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Rocking sensitivity of a dual-block stack - numerical simulation and experimental evidence

EARTHQUAKE ENGINEERING & STRUCTURAL DYNAMICS 2024年第1期53卷 366-391页

作者： Ceh, Nina Jelenic, Gordan Bicanic, Nenad Univ Rijeka Fac Civil Engn Radmile Matejcic 3 Rijeka 51000 Croatia

Historic monuments, drywall structures, and graphite blocks in AGR nuclear power plants are block-like structures that have to withstand rocking when subject to seismic excitation of their base, which can lead to overturning of some of their components and results in the collapse of the whole structure. We revisit the known nonlinear equations of motion for a dual-block stack and present the conditions for transition between the eight possible rocking configurations (due to initiation of rocking, opening of new contacts, and collisions between blocks). An algorithm for the numerical simulation of rocking of the dual-block stack is developed using the Newmark integration method, the Newton-Raphson iteration method, and a novel contact detection and resolution procedure. The algorithm is used to evaluate rocking stability of five dual-block stacks, one of which is compared to the results available in the literature. In parallel, a novel experimental program is designed and implemented, to validate the numerically obtained results using a shaking table. While most of the excitation conditions leading to stable rocking and limit values leading to overturning have been successfully validated, some discrepancies between the numerically and experimentally obtained results still exist and point to the need for improvement of the algorithm used, possibly through a more realistic energy-loss mechanism. Most importantly, we have confirmed the known theoretical prediction that splitting a single block into two half-size blocks benefits its rocking stability.

关键词： dual-block stack numerical investigation numerical algorithm partial overturning rocking stability assessment total overturning

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Physics-based numerical implementation framework towards multi-scale contact problem

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TRIBOLOGY INTERNATIONAL 2025年 202卷

作者： Yang, Tao Tang, Xiongfeng Yan, Zhixue Wang, Guoqing Zhao, Gai Peng, Hanmin Nanjing Univ Aeronaut & Astronaut State Key Lab Mech & Control Aerosp Struct Nanjing 210016 Peoples R China

This paper establishes a general computational framework to solve the muti-scale contact problem by integrating the statistical contact model with the finite element format. Compared to existing models, the proposed method is applicable to most geometric configurations and can effectively evaluate the pressure distribution. In this work, a modified Karush-Kuhn-Tucker (KKT) condition is proposed by the assumption that asperity height obeys the Gaussian distribution. Therefore, in the variational formula, the contact contribution is decomposed into body contribution and asperity contribution, corresponding to the nominal smooth surface and roughness, respectively. Then the linearization and constraint enforcement of these two components are derived, followed by a nonlinear Newton-Raphson-based iterative algorithm. The contact patch test and Hertz contact test are conducted, and the predicted results are consistent with the theoretical and experimental values, confirming the effectiveness and accuracy of the proposed approach. It is worth noting that in the Hertz contact test, the contact pressure distribution varies progressively with the roughness level and external force, tending to the Hertz limit or Gaussian limit. This means that the proposed method can be applied to any roughness and load. Finally, the contact behaviors of the transmission interface of a piezoelectric actuator, i.e., a typical multi-scale contact problem, are studied as an engineering application case.

关键词： Roughness Asperity contact numerical algorithm Multi-scale modelling

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numerical method research and characteristics analysis on frozen start-up process of high-temperature heat pipe

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APPLIED THERMAL ENGINEERING 2024年 257卷

作者： Wang, Weixiang Zhang, Kefan Dong, Sifan Wang, Shuai Chen, Hongli Univ Sci & Technol China Sch Nucl Sci & Technol Hefei 230026 Anhui Peoples R China Univ Sci & Technol China Deep Space Explorat Lab Hefei 230088 Anhui Peoples R China

