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A true 3D frictional hardening elastoplastic constitutive model of concrete based on a unified hardening/softening function

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 2018年 119卷 250-273页

作者： Wang, Guosheng Lu, Dechun Du, Xiuli Zhou, Xin Cao, Shengtao Beijing Univ Technol Inst Geotech & Underground Engn Beijing 100124 Peoples R China China Acad Bldg Res Beijing 100013 Peoples R China

This paper discusses three hardening modes of a shear-type yield surface and proposes a true three-dimensional (3D) frictional hardening method using the transformed stress. The proposed method reasonably reflects the stress-induced anisotropy of concrete for a wide range of hydrostatic pressures. A unified hardening/softening function is proposed based on the uniaxial compressive stress-strain relationship. The plastic potential function is obtained by studying the influence of linear and nonlinear plastic potential function on the dilatancy, and the relationship between the yield surface and plastic potential surface is analyzed. The loading-unloading criterion suitable for the softening behavior is obtained by transforming the yield function expressed by stress into the one expressed by strain. Furthermore, a true 3D frictional hardening elastoplastic constitutive model is established. The explicit stress integral algorithm and semi-implicit stress integral algorithm are used to implement the numerical computation. Finally, five sets of biaxial and triaxial test results of high-strength and normal-strength concrete are used to verify the established constitutive model. (C) 2018 Elsevier Ltd. All rights reserved.

关键词： Concrete True 3D frictional hardening Unified hardening/softening function Stress-induced anisotropy numerical algorithm

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The QR algorithm: 50 years later its genesis by John Francis and Vera Kublanovskaya and subsequent developments

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IMA JOURNAL OF numerical ANALYSIS 2009年第3期29卷 467-485页

作者： Golub, Gene Uhlig, Frank Stanford Univ Stanford CA 94305 USA Auburn Univ Dept Math & Stat Auburn AL 36849 USA

Fifty years after the invention of the QR algorithm by John Francis and Vera Kublanovskaya we reconstruct the ideas and the influences that led to its genesis from the originators' own recollections and their sour... 详细信息

关键词： QR algorithm numerical algorithm matrix computation matrix eigenvalue matrix eigenvector Francis Implicit Q Theorem John Francis Vera Kublanovskaya history of math history of computation

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Temporal finite element methods through the extended framework of Hamilton's principle

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART C-JOURNAL OF MECHANICAL ENGINEERING SCIENCE 2017年第2期231卷 263-278页

作者： Kim, Jinkyu Kim, Dongkeon Hanyang Univ Sch Architecture & Architectural Engn Kyeonggi Do South Korea Dong A Univ Dept Architectural Engn 37 Nakdong Daero 550 Beon Gil Busan 604714 South Korea

With basic ideas of mixed Lagrangian formulation and sequential assigning process for initial conditions, the extended framework of Hamilton's principle (EHP) was recently developed for continuum dynamics. Unlike the original Hamilton's principle, this new variational framework can fully take initial conditions into account for both linear and nonlinear dynamics, so that it provides a sound base to apply a finite element scheme over the temporal domain without any ambiguity. This paper describes temporal finite element approach stemming from the extended Hamilton's principle, which focuses initially on classical single-degree-of-freedom oscillators such as Kelvin-Voigt damped oscillator and an elasto-viscoplastic model. In each case, an appropriate weak form is provided and a corresponding formulation is discretized in the temporal domain with the adoption of Galerkin's method. Basic numerical properties are investigated for the developed numerical algorithms with several computational examples for the elasto-viscoplastic model. For the underlying conservative system, the present method is symplectic and unconditionally stable with respect to the time step. On the other hand, the method provides unconditionally stable and noniterative algorithm for the elasto-viscoplastic model.

关键词： Hamilton's principle Galerkin's method temporal finite element numerical algorithm unconditional stability

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Modeling and experimental validation of the contact characteristics for laying during automated fiber placement

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INTERNATIONAL JOURNAL OF ADVANCED MANUFACTURING TECHNOLOGY 2024年第12期131卷 5997-6011页

作者： Li, Yan He, Yuxiao Jiang, Junxia Wang, Han Zhu, Weidong Wang, Qing Cheng, Liang Zhejiang Univ Sch Mech Engn State Key Lab Fluid Power & Mechatron Syst Hangzhou 310027 Peoples R China Zhejiang Univ Sch Mech Engn Key Lab Adv Mfg Technol Zhejiang Prov Hangzhou 310027 Peoples R China Aerosp Syst Engn Shanghai Shanghai 201100 Peoples R China

In this paper, a theoretical model of the contact characteristics for layers on irregular surfaces is established by analyzing the contact deformation and slip ratio at the placement path points. Based on this model, a numerical algorithm for calculating the contact characteristics at any path point is proposed. The normal stress field, tangential stress field, and contact status of the contact area at four path points on the double-curved surface mold are obtained using the algorithm and verified through experiments. The results indicate that the model can be used to predict the contact characteristics at any placement path point, and the possible defects at points P3 and P4 are initially identified by analyzing the contact characteristics. In addition, compared to the 8-h computational time required for simulation calculation, this numerical algorithm takes only 20 ms to compute, which shows that the developed model has greatly reduced the calculation time.

