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Isogeometric analysis for free vibration of bidirectional functionally graded plates in the fluid medium

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Defence Technology（防务技术） 2022年第8期18卷 1311-1329页

作者： Quoc-Hoa Pham Phu-Cuong Nguyen Van Ke Tran Trung Nguyen-Thoi Faculty of Civil Engineering Ho Chi Minh City Open UniversityHo Chi Minh CityViet Nam Faculty of Mechanical Engineering Le Quy Don Technical UniversityHanoiViet Nam division of computational Mathematics and Engineering Institute for Computational ScienceTon Duc Thang UniversityHo Chi Minh CityViet Nam Faculty of Civil Engineering Ton Duc Thang UniversityHo Chi Minh CityViet Nam

This paper for first time proposes an isogeometric analysis (IGA) for free vibration response of bi-directional functionally graded (BDFG) rectangular plates in the fluid medium. Material properties of the BDFG plate change in both the thickness and length directions via power-law distributions and Mori-Tanaka model. The governing equation of motion of BDFG plate in the fluid-plate system is formulated basing on Hamilton's principle and the refined quasi three-dimensional (3D) plate theory with improved function f(z). The fluid velocity potential is derived from the boundary conditions of the fluid-plate system and is used to determine the added mass. The discrete system of equations is derived from the Galerkin weak form and numerically analyzed by IGA. The accuracy and reliability of the proposed solutions are verified by comparing the obtained results with those published in the literature. Moreover, the effects of the various parameters such as the interaction boundary condition, geometric parameter, submerged depth of plate, fluid density, fluid level, and the material volume control coefficients on the free vibration behavior of BDFG plate in the fluid medium are investigated in detail. Some major findings regarding the numerical results are withdrawn in conclusions.

关键词： Contact plate-fluid Refined quasi 3D plate theory Mori-Tanaka model Isogeometric analysis Bidirectional functionally graded plate

Existence of Canards under Non-generic Conditions

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Chinese Annals of Mathematics,Series B 2009年第3期30卷 239-250页

作者： Feng XIE Maoan HAN Department of Applied Mathematics Donghua University Shanghai 201620 China division of computational Science E-Institute of Shanghai Universities Shanghai Jiao Tong University Shanghai 200030China Department of Mathematics Shanghai Normal University Shanghai 200234 China

The canard phenomenon occurring in planar fast-slow systems under non-generic conditions is *** the critical manifold has a non-generic fold point,by using the method of asymptotic analysis combined with the recently developed blow-up technique,the existence of a canard is established and the asymptotic expansion of the parameter for which a canard exists is obtained.

关键词： Canard Slow manifold Singular perturbation Blow-up Non-genericcondition

Machine-learned interatomic potentials by active learning:amorphous and liquid hafnium dioxide

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npj computational Materials 2020年第1期6卷 803-810页

作者： Ganesh Sivaraman Anand Narayanan Krishnamoorthy Matthias Baur Christian Holm Marius Stan Gábor Csányi Chris Benmore Álvaro Vázquez-Mayagoitia Leadership Computing Facility Argonne National LaboratoryArgonneIL 60439USA Institute for computational Physics Universität StuttgartAllmandring 3Stuttgart 70569Germany Helmholtz-Institute Münster:Ionics in Energy Storage(IEK-12) Forschungszentrum Jülich GmbHCorrensstrasse 46Münster 48149Germany Applied Materials division Argonne National LaboratoryArgonneIL 60439USA Department of Engineering University of CambridgeTrumpington StreetCambridge CB21PZUK X-ray Science division Argonne National LaboratoryArgonneIL 60439USA computational Science division Argonne National LaboratoryArgonneIL 60439USA

We propose an active learning scheme for automatically sampling a minimum number of uncorrelated configurations for fitting the Gaussian Approximation Potential(GAP).Our active learning scheme consists of an unsupervised machine learning(ML)scheme coupled with a Bayesian optimization technique that evaluates the GAP *** apply this scheme to a Hafnium dioxide(HfO2)dataset generated from a“melt-quench”ab initio molecular dynamics(AIMD)*** results show that the active learning scheme,with no prior knowledge of the dataset,is able to extract a configuration that reaches the required energy fit ***,molecular dynamics(MD)simulations performed using this active learned GAP model on 6144 atom systems of amorphous and liquid state elucidate the structural properties of HfO2 with near ab initio precision and quench rates(i.e.,1.0 K/ps)not accessible via *** melt and amorphous X-ray structural factors generated from our simulation are in good agreement with *** addition,the calculated diffusion constants are in good agreement with previous ab initio studies.

关键词： amorphous dioxide scheme

Isogeometric cohesive zone model for thin shell delamination analysis based on Kirchhoff-Love shell model

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Frontiers of Structural and Civil Engineering 2020年第2期14卷 267-279页

作者： Tran Quoc THAI Timon RABCZUK Xiaoying ZHUANG Institute o f Continuum Mechanics Leibniz University of HannoverHannover 30167Germany division of computational Mechanics Ton Due Thang UniversityHo Chi Minh CityVietnam Faculty of Civil Engineering Ton Due Thang UniversityHo Chi Minh CityVietnam

We present a cohesive zone model for delamination in thin shells and composite *** isogeometric(IGA)thin shell model is based on Kirchhoff-Love ***-Uniform Rational B-Splines(NURBS)are used to discretize the exact mid-surface of the shell geometry exploiting their C 1-continuity property which avoids rotational degrees of *** fracture process zone is modeled by interface elements with a cohesive *** numerical examples are presented to test and validate the proposed formulation in predicting the delamination behavior of composite structures.