Future space exploration technology requires a long-life and reliable power source that is not reliant on solar energy. Space micro-reactors are able to meet this need, with Heat Pipe Cooled Reactors (HPR) emerging as a notable type of space micro-reactor that has attracted widespread attention in recent years. The HPR utilizes high-temperature alkali metal heat pipes for heat transfer, which presents certain complexities due to the solid state of the alkali metals working medium at room temperature. This results in a three-phase transition during the high-temperature heat pipes start-up process, which significantly impacts the heat transfer characteristics and dynamic behavior of the HPR start-up process. Consequently, thorough research is necessary in this area. numerical simulation is a crucial tool that can effectively analyze, predict, and guide experiments. This article utilizes the Finite Volume Method (FVM) to develop a simulation code for high-temperature heat pipe frozen start-up. Various physical models are integrated to describe different components of the heat pipe: the container is represented by a two-dimensional axisymmetric heat conduction equation, the wick region utilizes a Fixed Grid Method (FGM) to depict the melting process of the medium, and the vapor channel is described through a two-dimensional axisymmetric compressible laminar flow. The wick region and vapor channel are coupled through the evaporation and condensation of the medium. For the vapor channel, numerical methods such as SIMPLE and PISO are used for solving. Adaptive time step and OpenMP acceleration are employed in the code to enhance computational efficiency. Finally, by comparing the calculated results with experimental data, the feasibility and accuracy of the code are assessed, highlighting special phenomena during the start-up process. The findings confirm that the developed code accurately predicts parameter changes during start-up, and can serve as a heat pipe analysis mo

关键词： High-temperature heat pipe numerical algorithm High-speed compressible flow

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Matrix-less methods for the spectral approximation of large non-Hermitian Toeplitz matrices: A concise theoretical analysis and a numerical study

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numerical LINEAR ALGEBRA WITH APPLICATIONS 2024年第4期31卷 e2545-e2545页

作者： Bogoya, Manuel Ekstrom, Sven-Erik Serra-Capizzano, Stefano Vassalos, Paris Univ Valle Dept Matemat Cali Colombia Uppsala Univ Dept Informat Technol Div Sci Comp Box 337 SE-75105 Uppsala Sweden Univ Insubria Dipartimento Sci & Alta Tecnol Como Italy Athens Univ Econ & Business Sch Informat Sci & Technol Athens Greece

It is known that the generating function of a sequence of Toeplitz matrices may not describe the asymptotic distribution of the eigenvalues of the considered matrix sequence in the non-Hermitian setting. In a recent work, under the assumption that the eigenvalues are real, admitting an asymptotic expansion whose first term is the distribution function, fast algorithms computing all the spectra were proposed in different settings. In the current work, we extend this idea to non-Hermitian Toeplitz matrices with complex eigenvalues, in the case where the range of the generating function does not disconnect the complex field or the limiting set of the spectra, as the matrix-size tends to infinity, has one nonclosed analytic arc. For a generating function having a power singularity, we prove the existence of an asymptotic expansion, that can be used as a theoretical base for the respective numerical algorithm. Different generating functions are explored, highlighting different numerical and theoretical aspects;for example, non-Hermitian and complex symmetric matrix sequences, the reconstruction of the generating function, a consistent eigenvalue ordering, the requirements of high-precision data types. Several numerical experiments are reported and critically discussed, and avenues of possible future research are presented.

关键词： asymptotic expansion eigenvalues GLT sequences numerical algorithm spectral symbols Toeplitz matrices

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On numerical Solutions for a Class of Relativistic Quasilinear Schrödinger Equations

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BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY 2024年第4期50卷 1-20页

作者： Huang, Canwei Wang, Youjun South China Univ Technol Dept Math Guangzhou 510640 Peoples R China

We study the numerical solutions for a class of quasilinear Schr & ouml;dinger equations arising from the self-channeling of high-power ultra short lasers in matter, which are associated with energy functionals with nonlinear principle parts so that the classical algorithm cannot directly be used. By the method of variable replacement to transform the quasilinear Schr & ouml;dinger equation into an semilinear elliptic equation, the numerical mountain pass algorithm is then applied. Some numerical experiments are also performed, including zero potential, nonzero constant potential and singular problem.

关键词： Mountain pass solutions Quasilinear equations numerical algorithm

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On numerical study of constrained coupled shape optimization problems based on a new shape derivative method

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numerical METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS 2023年第3期39卷 2018-2059页

作者： Boulkhemair, Abdesslam Chakib, Abdelkrim Sadik, Azeddine UFR Sci & Tech Nantes Lab Math Jean Leray UMR6629 CNRS Nantes France Univ Sultan Moulay Slimane Fac Sci Tech Lab Math & Applicat BP 523 Beni Mellal Morocco

In this article, we deal with a numerical method for the approximation of a class of coupled shape optimization problems, which consist in minimizing an appropriate general volume cost functional subjected to coupled boundary value problems by means of a Neumann boundary transmission condition. We show the existence of the shape derivative of the cost functional and express it by means of support functions, using a new formula of shape derivative on a family of convex domains. This allows us to avoid the disadvantages related to the classical shape derivative method using vectors field. Then the numerical discretization is performed using the dual reciprocity boundary element method in order to avert the remeshing task required for the finite element method. Finally, we give some numerical results, based on the gradient method, showing the efficiency of the proposed approach.

