Constitutive modeling for geomaterials remains challenging because of limited data availability,strong nonlinearity,pressure sensitivity,and the non-smooth characteristics of commonly used yield surfaces.This study pr...Constitutive modeling for geomaterials remains challenging because of limited data availability,strong nonlinearity,pressure sensitivity,and the non-smooth characteristics of commonly used yield surfaces.This study presents a deep-learning-based constitutive method for geomaterials that incorporates a neural stress-integration procedure based on the cutting plane algorithm(CPA).Two compact fully connected networks are trained to learn the yield function and its stress gradient from an augmented stress-state dataset.The trained networks are then incorporated into a cutting plane return-mapping procedure,in which only first-order information is required for the plastic stress return.This avoids explicit analytical yield expressions and second-derivative evaluations and is therefore more naturally compatible with non-smooth Mohr-Coulomb-type yield-surface representations in a first-order returnmapping sense.Numerical results show that the proposed method reproduces the reference Mohr-Coulomb response along the examined monotonic triaxial compression paths.Compared with the finite-difference closest-point projection method(CPPM)implementation considered in this study,the CPA-based neural stress-update procedure requires fewer network calls per update,indicating a more economical implementation for the present learned constitutive framework.展开更多
The concept of cutting platform is proposed and realized based on the latest two step automated tape laying (Two step ATL)technology,which separates prepreg cutting process from tape laying to improve productivity for...The concept of cutting platform is proposed and realized based on the latest two step automated tape laying (Two step ATL)technology,which separates prepreg cutting process from tape laying to improve productivity for large parts with small features.Two step ATL is more efficient than conventional layup because ply patches are pre cut in a separate operation.The concept of the prepreg tape cutting experimental platform with two cutters is introduced.Further,based on the automatic tape laying trajectory planning software,a two cutter cutting algorithm is proposed.Cutting experiments are reported to validate both the concept of cutting platform and cutting algorithm.展开更多
This study presents a two-echelon inventory routing problem (2E-IRP) with an end-of-tour replenishment (ETR) policy whose distribution network consists of a supplier, several distribution centers (DCs) and several ret...This study presents a two-echelon inventory routing problem (2E-IRP) with an end-of-tour replenishment (ETR) policy whose distribution network consists of a supplier, several distribution centers (DCs) and several retailers on a multi-period planning horizon. A formulation of the problem based on vehicle indices is proposed in the form of a mixed integer linear program (MILP). The mathematical model of the problem is solved using a branch and cut (B&C) algorithm. The results of the tests are compared to the results of a branch and price (B&P) algorithm from the literature on 2E-IRP with a classical distribution policy. The results of the tests show that the B&C algorithm solves 197 out of 200 instances (98.5%). The comparison of the B&C and B&P results shows that 185 best solutions are obtained with the B&C algorithm on 197 instances (93.9%). Overall, the B&C algorithm achieves cost reductions ranging from 0.26% to 41.44% compared to the classic 2E-IRP results solved with the B&P algorithm, with an overall average reduction of 18.08%.展开更多
Computational Social Choice is an interdisciplinary research area involving Economics, Political Science,and Social Science on the one side, and Mathematics and Computer Science(including Artificial Intelligence and ...Computational Social Choice is an interdisciplinary research area involving Economics, Political Science,and Social Science on the one side, and Mathematics and Computer Science(including Artificial Intelligence and Multiagent Systems) on the other side. Typical computational problems studied in this field include the vulnerability of voting procedures against attacks, or preference aggregation in multi-agent systems. Parameterized Algorithmics is a subfield of Theoretical Computer Science seeking to exploit meaningful problem-specific parameters in order to identify tractable special cases of in general computationally hard problems. In this paper, we propose nine of our favorite research challenges concerning the parameterized complexity of problems appearing in this context. This work is dedicated to Jianer Chen, one of the strongest problem solvers in the history of parameterized algorithmics,on the occasion of his 60 th birthday.展开更多
Four new trigonometric Bernstein-like basis functions with two exponential shape pa- rameters are constructed, based on which a class of trigonometric Bézier-like curves, anal- ogous to the cubic Bézier curv...Four new trigonometric Bernstein-like basis functions with two exponential shape pa- rameters are constructed, based on which a class of trigonometric Bézier-like curves, anal- ogous to the cubic Bézier curves, is proposed. The corner cutting algorithm for computing the trigonometric Bézier-like curves is given. Any arc of an eliipse or a parabola can be represented exactly by using the trigonometric Bézier-like curves. The corresponding trigonometric Bernstein-like operator is presented and the spectral analysis shows that the trigonometric Bézier-like curves are closer to the given control polygon than the cu- bic Bézier curves. Based on the new proposed trigonometric Bernstein-like basis, a new class of trigonometric B-spline-like basis functions with two local exponential shape pa- rameters is constructed. The totally positive property of the trigonometric B-spline-like basis is proved. For different values of the shape parameters, the associated trigonometric B-spline-like curves can be C2 N FC3 continuous for a non-uniform knot vector, and C3 or C5 continuous for a uniform knot vector. A new class of trigonometric Bézier-like basis functions over triangular domain is also constructed. A de Casteljau-type algorithm for computing the associated trigonometric Bézier-like patch is developed. The conditions for G1 continuous joining two trigonometric Bézier-like patches over triangular domain arededuced.展开更多
基金funded by the Postgraduate Research&Practice Innovation Programof Jiangsu Province,grant number SJCX25_0268(Zijie He).
