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A solution framework for linear PDE-constrained mixed-integer problems

MATHEMATICAL PROGRAMMING 2021年第2期188卷 695-728页

作者： Gnegel, Fabian Fuegenschuh, Armin Hagel, Michael Leyffer, Sven Stiemer, Marcus Brandenburg Univ Technol Cottbus Senftenberg Pl Deutsch Einheit 1 D-03046 Cottbus Germany Helmut Schmidt Univ Univ Fed Armed Forces Hamburg Holstenhofweg 83 D-22043 Hamburg Germany Argonne Natl Lab Math & Comp Sci Div 9700 Cass Ave Lemont IL 60439 USA

We present a general numerical solution method for control problems with state variables defined by a linear PDE over a finite set of binary or continuous control variables. We show empirically that a naive approach that applies a numerical discretization scheme to the PDEs to derive constraints for a mixed-integer linear program (MILP) leads to systems that are too large to be solved with state-of-the-art solvers for MILPs, especially if we desire an accurate approximation of the state variables. Our framework comprises two techniques to mitigate the rise of computation times with increasing discretization level: First, the linear system is solved for a basis of the control space in a preprocessing step. Second, certain constraints are just imposed on demand via the IBM ILOG CPLEX feature of a lazy constraint callback. These techniques are compared with an approach where the relations obtained by the discretization of the continuous constraints are directly included in the MILP. We demonstrate our approach on two examples: modeling of the spread of wildfire and the mitigation of water contamination. In both examples the computational results demonstrate that the solution time is significantly reduced by our methods. In particular, the dependence of the computation time on the size of the spatial discretization of the PDE is significantly reduced.

关键词： Mixed-integer linear programming Partial differential equations finite-difference methods finite-element methods Convection-diffusion equation Global optimal control

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Bioinspired 3D-Printed Auxetic Structures with Enhanced Fatigue Behavior

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ADVANCED ENGINEERING MATERIALS 2024年第20期26卷

作者： Shirzad, Masoud Kang, Juhyun Kim, Garin Bodaghi, Mahdi Nam, Seung Yun Pukyong Natl Univ Ind Convergence Bion Engn 4-0 Busan 48513 South Korea Pukyong Natl Univ Dept Biomed Engn Busan 48513 South Korea Nottingham Trent Univ Sch Sci & Technol Dept Engn Nottingham NG11 8NS England Pukyong Natl Univ Div Smart Healthcare Major Biomed Engn Busan 48513 South Korea

Recently, auxetic metastructures have gained considerable attention in various fields of study due to their unique characteristics. This study aims to design and fabricate bioinspired auxetic structures and comprehensively investigate the static and dynamic mechanical properties of those architectures under tensile and compressive loads. A comparative analysis is carried out with a conventional structure, considering static tensile and compressive tests, as well as dynamic tension-tension and compression-compression assessments. Experimental measurements and finite-element analysis are utilized to evaluate various parameters of the scaffolds, such as Young's modulus, yield strength, energy absorption, stress distribution, Poisson's ratio, and fatigue properties. The findings reveal that bioinspired auxetic structures can appropriately mimic the physical attributes and stress-strain characteristics of human tissue, such as the Achilles tendon. Furthermore, these bioinspired auxetic structures significantly enhance the cycles to failure compared to conventional structures, accompanied by notable improvements in energy absorption. Among the auxetic structures, the star configuration exhibits remarkable tolerance to tensile fatigue loads, while the sharp sinus structure demonstrates the highest tolerance to cycles to failure under compression-compression loads. The static and fatigue properties of bioinspired auxetic structures indicate their potential for biomedical applications. The world of auxetic structures, where innovation meets resilience, is dived into, unlocking the potential of auxetic metastructures and harnessing bioinspiration and fatigue resistance. Herein, how bioinspired designs mimic human tissue is explored, offering enhanced fatigue resistance and static mechanical properties. The future of materials engineering with auxetics-revolutionizing biomedical applications and beyond-is *** (c) 2024 WILEY-VCH GmbH

关键词： bioinspired auxetics fatigues finite-element methods metamaterials tissue scaffolds

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Induction Motor Analysis by Considering Hysteresis Loops in Stator and Rotor

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IEEE TRANSACTIONS ON MAGNETICS 2021年第6期57卷 1-4页

作者： Yamazaki, Katsumi Kokubu, Shinichiro Chiba Inst Technol Dept Elect Elect & Comp Engn Narashino Chiba 2750016 Japan

This article describes the characteristic calculation of induction motors with the same shaped rotor bars in equal spaces by considering hysteresis loops in stator and rotor cores. A fast calculation method based on the symmetrical bar shape is proposed to realize this calculation. The validity of the calculation is confirmed by experimental results. It is clarified that the accuracies of the calculated motor characteristics are improved by considering the reaction field caused by the hysteresis phenomenon and eddy currents in the core.