关键词： cohesive zone model IGA Kirchhoff-Love model thin shell analysis delamination

SINGULARLY PERTURBED SOLUTION TO SEMILINEAR HIGHER ORDER REACTION DIFFUSION EQUATIONS WITH TWO PARAMETERS

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Annals of Differential Equations 2009年第1期25卷 91-96页

作者： Yao Jingsun, Mo Jiaqi (Dept. of Math., Anhui Normal University, Wuhu 241000, Anhui division of computational Science, E-Institutes of Shanghai Universities, at SJTU, Shanghai 200240) division of computational Science E-Institutes of Shanghai Universitiesat SJTU Shanghai 200240

A boundary value problem for semilinear higher order reaction diffusion equa-tions with two parameters is considered. Under suitable conditions, by the theory of differential inequalities, the existence and asymptotic... 详细信息

关键词： semilinear two parameters asymptotic solution singular perturba-tion

A Sample-Wise Data Driven Control Solver for the Stochastic Optimal Control Problem with Unknown Model Parameters

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Communications in computational Physics 2023年第4期33卷 1132-1163页

作者： Richard Archibald Feng Bao Jiongmin Yong computational Science and Mathematics division Oak Ridge National LaboratoryOak RidgeTennesseeUSA Department of Mathematics Florida State UniversityTallahasseeFloridaUSA Department of Mathematics University of Central FloridaOrlandoFloridaUSA

In this work,an efficient sample-wise data driven control solver will be developed to solve the stochastic optimal control problem with unknown model parameters.A direct filter method will be applied as an online parameter estimation method that dynamically estimates the target model parameters upon receiving the data,and a sample-wise optimal control solver will be provided to efficiently search for the optimal ***,an effective overarching algorithm will be introduced to combine the parameter estimator and the optimal control *** experiments will be carried out to demonstrate the effectiveness and the efficiency of the sample-wise data driven control method.

关键词： Stochastic optimal control parameter estimation optimal filter backward stochastic differential equations stochastic gradient descent

BOUNDARY PROCEDURES FOR THE TIME-DEPENDENT BURGERS' EQUATION UNDER UNCERTAINTY

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Acta Mathematica Scientia 2010年第2期30卷 539-550页

作者： Per Pettersson Jan Nordstrm Gianluca Iaccarino Mechanical Engineering and Institute for computational Mathematical Engineering Stanford University division of Scientific Computing Department of Information TechnologyUppsala University School of Mechanical Industrial and Aeronautical EngineeringUniversity of the Witvatersrand Department of Aeronautics and Systems Integration FOIThe Swedish Defense Research Agency

The Burgers＇ equation with uncertain initial and boundary conditions is approximated using a Polynomial Chaos Expansion （PCE） approach where the solution is represented as a series of stochastic, orthogonal polynomials. The resulting truncated PCE system is solved using a novel numerical discretization method based on spatial derivative operators satisfying the summation by parts property and weak boundary conditions to ensure stability. The resulting PCE solution yields an accurate quantitative description of the stochastic evolution of the system, provided that appropriate boundary conditions are available. The specification of the boundary data is shown to influence the solution; we will discuss the problematic implications of the lack of precisely characterized boundary data and possible ways of imposing stable and accurate boundary conditions.

关键词： stochastic Burgers' equation uncertainty quantification polynomial chaos

SPECTRAL AND SPECTRAL ELEMENT METHODS FOR HIGH ORDER PROBLEMS WITH MIXED BOUNDARY CONDITIONS

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Journal of computational Mathematics 2014年第4期32卷 392-411页

作者： Benyu Guo Chao Zhang Department of Mathematics Shanghai Normal University Shanghai 200234 China Scientific Computing Key Laboratory of Shanghai Universities Division of Computational Science of E-institute of Shanghai Universities Shanghai 200234 China Department of Mathematics Jiangsu Normal University Xuzhou 221116 China

In this paper, we investigate numerical methods for high order differential equations. We propose new spectral and spectral element methods for high order problems with mixed inhomogeneous boundary conditions, and prove their spectral accuracy by using the recent results on the Jacobi quasi-orthogonal approximation. Numerical results demonstrate the high accuracy of suggested algorithm, which also works well even for oscillating solutions.

关键词： Spectral and spectral element methods~ High order problems with mixedinhomogeneous boundary conditions.

A NEW PSEUDOSPECTRAL METHOD ON QUADRILATERALS

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Journal of computational Mathematics 2016年第4期34卷 365-384页

作者： Benyu Guo Hongli Jia Shanghai Normal University 200234 Shanghai P.R. China Scientific Computing Key Laboratory of Shanghai Universities division of computational Science of E-institute of Shanghai Universities Department of Mathematics Donghua University 200065 Shanghai P.R. China

In this paper, we investigate a new pseudospectral method for mixed boundary value problems defined on quadrilaterals. We introduce a new Legendre-Gauss type interpolation and establish the basic approximation results, which play important roles in pseudospectral method for partial differential equations defined on quadrilaterals. We propose pseudospee- tral method for two model problems and prove their spectral accuracy. Numerical results demonstrate their high efficiency. The approximation results developed in this paper are also applicable to other problems defined on complex domains.

关键词： Legendre-Gauss type interpolation on quadrilaterals Pseudospectral methodof mixed boundary value problems.