关键词： Automated fiber placement Contact characteristics numerical algorithm Laying process

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A local min-orthogonal method for finding multiple saddle points

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JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 2004年第1期291卷 66-81页

作者： Zhou, JX Texas A&M Univ Dept Math College Stn TX 77843 USA

The purpose of this paper is twofold. The first is to remove a possible ill-posedness related to a local minimax method developed in SIAM J. Sci. Comput. 23 (2001) 840-865, SIAM J. Sci. Comput. 24 (2002) 840-865 and the second is to provide a local characterization for nonminimax type saddle points. To do so, a local L-perpendicular to selection is defined and a necessary and sufficient condition for a saddle point is established, which leads to a min-orthogonal method. Those results exceed the scope of a minimax principle, the most popular approach in critical point theory. An example is given to illustrate the new theory. With this local characterization, the local minimax method in SIAM J. Sci. Comput. 23 (2001) 840-865, SIAM J. Sci. Comput. 24 (2002) 840-865 is generalized to a local min-orthogonal method for finding multiple saddle points. In a subsequent paper, this approach is applied to define a modified pseudo gradient (flow) of a functional for finding multiple saddle points in Banach spaces. (C) 2003 Elsevier Inc. All rights reserved.

关键词： multiple saddle points nontainimax solution local orthogonal selection local characterization numerical algorithm

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Modeling of the World Ocean circulation with the four-dimensional assimilation of temperature and salinity fields

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IZVESTIYA ATMOSPHERIC AND OCEANIC PHYSICS 2012年第1期48卷 15-29页

作者： Marchuk, G. I. Zalesny, V. B. Russian Acad Sci Inst Numer Math Moscow 119333 Russia

The problem of modeling the World Ocean circulation with the four-dimensional assimilation of temperature and salinity fields is considered. A mathematical model of the ocean general circulation and a numerical algorithm for its solution are formulated. The model equations are written in a sigma coordinate system on the sphere with the North Pole shifted to the point of the continent (60A degrees E, 60.5A degrees N). The model has a flexible numerical structure and consists of two parts: the forward prognostic model and its adjoint analog. The numerical algorithm for solving the forward and adjoint problems is based on the method of multicomponent splitting. This method includes splitting with respect to physical processes and geometric coordinates. Three series of numerical experiments are performed: (1) a test solution to the problem of the four-dimensional variational assimilation, (2) modeling of the World Ocean circulation with the variational assimilation of climatic temperature and salinity fields, and (3) modeling of the World Ocean circulation with the variational assimilation of climatic temperature and salinity fields and the data of Argo buoys. The results of calculations demonstrate the expediency of using the model of World Ocean circulation with the procedure of assimilating observational data for a description of the general structure of thermohaline fields.

关键词： mathematical modeling the World Ocean numerical algorithm variational assimilation observational data

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PSCAN'96: New software for simulation and optimization of complex RSFQ circuits

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IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY 1997年第2期7卷 2685-2689页

作者： Polonsky, S Shevchenko, P Kirichenko, A Zinoviev, D Rylyakov, A Dept. of Phys. State Univ. of New York Stony Brook NY USA

The first version of PSCAN program (Personal Superconductor Circuit ANalyzer) was introduced in 1991. The program is a general purpose superconductor circuit simulator with an emphasis on the design of Rapid Single-Flux-Quantum (RSFQ) circuits. In the intervening years a number of new features were gradually added to the program. In particular, verification of the correct circuit behavior was enhanced using a special hierarchical Single-Flux-Quantum Hardware Description Language (SFQHDL). Next, a fast heuristic algorithm for margin optimization was introduced, which increased the number of parameters that can be simultaneously optimized in reasonable CPU times. Finally, recently we improved the numerical algorithm used for the simulation by using sparse symmetric positive definite matrices (instead of general structure band matrices as before). As a result, simulation speed has increased almost tenfold. Now it takes about 30 seconds of a CPU time on HP715/100 workstation to run a 2,000-ps simulation of a 120-Josephson-junction circuit, and about a week to optimize all parameters of a two hundred Josephson junction circuit. We have merged all these improvements in a new version of our simulator, PSCAN'96, which will be released by the time of this conference.

