Abstract
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 distanceregularized 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.
Highlights
Structures containing cellular infills or micro/meso architectures can possess fine-tuned properties and extra functionalities with a low density [1,2,3,4]
As an extension to the conventional level set approach, Wang et al [26] employed a numerically robust parametric level set method (PLSM), in order to design a series of microstructures with different Poisson’s ratios. In this systematic computational design framework, the homogenization was used for calculating the material property and PLSM was used for updating the structural shape and topology
One thing needs to be mentioned is that with the analytical parametric level set function expression, the optimization results generated via PLSM can be manufactured via the high-resolution layer-image-based continuous liquid interface production (CLIP) 3D printing technology [63,73]
Summary
Structures containing cellular infills or micro/meso architectures can possess fine-tuned properties and extra functionalities with a low density [1,2,3,4]. As an extension to the conventional level set approach, Wang et al [26] employed a numerically robust parametric level set method (PLSM), in order to design a series of microstructures with different Poisson’s ratios In this systematic computational design framework, the homogenization was used for calculating the material property and PLSM was used for updating the structural shape and topology. The signed distance function can preserve the distance information directly This means with one level set function, a shell-infill multiscale structure can be designed [63,64,65]. A second stage optimization is directly carried out to find out the isotropic infill metamaterial layout With both the overall geometry and the infill structure design in hand, the local shape-preserving conformal mapping is performed to integrate them together. Under a linear elastic problem setting, the stress and the strain tensors of the homogeneous medium should be equal to the average stress and strain in the microstructure, as
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