关键词： finite-element methods induction motors magnetic cores magnetic hysteresis

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Shape-free polygonal hybrid displacement-function element method for analyses of Mindlin-Reissner plates

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ENGINEERING WITH COMPUTERS 2021年第3期37卷 1975-1998页

作者： Wu, Cheng-jin Cen, Song Shang, Yan Tsinghua Univ Sch Aerosp Engn Dept Engn Mech Beijing Peoples R China Tsinghua Univ AML Sch Aerosp Engn Beijing Peoples R China Nanjing Univ Aeronaut & Astronaut Coll Aerosp Engn State Key Lab Mech & Control Mech Struct Nanjing Peoples R China

A high-performance shape-free polygonal hybrid displacement-function finite-element method is proposed for analyses of Mindlin-Reissner plates. The analytical solutions of displacement functions are employed to construct element resultant fields, and the three-node Timoshenko's beam formulae are adopted to simulate the boundary displacements. Then, the element stiffness matrix is obtained by the modified principle of minimum complementary energy. With a simple division, the integration of all the necessary matrices can be performed within polygonal element region. Five new polygonal plate elements containing a mid-side node on each element edge are developed, in which element HDF-PE is for general case, while the other four, HDF-PE-SS1, HDF-PE-Free, IHDF-PE-SS1, and IHDF-PE-Free, are for the edge effects at different boundary types. Furthermore, the shapes of these new elements are quite free, i.e., there is almost no limitation on the element shape and the number of element sides. Numerical examples show that the new elements are insensitive to mesh distortions, possess excellent and much better performance and flexibility in dealing with challenging problems with edge effects, complicated loading, and material distributions.

关键词： finite-element methods Mindlin-Reissner plate Polygonal elements Hybrid displacement-function method Mesh distortion

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Research on the Dynamic Softening Mechanism of Dual-Phase Structure During Warm Forming of Fe-8.5Mn-1.5Al Medium-Manganese Steel

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STEEL RESEARCH INTERNATIONAL 2024年第9期95卷

作者： Liu, Xiu-Zheng Li, Xiao-Lin Sun, Ying Hou, Hongli Li, Hui-Ping Li, Zhi-Chao He, Lian-Fang Shandong Univ Sci & Technol Sch Mat Sci & Engn Qingdao 266510 Peoples R China Northwest Inst Nonferrous Met Res Xian 710016 Peoples R China

In this article, Fe-8.5Mn-1.5Al medium-manganese steel is taken as the research object, and Gleeble 3500 thermal simulation testing machine is used to conduct isothermal compression at different deformation temperatures, strain rates, and strains in its austenite ferrite two-phase zone. A constitutive model and a dynamic recrystallization volume fraction model for materials are established, and finite-element method is used to simulate the temperature, equivalent strain, and dynamic recrystallization volume fraction distribution in different regions of the workpiece under different deformation conditions. By comparing and analyzing the microstructure, finite-element simulation results, and hot working diagrams obtained from the experiment, the microscopic mechanism of dynamic softening of the material when ferrite and austenite coexist is explained;the transformation of the dynamic softening mechanism of the two phases with the hot deformation process is also explained. Early deformation mainly occurs in softer ferrite, which preferentially undergoes continuous dynamic recrystallization. Austenite has a lower stacking fault energy, and discontinuous dynamic recrystallization (DDRX) occurs when the dislocation density reaches a certain critical value. At the same time, when the strain reaches a certain level, the dynamic softening behavior of ferrite will also transform into DDRX. The optimal deformation conditions for Fe-8.5Mn-1.5Al medium-manganese steel during warm processing in the two-phase zone are a temperature of 720 degrees C, a strain rate of 0.01 s-1, and a large deformation zone. In this article, Fe-8.5Mn-1.5Al steel is taken as the research object, and isothermal compression is conducted at different deformation temperatures, strain rates, and strains in its austenite ferrite two-phase zone. A constitutive model and a dynamic recrystallization volume fraction model for materials are established, and finite-element method is used to simulate the temperatu

关键词： Avrami kinetics models dynamic recrystallizations finite-element methods medium-manganese steels thermal processing diagrams

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Variational construction of tubular and toroidal streamsurfaces for flow visualization

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PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES 2024年第2285期480卷 20230951-20230951页

作者： Li, Mingwu Kaszas, Balint Haller, George Southern Univ Sci & Technol Dept Mech & Aerosp Engn Shenzhen 518055 Peoples R China Swiss Fed Inst Technol Inst Mech Syst Leonhard Str 21 CH-8092 Zurich Switzerland

