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Development of a Three-Dimensional Multiscale Octree SBFEM for Viscoelastic Problems of Heterogeneous Materials

Computer Modeling in Engineering & Sciences 2024年第8期140卷 1831-1861页

作者： Xu Xu Xiaoteng Wang Haitian Yang Zhenjun Yang Yiqian He State Key Laboratory of Structural Analysis Optimization and CAE Software for Industrial EquipmentDepartment of Engineering MechanicsDalian University of TechnologyDalian116024China Hubei Key Laboratory of Geotechnical and Structural Safety School of Civil EngineeringWuhan UniversityWuhan430072China Mechanik–Materialtheorie Ruhr-Universität BochumBochum44801Germany

The multiscale method provides an effective approach for the numerical analysis of heterogeneous viscoelastic materials by reducing the degree of freedoms(DOFs).A basic framework of the Multiscale Scaled Boundary Finite Element Method(MsSBFEM)was presented in our previous works,but those works only addressed two-dimensional *** order to solve more realistic problems,a three-dimensional MsSBFEM is further developed in this *** the proposed method,the octree SBFEM is used to deal with the three-dimensional calculation for numerical base functions to bridge small and large scales,the three-dimensional image-based analysis can be conveniently conducted in small-scale and coarse nodes can be flexibly adjusted to improve the computational ***,the Temporally Piecewise Adaptive Algorithm(TPAA)is used to maintain the computational accuracy of multiscale analysis by adaptive calculation in time *** results of numerical examples show that the proposed method can significantly reduce the DOFs for three-dimensional viscoelastic analysis with good *** instance,the DOFs can be reduced by 9021 times compared with Direct numerical Simulation(DNS)with an average error of 1.87%in the third example,and it is very effective in dealing with three-dimensional complex microstructures directly based on images without any geometric modelling process.

关键词： Three-dimensionalmultiscale viscoelastic analysis numerical base functions octree SBFEM image-based analysis temporally piecewise adaptive algorithm

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A multiscale scaled boundary finite element method solving steady-state heat conduction problem with heterogeneous materials

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numerical HEAT TRANSFER PART B-FUNDAMENTALS 2023年第6期83卷 345-366页

作者： Wang, Xiaoteng Yang, Haitian He, Yiqian Dalian Univ Technol Dept Engn Mech State Key Lab Struct Anal Ind Equipment Dalian 116024 Peoples R China

A new numerical model is proposed by bridging small and large scales via the numerical base functions constructed by Scaled Boundary Finite Element Method (SBFEM) for the multiscale heterogeneous analysis of steady-state heat conduction problems. Utilizing the advantages of polygonal Scaled Boundary Finite Element (SBFE) and image-based quadtree gridding, the construction of base functions can be conveniently and efficiently conducted particularly for the heterogeneous media with complex geometries or singularity of heat flux at the small-scale, and the solution accuracy at the large-scale can be improved by increasing nodes of coarse element only without increasing new nodes inside. Consequently, the SBFEM based solutions at the large-scale can be solved with a reduced order and sufficient accuracy, and the solutions at the small-scale can be achieved using SBFEM based base functions. numerical examples are provided and the effectiveness of the proposed approach is stressed at both the large and small scales.

关键词： Heterogeneous materials multiscale analysis numerical base functions SBFEM steady-state heat conduction

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Multiscale Finite Element Method for Coupling Analysis of Heterogeneous Magneto-Electro-Elastic Structures in Thermal Environment

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Journal of Applied Mathematics and Physics 2024年第9期12卷 3099-3113页

作者： Xinyue Li Xiaolin Li Hangran Yang College of Construction Engineering Jilin University Changchun China

Magneto-electro-elastic (MEE) materials, a new type of composite intelligent materials, exhibit excellent multifield coupling effects. Due to the heterogeneity of the materials, it is challenging to use the traditional finite element method (FEM) for mechanical analysis. Additionally, the MEE materials are often in a complex service environment, especially under the influence of the thermal field with thermoelectric and thermomagnetic effects, which affect its mechanical properties. Therefore, this paper proposes the efficient multiscale computational method for the multifield coupling problem of heterogeneous MEE structures under the thermal environment. The method constructs a multi-physics field with numerical base functions (the displacement, electric potential, and magnetic potential multiscale base functions). It equates a single cell of heterogeneous MEE materials to a macroscopic unit and supplements the macroscopic model with a microscopic model. This allows the problem to be solved directly on a macroscopic scale. Finally, the numerical simulation results demonstrate that compared with the traditional FEM, the multiscale finite element method (MsFEM) can achieve the purpose of ensuring accuracy and reducing the degree of freedom, and significantly improving the calculation efficiency.