关键词： Analytical models Central Processing Unit Circuit analysis circuit analysis computing circuit optimisation Circuit simulation Circuit synthesis Circuit testing complex RSFQ circuits digital integrated circuits fast heuristic algorithm Hardware hardware description languages hierarchical HDL Josephson junctions Josephson-junction circuit margin optimization numerical algorithm optimization software PSCAN'96 rapid single-flux-quantum circuits SFQHDL simulation software simulation speed improvement software packages sparse matrices sparse symmetric positive definite matrices superconducting integrated circuits superconductor circuit simulator Symmetric matrices transient analysis verification

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Hybrid Bernstein Block-Pulse functions for solving system of fractional integro-differential equations

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INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 2018年第11期95卷 2287-2307页

作者： Hesameddini, E. Shahbazi, M. Shiraz Univ Technol Dept Math Sci POB 71555-313 Shiraz Iran

This paper deals with the numerical solution of system of fractional integro-differential equations. In this work, we approximate the unknown functions based on the hybrid Bernstein Block-Pulse functions, in conjunction with the collocation method. We introduce the Riemann-Liouville fractional integral operator for the hybrid Bernstein Block-Pulse functions. This operator will be approximated by the Gauss quadrature formula with respect to the Legendre weight function and then it is utilized to reduce the solution of the fractional integro-differential equations to a system of algebraic equations. This system can be easily solved by any usual numerical methods. The existence and uniqueness of the solution have been discussed. Moreover, the convergence analysis of this algorithm will be shown by preparing some theorems. numerical experiments are presented to show the superiority and efficiency of proposed method in comparison with some other well-known methods.

关键词： Hybrid Bernstein Block-Pulse functions system of fractional integro-differential equations convergence analysis numerical algorithm Gaussian quadrature

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A micro-macro description for pseudoelasticity of NiTi SMAs subjected to nonproportional deformations

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INTERNATIONAL JOURNAL OF PLASTICITY 2017年 90卷 44-65页

作者： Long, X. Peng, X. Fu, T. Tang, S. Hu, N. Chongqing Univ Dept Engn Mech Chongqing Peoples R China Chongqing Univ State Key Lab Coal Mine Disaster Dynam & Control Chongqing Peoples R China Chongqing Ind Polytech Coll Chongqing Peoples R China

A micro-macro constitutive model is developed and applied to the prediction of the pseudoelasticity (PE) of NiTi shape memory alloys (SMAs) subjected to nonproportional loadings. It is based on the work by Gall et al. and takes into account different elastic properties of the austenite and martensite. In the constitutive model for a single crystal, the activation of forward and inverse martensitic transformations and the volume fraction of each of the 24 martensite variants (MVs), and the interaction between the MVs are considered. The constitutive behavior of polycrystalline NiTi SMAs is obtained by assembling that of single crystals of different orientations with finite element method (FEM). The corresponding numerical algorithm and FEM model are developed, in which an additional step is adopted to get rid of the MVs that may irrationally be activated during transformation calculation, which directly reduces the dimension of the Jacobian and enables the convergence and stability of the numerical implement of the model, especially in the cases of complex multiaxial nonproportional deformation. A thin-walled cylindrical model is suggested for finite element analysis, in which the texture microstructure in the materials formed during the cold-drawn processes can be considered. It is shown that the MVs activated under tension are different from those under compression, and when subjected to shear deformation the MVs activated contain those appearing during tension, and more MVs activated may account for the larger slope in the shear stress-strain curve. The PE of NiTi SMAs subjected to uniaxial strain and nonproportional strain by some paths in epsilon - gamma/root 3 plane is simulated, and the satisfactory agreement between the simulated and experimental results demonstrates the validity of the approach developed. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Polycrystalline shape memory alloys Constitutive behavior Phase transformation Thermomechanical processes Microstructures numerical algorithm

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A limited-feedback approximation scheme for optimal switching problems with execution delays

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MATHEMATICAL METHODS OF OPERATIONS RESEARCH 2018年第3期87卷 347-382页

作者： Perninge, Magnus Linnaeus Univ Dept Phys & Elect Engn PG Vejdes Plats S-35252 Vaxjo Sweden

We consider a type of optimal switching problems with non-uniform execution delays and ramping. Such problems frequently occur in the operation of economical and engineering systems. We first provide a solution to the problem by applying a probabilistic method. The main contribution is, however, a scheme for approximating the optimal control by limiting the information in the state-feedback. In a numerical example the approximation routine gives a considerable computational performance enhancement when compared to a conventional algorithm.

关键词： Optimal switching Impulse control Real options Delivery lag Execution delay Stopping time Snell envelope numerical algorithm

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