Approximate streamsurfaces of a three-dimensional velocity field have recently been constructed as isosurfaces of the closest first integral of the velocity field. Such approximate streamsurfaces enable effective and efficient visualization of vortical regions in three-dimensional flows. Here we propose a variational construction of these approximate streamsurfaces to remove the limitation of Fourier series representation of the first integral in earlier work. Specifically, we use finite-element methods to solve a partial differential equation that describes the best approximate first integral for a given velocity field. We use several examples to demonstrate the power of our approach for three-dimensional flows in domains with arbitrary geometries and boundary conditions. These include generalized axisymmetric flows in the domains of a sphere (spherical vortex), a cylinder (cylindrical vortex) and a hollow cylinder (Taylor-Couette flow) as benchmark studies for various computational domains, non-integrable periodic flows (ABC and Euler flows) and Rayleigh-Benard convection flows. We also illustrate the use of the variational construction in extracting momentum barriers in Rayleigh-Benard convection.

关键词： first integral coherent structures finite-element methods

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Influences of Weld Nugget Shape and Material Gradient on the Shear Strength of Resistance Spot-Welded Joints

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STEEL RESEARCH INTERNATIONAL 2024年第4期95卷

作者： Schuster, Lilia Olfert, Viktoria Sherepenko, Oleksii Fehrenbach, Clemens Song, Shiyuan Hein, David Meschut, Gerson Biro, Elliot Muenstermann, Sebastian Fraunhofer Inst Mech Mat IWM Component Safety & Lightweight Construct Wohlerstr 11 D-79108 Freiburg Germany Univ Paderborn Lab Mat & Joining Technol LWF Pohlweg 47-49 D-33098 Paderborn Germany Univ Waterloo Dept Mech & Mechatron Engn 200 Univ Ave WestE3 3101D Waterloo ON Canada Rhein Westfal TH Aachen IEHK Steel Inst Intzestr 1 D-52072 Aachen Germany

Resistance spot-welded joints containing press-hardened steels are seen to exhibit a fracture mode called total dome failure, where the weld nugget completely separates from one steel sheet along the weld nugget edge. The effect of weld nugget shape and material property gradients is studied based on damage mechanics modeling and experimental validation to shed light on the underlying influencing factors. For a three-steel-sheet spot-welded joint combining DP600 (1.5 mm)-CR1900T (1.0 mm)-CR1900T (1.0 mm), experiments under shear loading reveal that fracture occurs in the DP600 sheet along the weld nugget edge. In subsequent numerical simulation studies with damage mechanics models whose parameters are independently calibrated for every involved material configuration, three variations of the geometrical joint configuration are considered-an approximation of the real joint, one variation with a steeper weld nugget shape, and one variation with a less pronounced gradient between weld nugget material and heat-affected zone material properties. The results of the finite-element simulations show that a shallower weld nugget and a more pronounced material gradient lead to a faster increase of plastic strain at the edge of the weld nugget and promote the occurrence of total dome failure. Total dome failure is a fracture mode of resistance spot-welded joints, where the weld nugget completely separates from one steel sheet along the weld nugget edge. This study looks at the role of weld nugget shape and material gradient in the occurrence of total dome failure by means of finite-element *** (c) 2024 WILEY-VCH GmbH

关键词： advanced high-strength steels finite-element methods resistance spot welding three-sheet joints total dome failures

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Vertically Stacked, Flip-Chip Wide Bandgap MOSFET Co-Optimized for Reliability and Switching Performance

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IEEE JOURNAL OF EMERGING AND SELECTED TOPICS IN POWER ELECTRONICS 2021年第4期9卷 3904-3915页

作者： Montazeri, Mahsa Huitink, David R. Wallace, Andrea Peng, Hongwu Seal, Sayan Luo, Fang Mantooth, H. Alan Univ Arkansas Mech Engn Dept Fayetteville AR 72701 USA Univ Arkansas Dept Elect Engn Fayetteville AR 72701 USA Northrop Grumman Linthicum Hts MD 21090 USA Clemson Univ Comp Engn Dept Clemson SC 29634 USA Cree Inc Fayetteville AR 72701 USA Univ Arkansas Elect Engn Dept Fayetteville AR 72701 USA SUNY Stony Brook Elect & Comp Engn Dept Stony Brook NY 11794 USA

