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Integration of nanoindentation and Finite element method for interpretable tensile properties:A crossscale calculation method of uneven joints

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Chinese Journal of Aeronautics 2023年第6期36卷 233-248页

作者： Kun GAO Zhiying LIU Xiuli SHEN Lizhong LANG Shaojing DONG School of Energy and Power Engineering Beihang UniversityBeijing100191China Department of Materials Science and Engineering University of TorontoTorontoON M5S 3E4Canada

Nanoindentation testing and its Reverse Analysis method(RAM)show great potential in understanding the tensile properties of metallic alloys with various microstructures.Nevertheless,the tensile properties of heterogeneous materials such as nickel-based superalloy welded joints have not been well interpreted by combining the microstructures and nanoindentation results,due to their diverse and complex microscopic zones,which throws shade on the properties of separated zones in the material.Here we demonstrated a new method of implanting nanoindentation results into Finite element method(FEM)and applied the method to the welded joints with the zones of various microstructure features.The local properties are calculated by the nanoindentation data using RAM,and used as input of finite element(FE)simulation of an identical indentation process,to in turn verify the accuracy and reliability of the reverse model.The simulation results reveal that the global mechanical behaviors,such as Young's modulus,yield strength and strain hardening exponent,are related to the local properties to a great extent.Thus,the global properties can be verified by simulation straight after experiments,taking consideration of local properties and dimension parameters of different zones.It is shown that the maximum error between calculation of RAM and testing is within 5.1%in different zones,and the errors of maximum indentation depth and residual depth obtained by FE simulation are less than 2.4%,which indicates that the method provides a reliable prediction of mechanical properties of superalloy welded joints.

关键词： Finite element method Nanoindentation Reverse analysis method Tensile properties Welded joints

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A Peridynamics-Based Finite element method(PeriFEM)for Quasi-Static Fracture Analysis

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Acta Mechanica Solida Sinica 2022年第3期35卷 446-460页

作者： Fei Han Zhibin Li State Key Laboratory of Structural Analysis for Industrial Equipment Department of Engineering MechanicsDalian University of TechnologyDalian 116023China

In this paper,a peridynamics-based Finite element method(PeriFEM)is proposed for the quasi-static fracture analysis,which is of the consistent computational framework with the classical Finite element method(FEM).First,the integral domain of peridynamics is reconstructed,and a new type of element called peridynamic element(PE)is defined.Although PEs are generated by the continuous elements(CEs)of classical FEM,they do not affect each other.Then,spatial discretization is performed based on PEs and CEs,and the linear equations about nodal displacement are established according to the principle of minimum potential energy.Besides,cracks are characterized as degradation of the mechanical properties of PEs.Finally,the validity of the proposed method is demonstrated through numerical examples.

关键词： Peridynamics Finite element method Fracture Damage

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Time-domain Finite element method for Transient Electric Field and Transient Charge Density on Dielectric Interface

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CSEE Journal of Power and Energy Systems 2022年第1期8卷 143-154页

作者： Teng Wen Xiang Cui Xuebao Li Hao Ma Zhibin Zhao State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources North China Electric Power UniversityBeijing 102206China

This paper is devoted to solving the transient electric field and transient charge density on the dielectric interface under the electroquasistatic(EQS)field conditions with high accuracy.The proposed method is suitable for both 2-D and 3-D applications.Firstly,the governing equations represented by scalar electric potential are discretized by the nodal Finite element method(FEM)in space and the finite difference method in time.Secondly,the transient constrained electric field equation on the boundary(TCEFEB)is derived to calculate the normal component of the transient electric field intensities on the Dirichlet boundary and dielectric interface as well as the transient charge density on the dielectric interface.Finally,a 2-D numerical example is employed to demonstrate the validity of the proposed method.Furthermore,the comparisons of the numerical accuracy of the proposed method in this paper with the existing FEMs for electric field intensity and charge density on the dielectric interface are conducted.The results show that the numerical accuracy of the proposed method for calculating the normal component of transient electric field intensities on the Dirichlet boundary and dielectric interface as well as the transient charge density on the dielectric interface is close to that of nodal electric potential and an order of magnitude higher than those of existing FEMs.

关键词： Electroquasistatic field composite insulation structure transient constrained electric field equation on the boundary Finite element method interface charge time-domain

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UNCONDITIONALLY OPTIMAL ERROR ANALYSIS OF THE SECOND-ORDER BDF Finite element method FOR THE KURAMOTO-TSUZUKI EQUATION

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Journal of Computational Mathematics 2023年第2期41卷 211-223页

作者： Yuan Li Xuewei Cui College of Mathematics and Physics Wenzhou UniversityWenzhou 325035China

This paper aims to study a second-order semi-implicit BDF finite element scheme for the Kuramoto-Tsuzuki equations in two dimensional and three dimensional spaces.The proposed scheme is stable and the nonlinear term is linearized by the extrapolation technique.Moreover,we prove that the error estimate in L^(2)-norm is unconditionally optimal which means that there has not any restriction on the time step and the mesh size.Finally,numerical results are displayed to illustrate our theoretical analysis.

关键词： Kuramoto-Tsuzuki equations BDF scheme Finite element method Optimal error analysi

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Convergence of Weak Galerkin Finite element method for Second Order Linear Wave Equation in Heterogeneous Media

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Numerical Mathematics(Theory,methods and Applications) 2023年第2期16卷 323-347页

作者： Bhupen Deka Papri Roy Naresh Kumar Raman Kumar Department of Mathematics Indian Institute of Technology GuwahatiGuwahati 781039India

Weak Galerkin Finite element method is introduced for solving wave equation with interface on weak Galerkin finite element space(Pk(K),P_(k−1)(∂K),[P_(k−1)(K)]^(2)).Optimal order a priori error estimates for both space-discrete scheme and implicit fully discrete scheme are derived in L1(L2)norm.This method uses totally discontinuous functions in approximation space and allows the usage of finite element partitions consisting of general polygonal meshes.finite element algorithm presented here can contribute to a variety of hyperbolic problems where physical domain consists of heterogeneous media.