摘要Constitutive modeling for geomaterials remains challenging because of limited data availability,strong nonlinearity,pressure sensitivity,and the non-smooth characteristics of commonly used yield surfaces.This study presents a deep-learning-based constitutive method for geomaterials that incorporates a neural stress-integration procedure based on the cutting plane algorithm(CPA).Two compact fully connected networks are trained to learn the yield function and its stress gradient from an augmented stress-state dataset.The trained networks are then incorporated into a cutting plane return-mapping procedure,in which only first-order information is required for the plastic stress return.This avoids explicit analytical yield expressions and second-derivative evaluations and is therefore more naturally compatible with non-smooth Mohr-Coulomb-type yield-surface representations in a first-order returnmapping sense.Numerical results show that the proposed method reproduces the reference Mohr-Coulomb response along the examined monotonic triaxial compression paths.Compared with the finite-difference closest-point projection method(CPPM)implementation considered in this study,the CPA-based neural stress-update procedure requires fewer network calls per update,indicating a more economical implementation for the present learned constitutive framework.
基金supported by the National Science and Technology Major Project(No.2016ZX04002-005)
摘要The concept of cutting platform is proposed and realized based on the latest two step automated tape laying (Two step ATL)technology,which separates prepreg cutting process from tape laying to improve productivity for large parts with small features.Two step ATL is more efficient than conventional layup because ply patches are pre cut in a separate operation.The concept of the prepreg tape cutting experimental platform with two cutters is introduced.Further,based on the automatic tape laying trajectory planning software,a two cutter cutting algorithm is proposed.Cutting experiments are reported to validate both the concept of cutting platform and cutting algorithm.
摘要This study presents a two-echelon inventory routing problem (2E-IRP) with an end-of-tour replenishment (ETR) policy whose distribution network consists of a supplier, several distribution centers (DCs) and several retailers on a multi-period planning horizon. A formulation of the problem based on vehicle indices is proposed in the form of a mixed integer linear program (MILP). The mathematical model of the problem is solved using a branch and cut (B&C) algorithm. The results of the tests are compared to the results of a branch and price (B&P) algorithm from the literature on 2E-IRP with a classical distribution policy. The results of the tests show that the B&C algorithm solves 197 out of 200 instances (98.5%). The comparison of the B&C and B&P results shows that 185 best solutions are obtained with the B&C algorithm on 197 instances (93.9%). Overall, the B&C algorithm achieves cost reductions ranging from 0.26% to 41.44% compared to the classic 2E-IRP results solved with the B&P algorithm, with an overall average reduction of 18.08%.
基金supported by the Deutsche Forschungsgemeinschaft, project PAWS (NI 369/10)supported by the Studienstiftung des Deutschen Volkes+2 种基金supported by DFG "Cluster of Excellence Multimodal Computing and Interaction"supported by DIAMANT (a mathematics cluster of the Netherlands Organization for Scientific Research NWO)the Alexander von Humboldt Foundation, Bonn, Germany
摘要Computational Social Choice is an interdisciplinary research area involving Economics, Political Science,and Social Science on the one side, and Mathematics and Computer Science(including Artificial Intelligence and Multiagent Systems) on the other side. Typical computational problems studied in this field include the vulnerability of voting procedures against attacks, or preference aggregation in multi-agent systems. Parameterized Algorithmics is a subfield of Theoretical Computer Science seeking to exploit meaningful problem-specific parameters in order to identify tractable special cases of in general computationally hard problems. In this paper, we propose nine of our favorite research challenges concerning the parameterized complexity of problems appearing in this context. This work is dedicated to Jianer Chen, one of the strongest problem solvers in the history of parameterized algorithmics,on the occasion of his 60 th birthday.
基金We, wish to express our gratitude to the referees for their valuable re- marks for improvements. The research is supported by the National Natural Science Foun-dation of China (No. 60970097, No. 11271376), Postdoctoral Science Foundation of China (2015M571931), and Graduate Students Scientific Research Innovation Project of Hunan Province (No. CX2012Blll).
摘要Four new trigonometric Bernstein-like basis functions with two exponential shape pa- rameters are constructed, based on which a class of trigonometric Bézier-like curves, anal- ogous to the cubic Bézier curves, is proposed. The corner cutting algorithm for computing the trigonometric Bézier-like curves is given. Any arc of an eliipse or a parabola can be represented exactly by using the trigonometric Bézier-like curves. The corresponding trigonometric Bernstein-like operator is presented and the spectral analysis shows that the trigonometric Bézier-like curves are closer to the given control polygon than the cu- bic Bézier curves. Based on the new proposed trigonometric Bernstein-like basis, a new class of trigonometric B-spline-like basis functions with two local exponential shape pa- rameters is constructed. The totally positive property of the trigonometric B-spline-like basis is proved. For different values of the shape parameters, the associated trigonometric B-spline-like curves can be C2 N FC3 continuous for a non-uniform knot vector, and C3 or C5 continuous for a uniform knot vector. A new class of trigonometric Bézier-like basis functions over triangular domain is also constructed. A de Casteljau-type algorithm for computing the associated trigonometric Bézier-like patch is developed. The conditions for G1 continuous joining two trigonometric Bézier-like patches over triangular domain arededuced.