关键词： Multiscale Finite Element Method Magneto-Electro-Elastic Multifield Coupling numerical base functions

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MULTISCALE FINITE ELEMENT METHOD FOR A HIGHLY EFFICIENT COUPLING ANALYSIS OF HETEROGENEOUS MAGNETO-ELECTRO-ELASTIC MEDIA

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INTERNATIONAL JOURNAL FOR MULTISCALE COMPUTATIONAL ENGINEERING 2018年第1期16卷 77-100页

作者： Fu, Ping Liu, Hui Chu, Xihua Qu, Wenzhong Wuhan Univ Sch Civil Engn Dept Engn Mech Wuhan 430072 Hubei Peoples R China Yangtze River Sci Res Inst Key Lab Geotech Mech & Engn Minist Water Resource Wuhan 430010 Hubei Peoples R China

In this paper, an efficient multiscale computational method is presented for the coupling field analysis of heterogeneous magneto-electro-elastic media. In this method, the displacement, electric, and magnetic potential multiscale base functions that contain the coupling effects between different physical fields are firstly constructed. By virtue of these numerical base functions, the effective material properties of the heterogeneous media could be reflected to the macroscopic scale. Thus, a single heterogeneous magneto-electro-elastic unit cell can be equivalent into a coarse element and the original multiphysics coupling boundary value problem could be solved on the macroscopic scale directly, which will save a significant amount of computing time and resources. According to the macroscopic solutions, the microscopic mechanical, electrical, and magnetic responses can be further recovered by downscaling computation using the above constructed multiscale base functions. Finally, several numerical examples are carried out to illustrate the effectiveness and correctness of the proposed multiscale method. The comparison between the present results on the macroscopic coarse-scale mesh and those calculated by the standard FEM on the microscopic fine -scale mesh indicates that the proposed multiscale method not only can provide accurate coupling responses of heterogeneous electro-magneto-elastic media but also has high computational efficiency.

关键词： multiscale finite element method electro-magneto-mechanical coupling analysis heterogeneity numerical base functions

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A coupling extended multiscale finite element method for dynamic analysis of heterogeneous saturated porous media

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INTERNATIONAL JOURNAL FOR numerical METHODS IN ENGINEERING 2015年第1期104卷 18-47页

作者： Li, Hui Zhang, Hongwu Zheng, Yonggang Dalian Univ Technol Fac Vehicle Engn & Mech Dept Engn Mech State Key Lab Struct Anal Ind Equipment Dalian 116024 Peoples R China

A coupling extended multiscale finite element method (CEMsFEM) is developed for the dynamic analysis of heterogeneous saturated porous media. The coupling numerical base functions are constructed by a unified method with an equivalent stiffness matrix. To improve the computational accuracy, an additional coupling term that could reflect the interaction of the deformations among different directions is introduced into the numerical base functions. In addition, a kind of multi-node coarse element is adopted to describe the complex high-order deformation on the boundary of the coarse element for the two-dimensional dynamic problem. The coarse element tests show that the coupling numerical base functions could not only take account of the interaction of the solid skeleton and the pore fluid but also consider the effect of the inertial force in the dynamic problems. On the other hand, based on the static balance condition of the coarse element, an improved downscaling technique is proposed to directly obtain the satisfying microscopic solutions in the CEMsFEM. Both one-dimensional and two-dimensional numerical examples of the heterogeneous saturated porous media are carried out, and the results verify the validity and the efficiency of the CEMsFEM by comparing with the conventional finite element method. Copyright (c) 2015 John Wiley & Sons, Ltd.