关键词： boundary element convex domain coupled problem numerical algorithm shape derivative shape optimization support function

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numerical Solution of High-Precision Multiconstant Equations of State

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MOSCOW UNIVERSITY PHYSICS BULLETIN 2025年第1期80卷 189-193页

作者： Koldoba, E. V. Lomonosov Moscow State Univ Fac Mech & Math Dept Computat Mech Moscow 119991 Russia

In certain pressure and temperature ranges, high-precision thermal equations of state possess multiple roots, with only one being the desired physical solution to the problem. This paper considers methods for setting initial values to calculate the desired root of the equation. A method for verifying the found root has been developed, enabling the exclusion of nonphysical solutions. The proposed approach allows for the construction of a robust algorithm for numerically solving transcendental equations of state for practical applications.

关键词： numerical algorithm multiparameter equation of state Benedict-Webb-Rubin equation Pedersen's model

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numerical and experimental study of the viscosity and mechanical parameters effect on tow feeding quality during automated fiber placement

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JOURNAL OF MANUFACTURING PROCESSES 2023年 96卷 31-40页

作者： Li, Yan Zheng, Chenggan Jiang, Junxia Wang, Han Zhu, Weidong Wang, Qing Chen, Chao Zhang, Shuai Ke, Yinglin 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 Hiwing Mat Ind Co Ltd Suzhou 215131 Peoples R China

For automated fiber placement (AFP), it is crucial to research the contact characteristics between tow and roller during the tow feeding process. However, it has not been widely explored. In this paper, a theoretical model of contact characteristics for the tow feeding process is established by analyzing the distribution of normal stress, tangential stress, adhesion zone, and slip zone, respectively. The model proposed a numerical algorithm for calculating the contact characteristic. Then the contact characteristic of the tow feeding system can be acquired and validated by the experiment and finite element method. The model that provides theoretical support for AFP optimization. Furthermore, proper pressure (P = 0.6Mpa) and tension (T = 3 N) for towpreg feeding under experimental conditions were obtained.

关键词： Automated fiber placement Tow feeding system Contact characteristic numerical algorithm

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A numerical algorithm for a class of BSDEs via the branching process

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STOCHASTIC PROCESSES AND THEIR APPLICATIONS 2014年第2期124卷 1112-1140页

作者： Henry-Labordere, Pierre Tan, Xiaolu Touzi, Nizar Univ Paris 09 CEREMADE F-75775 Paris 16 France Ecole Polytech Paris Ctr Math Appl Paris France

We give a study to the algorithm for semi-linear parabolic PDEs in Henry-Labordere (2012) and then generalize it to the non-Markovian case for a class of Backward SDEs (BSDEs). By simulating the branching process, the algorithm does not need any backward regression. To prove that the numerical algorithm converges to the solution of BSDEs, we use the notion of viscosity solution of path dependent PDEs introduced by Ekren et al. (to appear) [5] and extended in Ekren et al. (2012) [6,7]. (C) 2013 Elsevier B.V. All rights reserved.

关键词： numerical algorithm BSDEs Branching process Viscosity solution Path dependent PDEs

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High accuracy analysis of three-dimensional axisymmetric nonlinear boundary integral equations☆

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ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS 2025年 176卷

作者： Li, Hu Huang, Jin Chengdu Normal Univ Sch Math Chengdu 611130 Peoples R China Univ Elect Sci & Technol China Sch Math Sci Chengdu 611731 Peoples R China

In this paper, we consider the numerical solutions of three-dimensional axisymmetric nonlinear boundary integral equations with logarithmic kernel. A numerical algorithm with using extrapolation twice is developed to solve the equations, which possesses the low computing complexities and high accuracy. The asymptotic compact operator theory is used to prove the convergence of the algorithm. The efficiency of the algorithm is illustrated by numerical examples.

关键词： numerical algorithm Quadratic extrapolation Axisymmetric nonlinear boundary integral equations

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