A methodology for topology optimization based on element independent nodal density(EIND) is developed.Nodal densities are implemented as the design variables and interpolated onto element space to determine the densit...A methodology for topology optimization based on element independent nodal density(EIND) is developed.Nodal densities are implemented as the design variables and interpolated onto element space to determine the density of any point with Shepard interpolation function.The influence of the diameter of interpolation is discussed which shows good robustness.The new approach is demonstrated on the minimum volume problem subjected to a displacement constraint.The rational approximation for material properties(RAMP) method and a dual programming optimization algorithm are used to penalize the intermediate density point to achieve nearly 0-1 solutions.Solutions are shown to meet stability,mesh dependence or non-checkerboard patterns of topology optimization without additional constraints.Finally,the computational efficiency is greatly improved by multithread parallel computing with OpenMP.展开更多
In the present study,we propose to integrate the bilateral filter into the Shepard-interpolation-based method for the optimization of composite structures.The bilateral filter is used to avoid defects in the structure...In the present study,we propose to integrate the bilateral filter into the Shepard-interpolation-based method for the optimization of composite structures.The bilateral filter is used to avoid defects in the structure that may arise due to the gap/overlap of adjacent fiber tows or excessive curvature of fiber tows.According to the bilateral filter,sensitivities at design points in the filter area are smoothed by both domain filtering and range filtering.Then,the filtered sensitivities are used to update the design variables.Through several numerical examples,the effectiveness of the method was verified.展开更多
The low accuracy using unstructured meshes to solve complicated geometry problems is a significant challenge in practical engineering.It is the key to solve this issue through enhancing the accuracy of tetrahedral ele...The low accuracy using unstructured meshes to solve complicated geometry problems is a significant challenge in practical engineering.It is the key to solve this issue through enhancing the accuracy of tetrahedral element.This work develops a simple strategy to enhance the accuracy of tetrahedral element with the Shepard interpolation function.In which the strain field is reconstructed by introducing the weighted strains of adjacent tetrahedral elements to central tetrahedral element.The stiffness of the discrete system is significantly softened with this simple operation,which leads to a great accuracy improvement.Furthermore,this simple modification makes linear tetrahedral element owns higher accuracy even compared with hexahedral element.The high precision tetrahedral element makes finite element analysis more acceptable for engineers.It provides a novel solution to finite element analysis using unstructured meshes for practical engineering problems with complicated geometry.In order to validate the accuracy and feasibility of present modified tetrahedral element(M-T4)in complicated geometry problems,several engineering examples are performed,including linear static analysis,modal analysis,frequency response analysis,transient response analysis,and response spectrum analysis.The remarkable performance of the M-T4 suggests its wide applicability to practical engineering problems.展开更多
基金Projects(11372055,11302033)supported by the National Natural Science Foundation of ChinaProject supported by the Huxiang Scholar Foundation from Changsha University of Science and Technology,ChinaProject(2012KFJJ02)supported by the Key Labortory of Lightweight and Reliability Technology for Engineering Velicle,Education Department of Hunan Province,China
文摘A methodology for topology optimization based on element independent nodal density(EIND) is developed.Nodal densities are implemented as the design variables and interpolated onto element space to determine the density of any point with Shepard interpolation function.The influence of the diameter of interpolation is discussed which shows good robustness.The new approach is demonstrated on the minimum volume problem subjected to a displacement constraint.The rational approximation for material properties(RAMP) method and a dual programming optimization algorithm are used to penalize the intermediate density point to achieve nearly 0-1 solutions.Solutions are shown to meet stability,mesh dependence or non-checkerboard patterns of topology optimization without additional constraints.Finally,the computational efficiency is greatly improved by multithread parallel computing with OpenMP.
基金This research work was supported by the National Natural Science Foundation of China(Grant No.51975227)the Natural Science Foundation for Distinguished Young Scholars of Hubei Province,China(Grant No.2017CFA044).
文摘In the present study,we propose to integrate the bilateral filter into the Shepard-interpolation-based method for the optimization of composite structures.The bilateral filter is used to avoid defects in the structure that may arise due to the gap/overlap of adjacent fiber tows or excessive curvature of fiber tows.According to the bilateral filter,sensitivities at design points in the filter area are smoothed by both domain filtering and range filtering.Then,the filtered sensitivities are used to update the design variables.Through several numerical examples,the effectiveness of the method was verified.
基金supported by the National Key R&D Program of China(No.2022YFB2503505)National Natural Science Foundation of China(No.12002124)+3 种基金National Natural Science Foundation of China(No.12302259)China Postdoctoral Science Foundation(No.2021M690965)Changsha Municipal Natural Science Foundation(No.kq2014035)Natural Science Foundation of Hunan Province(No.2022JJ40031).
文摘The low accuracy using unstructured meshes to solve complicated geometry problems is a significant challenge in practical engineering.It is the key to solve this issue through enhancing the accuracy of tetrahedral element.This work develops a simple strategy to enhance the accuracy of tetrahedral element with the Shepard interpolation function.In which the strain field is reconstructed by introducing the weighted strains of adjacent tetrahedral elements to central tetrahedral element.The stiffness of the discrete system is significantly softened with this simple operation,which leads to a great accuracy improvement.Furthermore,this simple modification makes linear tetrahedral element owns higher accuracy even compared with hexahedral element.The high precision tetrahedral element makes finite element analysis more acceptable for engineers.It provides a novel solution to finite element analysis using unstructured meshes for practical engineering problems with complicated geometry.In order to validate the accuracy and feasibility of present modified tetrahedral element(M-T4)in complicated geometry problems,several engineering examples are performed,including linear static analysis,modal analysis,frequency response analysis,transient response analysis,and response spectrum analysis.The remarkable performance of the M-T4 suggests its wide applicability to practical engineering problems.
