Nowadays, more and more attentions are paid to electromagnetic incremental forming（EMIF）, especially for a part with a large-scale size, e.g., an integral panel with stiffened ribs. In this work, the bending of a pa...Nowadays, more and more attentions are paid to electromagnetic incremental forming（EMIF）, especially for a part with a large-scale size, e.g., an integral panel with stiffened ribs. In this work, the bending of a panel into a double-curvature profile via EMIF is carried out experimentally and evaluated by comparing the formed profile with the desired profile. During the process,discharges at four positions along different discharge paths are designed. The effects of forming parameters on the die-fittingness of the workpiece are discussed, for which two evaluation indices are used to judge forming results. The results show that a discharge voltage in an incremental mode is helpful to improve the fittingness and avoid the collision rebound against the die at the same time.Discharging at the diagonal positions with the ‘‘X＂ discharge path exhibits the minimal shape deviation and the best forming uniformity. On the contrary, discharging at the parallel positions with the ‘‘Z＂ discharge path obtains the worst forming quality. Overlap of the coil at different positions should be given during EMIF; however, a lower overlap rate of the coil helps improve the forming quality. The results obtained in this work are useful for forming integral panels with stiffened ribs via the EMIF process.展开更多
In this paper, we use the discontinuous exact penalty functions to solve the constrained minimization problems with an integral approach. We examine a general form of the constrained deviation integral and its analyti...In this paper, we use the discontinuous exact penalty functions to solve the constrained minimization problems with an integral approach. We examine a general form of the constrained deviation integral and its analytical properties. The optimality conditions of the penalized minimization problems are proven. To implement the al- gorithm, the cross-entropy method and the importance sampling are used based on the Monte-Carlo technique. Numerical tests show the effectiveness of the proposed algorithm.展开更多
A new concept of convergence （R-convergence） of a sequence of measures is applied to characterize global minimizers in a functional space as a sequence of approximate solutions in finite-dimensional spaces. A deviat...A new concept of convergence （R-convergence） of a sequence of measures is applied to characterize global minimizers in a functional space as a sequence of approximate solutions in finite-dimensional spaces. A deviation integral approach is used to find such solutions. For a constrained problem, a penalized deviation integral algorithm is proposed to convert it to unconstrained ones. A numerical example on an optimal control problem with non-convex state constraints is given to show the effectiveness of the algorithm.展开更多
基金supported by the National Science Fund for Distinguished Young Scholars of China (No.51625505)the Key Program Project of the Joint Fund of Astronomy and National Natural Science Foundation of China (No.U1537203)the National Key Basic Research Program of China (No.2011CB012804)
文摘Nowadays, more and more attentions are paid to electromagnetic incremental forming（EMIF）, especially for a part with a large-scale size, e.g., an integral panel with stiffened ribs. In this work, the bending of a panel into a double-curvature profile via EMIF is carried out experimentally and evaluated by comparing the formed profile with the desired profile. During the process,discharges at four positions along different discharge paths are designed. The effects of forming parameters on the die-fittingness of the workpiece are discussed, for which two evaluation indices are used to judge forming results. The results show that a discharge voltage in an incremental mode is helpful to improve the fittingness and avoid the collision rebound against the die at the same time.Discharging at the diagonal positions with the ‘‘X＂ discharge path exhibits the minimal shape deviation and the best forming uniformity. On the contrary, discharging at the parallel positions with the ‘‘Z＂ discharge path obtains the worst forming quality. Overlap of the coil at different positions should be given during EMIF; however, a lower overlap rate of the coil helps improve the forming quality. The results obtained in this work are useful for forming integral panels with stiffened ribs via the EMIF process.
基金supported by the National Natural Science Foundation of China (No. 10771133)the KeyDisciplines of Shanghai Municipality (Operations Research and Cybernetics) (No. S30104)
文摘In this paper, we use the discontinuous exact penalty functions to solve the constrained minimization problems with an integral approach. We examine a general form of the constrained deviation integral and its analytical properties. The optimality conditions of the penalized minimization problems are proven. To implement the al- gorithm, the cross-entropy method and the importance sampling are used based on the Monte-Carlo technique. Numerical tests show the effectiveness of the proposed algorithm.
基金Project supported by the National Natural Science Foundation of China(No.11071158)Shanghai Leading Academic Discipline Project(No.S30104)
文摘A new concept of convergence （R-convergence） of a sequence of measures is applied to characterize global minimizers in a functional space as a sequence of approximate solutions in finite-dimensional spaces. A deviation integral approach is used to find such solutions. For a constrained problem, a penalized deviation integral algorithm is proposed to convert it to unconstrained ones. A numerical example on an optimal control problem with non-convex state constraints is given to show the effectiveness of the algorithm.