关键词： Wave equation heterogeneous medium Finite element method weak Galerkin method semidiscrete and fully discrete schemes optimal error estimates

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ANALYSIS OF A FULLY DISCRETE Finite element method FOR PARABOLIC INTERFACE PROBLEMS WITH NONSMOOTH INITIAL DATA

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Journal of Computational Mathematics 2022年第5期40卷 777-793页

作者： Kai Wang Na Wang Department of Mathematics Southern University of Science and TechnologyShenzhen 518005China Applied and Computational Mathematics Division Beijing Computational Science Research CenterBeijing 100193China

This article concerns numerical approximation of a parabolic interface problem with general L 2 initial value.The problem is discretized by a Finite element method with a quasi-uniform triangulation of the domain fitting the interface,with piecewise linear approximation to the interface.The semi-discrete finite element problem is furthermore discretized in time by the k-step backward difference formula with k=1,...,6.To maintain high-order convergence in time for possibly nonsmooth L 2 initial value,we modify the standard backward difference formula at the first k−1 time levels by using a method recently developed for fractional evolution equations.An error bound of O(t−k nτk+t−1 n h 2|log h|)is established for the fully discrete Finite element method for general L 2 initial data.

关键词： Parabolic interface problem Finite element method Backward difference formulae Error estimate Nonsmooth initial data.

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Error estimates of a Finite element method for stochastic time-fractional evolution equations with fractional Brownian motion

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International Journal of Modeling, Simulation, and Scientific Computing 2022年第1期13卷 192-213页

作者： Jingyun Lv Key Laboratory of Systems and Control Institute of Systems Science Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 P.R.China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing 100049 P.R.China

The aim of this paper is to consider the convergence of the numerical methods for stochastic time-fractional evolution equations driven by fractional Brownian motion.The spatial and temporal regularity of the mild solution is given.The numerical scheme approximates the problem in space by the Galerkin Finite element method and in time by the backward Euler convolution quadrature formula,and the noise by the L 2-projection.The strong convergence error estimates for both semi-discrete and fully discrete schemes are established.A numerical example is presented to verify our theoretical analysis.

关键词： Stochastic time-fractional evolution equations Finite element method error estimates fractional Brownian motion

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A SECOND ORDER UNCONDITIONALLY CONVERGENT Finite element method FOR THE THERMAL EQUATION WITH JOULE HEATING PROBLEM

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Journal of Computational Mathematics 2022年第3期40卷 354-372页

作者： Xiaonian Long Qianqian Ding College of Mathematics and Information Science Henan University of Economics and LawZhengzhou 450045China School of Mathematics Shandong UniversityJinan 250100China

In this paper,we study the finite element approximation for nonlinear thermal equation.Because the nonlinearity of the equation,our theoretical analysis is based on the error of temporal and spatial discretization.We consider a fully discrete second order backward difference formula based on a Finite element method to approximate the temperature and electric potential,and establish optimal L^(2) error estimates for the fully discrete finite element solution without any restriction on the time-step size.The discrete solution is bounded in infinite norm.Finally,several numerical examples are presented to demonstrate the accuracy and efficiency of the proposed method.

关键词： Thermal equation Joule heating Finite element method Unconditional convergence Second order backward difference formula Optimal L^(2)-estimate

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SAV Finite element method for the Peng-Robinson Equation of State with Dynamic Boundary Conditions

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Advances in Applied Mathematics and Mechanics 2023年第1期15卷 139-158页

作者： Changhui Yao Zhaoyue Du Lei Yang School of Mathematics and Statistics Zhengzhou UniversityZhengzhouHenan 450001China Faculty of Information Technology Macao University of Science and TechnologyMacao

In this paper,the Peng-Robinson equation of state with dynamic boundary conditions is discussed,which considers the interactions with solid walls.At first,the model is introduced and the regularization method on the nonlinear term is adopted.Next,The scalar auxiliary variable(SAV)method in temporal and Finite element method in spatial are used to handle the Peng-Robinson equation of state.Then,the energy dissipation law of the numerical method is obtained.Also,we acquire the convergence of the discrete SAV Finite element method(FEM).Finally,a numerical example is provided to confirm the theoretical result.

关键词： Peng-Robinson equation of state dynamic boundary conditions scalar auxiliary variable Finite element method error estimates

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A Conservative SAV-RRK Finite element method for the Nonlinear Schrodinger Equation

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Advances in Applied Mathematics and Mechanics 2023年第3期15卷 583-601页

作者： Jun Yang Nianyu Yi School of Mathematics and Computational Science Xiangtan UniversityXiangtanHunan 411105China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan UniversityXiangtanHunan 411105China

Abstract.In this paper,we propose,analyze and numerically validate a conservative Finite element method for the nonlinear Schrodinger equation.A scalar auxiliary variable(SAV)is introduced to reformulate the nonlinear Schrodinger equation into an equivalent system and to transform the energy into a quadratic form.We use the standard continuous Finite element method for the spatial discretization,and the relaxation Runge-Kutta method for the time discretization.Both mass and energy conservation laws are shown for the semi-discrete finite element scheme,and also preserved for the full-discrete scheme with suitable relaxation coefficient in the relaxation Runge-Kutta method.Numerical examples are presented to demonstrate the accuracy of the proposed method,and the conservation of mass and energy in long time simulations.

关键词： Schrodinger equation mass conservation energy conservation Finite element method relaxation Runge-Kutta scalar auxiliary variable

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