This work puts forward an explicit isogeometric topology optimization(ITO)method using moving morphable components(MMC),which takes the suitably graded truncated hierarchical B-Spline based isogeometric analysis as th...This work puts forward an explicit isogeometric topology optimization(ITO)method using moving morphable components(MMC),which takes the suitably graded truncated hierarchical B-Spline based isogeometric analysis as the solver of physical unknown(SGTHB-ITO-MMC).By applying properly basis graded constraints to the hierarchical mesh of truncated hierarchical B-splines(THB),the convergence and robustness of the SGTHB-ITOMMC are simultaneously improved and the tiny holes occurred in optimized structure are eliminated,due to the improved accuracy around the explicit structural boundaries.Moreover,an efficient computational method is developed for the topological description functions(TDF)ofMMC under the admissible hierarchicalmesh,which consists of reducing the dimensionality strategy for design space and the locally computing strategy for hierarchical mesh.We apply the above SGTHB-ITO-MMC with improved efficiency to a series of 2D and 3Dcompliance design problems.The numerical results show that the proposed SGTHB-ITO-MMC method outperforms the traditional THB-ITO-MMCmethod in terms of convergence rate and efficiency.Therefore,the proposed SGTHB-ITO-MMC is an effective way of solving topology optimization(TO)problems.展开更多
Directly applying the B-spline interpolation function to process plate cams in a computer numerical control(CNC)system may produce verbose tool-path codes and unsmooth trajectories.This paper is devoted to addressing ...Directly applying the B-spline interpolation function to process plate cams in a computer numerical control(CNC)system may produce verbose tool-path codes and unsmooth trajectories.This paper is devoted to addressing the problem of B-splinefitting for cam pitch curves.Considering that the B-spline curve needs to meet the motion law of the follower to approximate the pitch curve,we use the radial error to quantify the effects of thefitting B-spline curve and the pitch curve.The problem thus boils down to solving a difficult global optimization problem tofind the numbers and positions of the control points or data points of the B-spline curve such that the cumulative radial error between thefitting curve and the original curve is minimized,and this problem is attempted in this paper with a double deep Q-network(DDQN)reinforcement learning(RL)algorithm with data points traceability.Specifically,the RL envir-onment,actions set and current states set are designed to facilitate the search of the data points,along with the design of the reward function and the initialization of the neural network.The experimental results show that when the angle division value of the actions set isfixed,the proposed algorithm can maximize the number of data points of the B-spline curve,and accurately place these data points to the right positions,with the minimum average of radial errors.Our work establishes the theoretical foundation for studying splinefitting using the RL method.展开更多
A B-spline Interpolation Transport Solver(BITS) based on a collocation method is developed. It solves transport equations as a generalized interpolation problem, taking the first-order accuracy in time and the second-...A B-spline Interpolation Transport Solver(BITS) based on a collocation method is developed. It solves transport equations as a generalized interpolation problem, taking the first-order accuracy in time and the second-order accuracy in space along with a predictor–corrector or under-relaxation iteration method. Numerical tests show that BITS can solve one-dimensional transport equations for tokamak plasma more accurately without additional computation cost, compared to the finite difference method transport solver which is widely used in existing tokamak transport codes.展开更多
基金supported by the National Key R&D Program of China (2020YFB1708300)the Project funded by the China Postdoctoral Science Foundation (2021M701310).
文摘This work puts forward an explicit isogeometric topology optimization(ITO)method using moving morphable components(MMC),which takes the suitably graded truncated hierarchical B-Spline based isogeometric analysis as the solver of physical unknown(SGTHB-ITO-MMC).By applying properly basis graded constraints to the hierarchical mesh of truncated hierarchical B-splines(THB),the convergence and robustness of the SGTHB-ITOMMC are simultaneously improved and the tiny holes occurred in optimized structure are eliminated,due to the improved accuracy around the explicit structural boundaries.Moreover,an efficient computational method is developed for the topological description functions(TDF)ofMMC under the admissible hierarchicalmesh,which consists of reducing the dimensionality strategy for design space and the locally computing strategy for hierarchical mesh.We apply the above SGTHB-ITO-MMC with improved efficiency to a series of 2D and 3Dcompliance design problems.The numerical results show that the proposed SGTHB-ITO-MMC method outperforms the traditional THB-ITO-MMCmethod in terms of convergence rate and efficiency.Therefore,the proposed SGTHB-ITO-MMC is an effective way of solving topology optimization(TO)problems.
基金supported by Fujian Province Nature Science Foundation under Grant No.2018J01553.
文摘Directly applying the B-spline interpolation function to process plate cams in a computer numerical control(CNC)system may produce verbose tool-path codes and unsmooth trajectories.This paper is devoted to addressing the problem of B-splinefitting for cam pitch curves.Considering that the B-spline curve needs to meet the motion law of the follower to approximate the pitch curve,we use the radial error to quantify the effects of thefitting B-spline curve and the pitch curve.The problem thus boils down to solving a difficult global optimization problem tofind the numbers and positions of the control points or data points of the B-spline curve such that the cumulative radial error between thefitting curve and the original curve is minimized,and this problem is attempted in this paper with a double deep Q-network(DDQN)reinforcement learning(RL)algorithm with data points traceability.Specifically,the RL envir-onment,actions set and current states set are designed to facilitate the search of the data points,along with the design of the reward function and the initialization of the neural network.The experimental results show that when the angle division value of the actions set isfixed,the proposed algorithm can maximize the number of data points of the B-spline curve,and accurately place these data points to the right positions,with the minimum average of radial errors.Our work establishes the theoretical foundation for studying splinefitting using the RL method.
基金the National MCF Energy R&D Program of China(No.2019YFE03040004)the Comprehensive Research Facility for Fusion Technology Program of China(No.2018-000052-73-01-001228)the National MCF Energy R&D Program of China(No.2019YFE03060000)。
文摘A B-spline Interpolation Transport Solver(BITS) based on a collocation method is developed. It solves transport equations as a generalized interpolation problem, taking the first-order accuracy in time and the second-order accuracy in space along with a predictor–corrector or under-relaxation iteration method. Numerical tests show that BITS can solve one-dimensional transport equations for tokamak plasma more accurately without additional computation cost, compared to the finite difference method transport solver which is widely used in existing tokamak transport codes.
