity and efficiency of the proposed method are illustrated by benchmark examples.
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An improved artificial bee colony algorithm with MaxTF heuristic rule for two-sided assembly line balancing problem
Xiaokun DUAN, Bo WU, Youmin HU, Jie LIU, Jing XIONG
Front. Mech. Eng.. 2019, 14 (2): 241-253.
https://doi.org/10.1007/s11465-018-0518-6
Two-sided assembly line is usually used for the assembly of large products such as cars, buses, and trucks. With the development of technical progress, the assembly line needs to be reconfigured and the cycle time of the line should be optimized to satisfy the new assembly process. Two-sided assembly line balancing with the objective of minimizing the cycle time is called TALBP-2. This paper proposes an improved artificial bee colony (IABC) algorithm with the MaxTF heuristic rule. In the heuristic initialization process, the MaxTF rule defines a new task’s priority weight. On the basis of priority weight, the assignment of tasks is reasonable and the quality of an initial solution is high. In the IABC algorithm, two neighborhood strategies are embedded to balance the exploitation and exploration abilities of the algorithm. The employed bees and onlooker bees produce neighboring solutions in different promising regions to accelerate the convergence rate. Furthermore, a well-designed random strategy of scout bees is developed to escape local optima. The experimental results demonstrate that the proposed MaxTF rule performs better than other heuristic rules, as it can find the best solution for all the 10 test cases. A comparison of the IABC algorithm and other algorithms proves the effectiveness of the proposed IABC algorithm. The results also denote that the IABC algorithm is efficient and stable in minimizing the cycle time for the TALBP-2, and it can find 20 new best solutions among 25 large-sized problem cases.
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