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...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 equatiodriven 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.展开更多
利用全局支撑径向基函数插值初始水平集函数,以水平集函数为设计变量,以结构柔度和散热弱度的加权函数为目标函数,基于参数化水平集法(Parameterized level set method,PLSM)建立了正交各向异性结构的热力耦合多目标拓扑优化模型。结合...利用全局支撑径向基函数插值初始水平集函数,以水平集函数为设计变量,以结构柔度和散热弱度的加权函数为目标函数,基于参数化水平集法(Parameterized level set method,PLSM)建立了正交各向异性结构的热力耦合多目标拓扑优化模型。结合数值算例研究了权系数、材料方向角、泊松比因子和热导率因子对PLSM多目标最优拓扑结构和目标函数的影响,并给出了相关参数的合理取值范围;在3D打印实物的基础上完成了最优各向异性拓扑结构的性能分析,并与各向同性结构进行了对比讨论。结果表明,PLSM最优拓扑结构比变密度法的拓扑结构边界更光滑、清晰,不会出现中间密度和锯齿等现象;同时正交各向异性结构的温度场、位移场和应力场比各向同性结构均有较好地改善,加权目标函数、结构柔度和散热弱度分别降低了55%、3.18%和81.1%。展开更多
针对利用传统水平集法(level set method,LSM)进行热传导结构拓扑优化计算过程复杂及计算效率低等问题,本文将参数化水平集法(parametric level set method,PLSM)引入热传导结构拓扑优化中,通过紧支径向基函数(compactly supported-radi...针对利用传统水平集法(level set method,LSM)进行热传导结构拓扑优化计算过程复杂及计算效率低等问题,本文将参数化水平集法(parametric level set method,PLSM)引入热传导结构拓扑优化中,通过紧支径向基函数(compactly supported-radial basis functions,CS-RBFs)插值初始的水平集函数,建立了以CS-RBFs的插值系数为设计变量,结构的散热弱度为目标函数以及材料体积为约束的热传导结构拓扑优化模型,再通过移动渐近线法(method of moving asymptotes,MMA)更新CS-RBFs的插值系数,结构的优化过程转化为插值系数的更新过程,由此得到最优拓扑。数值算例结果表明利用参数化水平集法(PLSM)与传统的水平集法(LSM)得到的拓扑结果基本一致,验证了该法的可行性和有效性。展开更多
This paper proposes a new level-set-based shape recovery approach that can be applied to a wide range of binary tomography reconstructions.In this technique,we derive generic evolution equations for shape reconstructi...This paper proposes a new level-set-based shape recovery approach that can be applied to a wide range of binary tomography reconstructions.In this technique,we derive generic evolution equations for shape reconstruction in terms of the underlying level-set parameters.We show that using the appropriate basis function to parameterize the level-set function results in an optimization problem with a small number of parameters,which overcomes many of the problems associated with the traditional level-set approach.More concretely,in this paper,we use Gaussian functions as a basis function placed at sparse grid points to represent the parametric level-set function and provide more flexibility in the binary representation of the reconstructed image.In addition,we suggest a convex optimization method that can overcome the problem of the local minimum of the cost function by successfully recovering the coefficients of the basis function.Finally,we illustrate the performance of the proposed method using synthetic images and real X-ray CT projection data.We show that the proposed reconstruction method compares favorably to various state-of-the-art reconstruction techniques for limited-data tomography,and it is also relatively stable in the presence of modest amounts of noise.Furthermore,the shape representation using a compact Gaussian radial basis function works well.展开更多
基金the National Science Foundation of the United States(Grant Nos.CMMI1462270 and CMMI1762287)Ford University Research Program(URP),and the start-up fund from the State University of New York at Stony Brook.
文摘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 equatiodriven 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.
文摘利用全局支撑径向基函数插值初始水平集函数,以水平集函数为设计变量,以结构柔度和散热弱度的加权函数为目标函数,基于参数化水平集法(Parameterized level set method,PLSM)建立了正交各向异性结构的热力耦合多目标拓扑优化模型。结合数值算例研究了权系数、材料方向角、泊松比因子和热导率因子对PLSM多目标最优拓扑结构和目标函数的影响,并给出了相关参数的合理取值范围;在3D打印实物的基础上完成了最优各向异性拓扑结构的性能分析,并与各向同性结构进行了对比讨论。结果表明,PLSM最优拓扑结构比变密度法的拓扑结构边界更光滑、清晰,不会出现中间密度和锯齿等现象;同时正交各向异性结构的温度场、位移场和应力场比各向同性结构均有较好地改善,加权目标函数、结构柔度和散热弱度分别降低了55%、3.18%和81.1%。
文摘针对利用传统水平集法(level set method,LSM)进行热传导结构拓扑优化计算过程复杂及计算效率低等问题,本文将参数化水平集法(parametric level set method,PLSM)引入热传导结构拓扑优化中,通过紧支径向基函数(compactly supported-radial basis functions,CS-RBFs)插值初始的水平集函数,建立了以CS-RBFs的插值系数为设计变量,结构的散热弱度为目标函数以及材料体积为约束的热传导结构拓扑优化模型,再通过移动渐近线法(method of moving asymptotes,MMA)更新CS-RBFs的插值系数,结构的优化过程转化为插值系数的更新过程,由此得到最优拓扑。数值算例结果表明利用参数化水平集法(PLSM)与传统的水平集法(LSM)得到的拓扑结果基本一致,验证了该法的可行性和有效性。
基金This work was supported by JST-CREST Grant Number JPMJCR1765,Japan.
文摘This paper proposes a new level-set-based shape recovery approach that can be applied to a wide range of binary tomography reconstructions.In this technique,we derive generic evolution equations for shape reconstruction in terms of the underlying level-set parameters.We show that using the appropriate basis function to parameterize the level-set function results in an optimization problem with a small number of parameters,which overcomes many of the problems associated with the traditional level-set approach.More concretely,in this paper,we use Gaussian functions as a basis function placed at sparse grid points to represent the parametric level-set function and provide more flexibility in the binary representation of the reconstructed image.In addition,we suggest a convex optimization method that can overcome the problem of the local minimum of the cost function by successfully recovering the coefficients of the basis function.Finally,we illustrate the performance of the proposed method using synthetic images and real X-ray CT projection data.We show that the proposed reconstruction method compares favorably to various state-of-the-art reconstruction techniques for limited-data tomography,and it is also relatively stable in the presence of modest amounts of noise.Furthermore,the shape representation using a compact Gaussian radial basis function works well.