关键词： heterogeneous saturated porous media extended multiscale finite element method numerical base functions multi-node coarse element improved downscaling technique dynamic problem

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A MULTISCALE COMPUTATIONAL METHOD FOR 2D ELASTOPLASTIC DYNAMIC ANALYSIS OF HETEROGENEOUS MATERIALS

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INTERNATIONAL JOURNAL FOR MULTISCALE COMPUTATIONAL ENGINEERING 2014年第2期12卷 127-154页

作者： Zhang, Hongwu Liu, Hui Dalian Univ Technol Fac Vehicle Engn & Mech Dept Engn Mech State Key Lab Struct Anal Ind Equipment Dalian 116024 Peoples R China

The elastoplastic dynamic analysis of heterogeneous materials is studied based on the multiscale computational method developed in our previous work (Zhang et al., 2013). The basic principles of this method are introduced briefly. To describe the complex deformation, a 2D multinode coarse element is proposed. In addition, to improve the computational accuracy for the dynamic problems, mode base functions are introduced into the multiscale numerical base functions to consider the dynamic effect of the structure. For nonlinear elastic or elastoplastic dynamic problems, the microscopic unbalanced nodal force cannot be projected to the macroscopic level effectively only by the displacement and mode base functions when the nonlinear material deformation occurs during the computation. So a correction technique of the local displacement is applied to deal with the unprojected microscopic unbalance forces within the coarse element. Furthermore, the computational procedures of a two-scale modeling are proposed within the framework of nonlinear dynamic analysis. Extensive numerical experiments are carried out and the results are compared with the traditional finite element method (FEM) which is applied directly on the fine-scale mesh. It is shown that the proposed multiscale method can obtain excellent precision of the nonlinear dynamic response of the elastoplastic heterogeneous materials. Moreover, the computation comparisons indicate that the proposed method spends less computer memory and CPU time than the traditional FEM.

关键词： multiscale computational method heterogeneous material elastoplastic dynamic analysis numerical base functions

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Multiscale nonlinear thermoelastic analysis of heterogeneous multiphase materials with temperature-dependent properties

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FINITE ELEMENTS IN ANALYSIS AND DESIGN 2014年 88卷 97-117页

作者： Zhang, H. W. Yang, D. S. Zhang, S. Zheng, Y. G. Dalian Univ Technol Fac Vehicle Engn & Mech Dept Engn Mech State Key Lab Struct Anal Ind Equipment Dalian 116024 Peoples R China

A pre-correction multiscale strategy is developed for the nonlinear thermoelastic analysis of heterogeneous multiphase materials with temperature-dependent properties. In this strategy, based on the multiscale finite element formulation, the numerical base functions (NBFs) are constructed in order to bring the microscopic heterogeneous properties to the macroscopic response. By constructing the microscopic perturbed pre-correction the inaccuracy of the NBFs due to the temperature-dependent properties is better considered, as well as the influence of the microscopic loads. Then the pre-correction multiscale strategy is implemented for the nonlinear heat conduction and thermoelastic analysis. Finally several representative numerical examples are presented and the results indicate that the proposed strategy is efficient and accurate for modeling heterogeneous multiphase materials. (C) 2014 Elsevier B.V. All rights reserved.

关键词： Nonlinear thermoelastic analysis Heterogeneous multiphase material Pre-correction multiscale strategy numerical base functions

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A uniform multiscale method for 3D static and dynamic analyses of heterogeneous materials

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COMPUTATIONAL MATERIALS SCIENCE 2013年 79卷 159-173页

作者： Liu, H. Zhang, H. W. Dalian Univ Technol Dept Engn Mech Fac Vehicle Engn & Mech State Key Lab Struct Anal Ind Equipment Dalian 116024 Peoples R China

In this paper, a uniform multiscale method is developed for 3D static and dynamic analyses of heterogeneous materials based on our previous work (H. W. Zhang, H. Liu, J.K. Wu, International Journal for numerical Methods in Engineering 93 (2013) 714-746). A new 3D multi-node coarse element is provided to simulate the complex deformation and the approach is elaborated to construct the displacement base functions numerically. For the dynamic problems, to consider the effect of the interior forces of the structure, the mode base functions are introduced for improving the computational accuracy. In addition, the orthogonality between the displacement and mode base functions indicates that this proposed multiscale method can be used for the static and dynamic analyses uniformly. Finally, several typical numerical examples are carried out to verify the validity and high efficiency of this multiscale method by comparison with the reference solutions. (C) 2013 Elsevier B. V. All rights reserved.

关键词： Multiscale computational method Dynamic analysis numerical base functions Heterogeneous materials

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