基于固体各向同性材料惩罚模型(Solid isotropic material with penalization,SIMP)是一种常用的拓扑优化模型,因其计算效率较高而应用广泛。在工程实际中,采用单一材料的结构往往难以满足较好地综合性能,而功能梯度材料结构能充分发挥...基于固体各向同性材料惩罚模型(Solid isotropic material with penalization,SIMP)是一种常用的拓扑优化模型,因其计算效率较高而应用广泛。在工程实际中,采用单一材料的结构往往难以满足较好地综合性能,而功能梯度材料结构能充分发挥其组成的各相材料的优点,在满足轻量化、高强度的要求的同时,达到良好的经济效益,在工程上应用广泛。然而,传统的SIMP法由于其预先设定材料属性,对功能梯度材料变刚度的结构体拓扑优化稍显不足,本文提出了一种基于有限元素法,采用功能梯度材料的变刚度改进方法,采用改进的SIMP法进行优化问题的求解,使得变刚度结构经过优化后其强度得到提高的同时,充分发挥功能梯度材料其各相组成材料的特性,合理分配材料使用进而降低成本。最后在MATLAB环境中以悬臂梁结构为算例模型验证了该方法的可行性,具有十分广阔的应用前景。展开更多
The design methods for gradient coils are mostly based on discrete extrinsic methods(e.g.,the BioteSavart integration calculation),for which the surface normal vector strongly influences any numerical calculation of t...The design methods for gradient coils are mostly based on discrete extrinsic methods(e.g.,the BioteSavart integration calculation),for which the surface normal vector strongly influences any numerical calculation of the discretized surface.Previous studies are mostly based on regular or analytical surfaces,which allow normal vectors to be expressed analytically.For certain applications,design methods for extending currentcarrying surfaces from developable or analytic geometries to arbitrary surfaces generated from a scanned point cloud are required.The key task is to correctly express the discretized normal vectors to ensure geometrical accuracy of the designed coils.Mathematically,it has been proven that applying a Delaunay triangulation to approximate a smooth surface can result in the discrete elemental normal vectors converging to those of the original surface.Accordingly,this article uses Delaunay triangulation to expand upon previous design methods so that they encompass arbitrary piecewise continuous surfaces.Two design methods,the stream function and the so-called solid isotropic material with penalization(SIMP)method,are used to design circumvolute and noncircumvolute gradient coils on general surfaces.展开更多
基于变密度方法中的SIMP(Solid Isotropic Material with Penalization)模型,提出一种多复合材料3D打印制造的拓扑优化方法对四足机器人腿部结构进行优化设计。采用体积约束下最小应力的优化方式,同时引入复合材料的本构矩阵,使得优化...基于变密度方法中的SIMP(Solid Isotropic Material with Penalization)模型,提出一种多复合材料3D打印制造的拓扑优化方法对四足机器人腿部结构进行优化设计。采用体积约束下最小应力的优化方式,同时引入复合材料的本构矩阵,使得优化结果更加合理。针对四足机器人常见工况进行静力学分析,并对最大位移下的载荷情况进行拓扑优化设计。为了验证优化后腿部结构的强度,分别制备拓扑增强和轮廓增强腿部结构并进行试验分析。试验结果表明,拓扑增强结构最大位移比轮廓增强结构在外摆工况下降低了53.57%。拓扑增强结构承载比在0°和30°外摆工况下比轮廓增强结构分别提升了17.98%和24.57%。通过对四足机器人腿部结构优化前后的试验对比可知,经过拓扑优化设计,四足机器人腿部结构力学性能得到提升,优化设计具有可行性。该拓扑优化方法对于提高产品力学性能,具有一定作用。展开更多
文摘基于固体各向同性材料惩罚模型(Solid isotropic material with penalization,SIMP)是一种常用的拓扑优化模型,因其计算效率较高而应用广泛。在工程实际中,采用单一材料的结构往往难以满足较好地综合性能,而功能梯度材料结构能充分发挥其组成的各相材料的优点,在满足轻量化、高强度的要求的同时,达到良好的经济效益,在工程上应用广泛。然而,传统的SIMP法由于其预先设定材料属性,对功能梯度材料变刚度的结构体拓扑优化稍显不足,本文提出了一种基于有限元素法,采用功能梯度材料的变刚度改进方法,采用改进的SIMP法进行优化问题的求解,使得变刚度结构经过优化后其强度得到提高的同时,充分发挥功能梯度材料其各相组成材料的特性,合理分配材料使用进而降低成本。最后在MATLAB环境中以悬臂梁结构为算例模型验证了该方法的可行性,具有十分广阔的应用前景。
基金the National Natural Science Foundation of China under grant No.51675506.JGK acknowledges support from an EU2020 FET grant(737043 TiSuMR)the Deutsche Forschungsgesellschaft(DFG)(grant KO 1883/20-1 Metacoils)funding within the framework of the German Excellence Initiative under grant EXC 2082“3D Matter Made to Order”,from the VirtMat initiative“Virtual Materials Design”,and from an ERC Synergy Grant(951459,HiSCORE),European Union.
文摘The design methods for gradient coils are mostly based on discrete extrinsic methods(e.g.,the BioteSavart integration calculation),for which the surface normal vector strongly influences any numerical calculation of the discretized surface.Previous studies are mostly based on regular or analytical surfaces,which allow normal vectors to be expressed analytically.For certain applications,design methods for extending currentcarrying surfaces from developable or analytic geometries to arbitrary surfaces generated from a scanned point cloud are required.The key task is to correctly express the discretized normal vectors to ensure geometrical accuracy of the designed coils.Mathematically,it has been proven that applying a Delaunay triangulation to approximate a smooth surface can result in the discrete elemental normal vectors converging to those of the original surface.Accordingly,this article uses Delaunay triangulation to expand upon previous design methods so that they encompass arbitrary piecewise continuous surfaces.Two design methods,the stream function and the so-called solid isotropic material with penalization(SIMP)method,are used to design circumvolute and noncircumvolute gradient coils on general surfaces.
文摘基于变密度方法中的SIMP(Solid Isotropic Material with Penalization)模型,提出一种多复合材料3D打印制造的拓扑优化方法对四足机器人腿部结构进行优化设计。采用体积约束下最小应力的优化方式,同时引入复合材料的本构矩阵,使得优化结果更加合理。针对四足机器人常见工况进行静力学分析,并对最大位移下的载荷情况进行拓扑优化设计。为了验证优化后腿部结构的强度,分别制备拓扑增强和轮廓增强腿部结构并进行试验分析。试验结果表明,拓扑增强结构最大位移比轮廓增强结构在外摆工况下降低了53.57%。拓扑增强结构承载比在0°和30°外摆工况下比轮廓增强结构分别提升了17.98%和24.57%。通过对四足机器人腿部结构优化前后的试验对比可知,经过拓扑优化设计,四足机器人腿部结构力学性能得到提升,优化设计具有可行性。该拓扑优化方法对于提高产品力学性能,具有一定作用。