Silicon carbide (SiC) wide-bandgap semiconductors (WBGs) offer a significant improvement in high voltage and high-temperature stability;however, their associated packaging often can impede electrical performance and reliability. In this study, a new flip-chip package, implementing a vertically oriented metal oxide semiconductor field effect transistor (MOSFET) was investigated to achieve co-optimized thermomechanical reliability with low parasitic inductance. The architecture improves upon wire-bonded packages by allowing for top-side cooling and reduced power loop inductance. Herein, the design effects of solder material and diameter as well as pitch size and drain connector geometry on thermal cycling reliability of the device were investigated using finite-element methods. Additionally, thermal resistance in association with a parasitic inductance of varying drain connector architectures is compared while utilizing symmetry to facilitate manufacturability. By considering the complex effects of geometry and material, the optimal architecture was selected and fabricated. When comparing to a prior flip-chip design effort, this simulation-based design optimization was able to improve the solder fatigue life up to 11 times while reducing parasitic inductance by 30 times. Experimentally, the associated electrical performance of the novel device showed improved switching behavior in double-pulse testing of a half-bridge module, with nearly negligible overshoot voltage on switching, where an equivalent discrete package exhibited similar to 100% overshoot and similar to 24% inductance improvement at the module level.

关键词： Design co-optimization finite-element methods flip-chip device metal oxide semiconductor field effect transistor (MOSFET) switches parasitic inductance reliability wide bandgap packaging

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Multilevel Multiplicative Interval Uncertainty in Linear Structural Analysis

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ASCE-ASME JOURNAL OF RISK AND UNCERTAINTY IN ENGINEERING SYSTEMS PART A-CIVIL ENGINEERING 2023年第4期9卷

作者： Mullen, Robert L. Muhanna, Rafi L. Univ South Carolina Dept Civil & Environm Engn Columbia SC 29208 USA Georgia Inst Technol Dept Civil & Environm Engn Atlanta GA 30332 USA

Interval treatments of uncertainty are plagued by dependency issues in their implementation. Ignoring the dependency among interval values can lead to a significant overestimation of the bounds on calculated uncertain responses. However, the clever implementation of operation order and other dependency effects in interval computations can result in models for the uncertainty that provide sharp bounds for multidomain uncertainty dependency in physical systems. In this paper, we explore an interval analysis of structural systems-specifically, systems where one or more groups of structural elements are subject to a global uncertainty in a value of a property and, concomitantly, each element has an additional intragroup uncertainty. Consider a typical scenario where the steel for structural elements is from a single batch (has unknown but identical modulus and strength) while each element has uncertainty in its stiffness from both modulus and geometric variations. To address the relationship between overall group uncertainty and local uncertainty, a product of interval variables is employed. The dependency for element level uncertainty (i.e., area) is addressed by the element-by-element methods of Muhanna and Mullen, while the group dependency is addressed by a new group-by-group method where a single interval value multiplies the entire substructure matrix. Example calculations are presented to compare the results of the new multilevel fixed-point method with conventional interval finite element calculations and with all combinations of endpoints, sensitivity-based methods, and two optimization methods. In general, only the fixed-point methods provide a guaranteed enclosure. Both solution accuracy, as well as computational requirements of the methods, will be assessed.

关键词： finite-element methods Interval uncertainty Dependency Fixed-point

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Fire resistance of bi-directionally prestressed concrete under extreme fire loading

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PROCEEDINGS OF THE INSTITUTION OF CIVIL ENGINEERS-STRUCTURES AND BUILDINGS 2021年第9期174卷 749-764页

作者： Choi, Ji-Hun Yang, Dal-Hun Choi, Seung-Jai Yi, Seong-Tae Kim, Jang-Ho Jay Yonsei Univ Sch Civil & Environm Engn Seoul South Korea Korea Inst Civil Engn & Bldg Technol Dept Struct Engn Res Gyeonggi South Korea Inha Tech Coll Dept Civil & Environm Engn Incheon South Korea

Infrastructures such as prestressed concrete containment vessels (PCCVs) and liquid gas storage tanks are constructed as bi-directional prestressed concrete (PSC) structures to ensure outstanding leak-tight storage and shielding performance. However, PSC structures exhibit severe vulnerability to high-temperature fire due to the high-strength concrete used and the application of prestressing (PS) stresses to increase the strength of the structures. The PCCV of a 1400 MW advanced power reactor was selected as the target for study. A scaled-down model of the PCCV outer wall was fabricated and tested to determine its resistance to a standard fire-loading scenario. Furthermore, different PS forces were applied to the specimens to evaluate the effect of concrete confinement on the fire resistance. Test data of temperature distribution, PS force loss and residual strength capacity were obtained. The experimental data were used for calibration of a commercial finite-element simulation program (Midas FEA) for structural fire analysis of real-scale concrete structure and infrastructure. The simulation and test results showed significant similarity and the result trends were accurate.

关键词： finite-element methods prestressed concrete slabs & plates temperature-related & thermal effects

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