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Applied Mathematics and Mechanics(English Edition) 2023年第1期44卷 53-72页

作者： Zheng GONG Yinxiao ZHANG Ernian pan Chao ZHANG School of Aeronautics Northwestern Polytechnical UniversityXi'an 710072China Joint International Research Laboratory of Impact Dynamics and Its Engineering Applications Xi'an 710072China Civil Engineering and Institute of Pioneer Semiconductor Innovation Yang Ming Chiao Tung UniversityHsinchu 30010TaiwanChina School of Civil Aviation Northwestern Polytechnical UniversityXi'an 710072China

In this paper,by defining a general potential energy for the multiphase coupled multiferroics and applying the minimum energy principle,the coupled governing equations are derived.This system of equations is then discretized as a general three-dimensional(3D)finite element(FE)model based on the COMSOL software.After validating the formulation,it is then applied to the analysis and design of the common sandwich structure of multiferroics composites.Under the typical static loading,the effects of general lateral boundary conditions,material grading,nonlinearity,as well as polarization orientation on the composites are analyzed.For the magneto-electro-elastic(MEE)sandwich made of piezoelectric BaTiO_(3)and magnetostrictive CoFe_(2)O_(4)with different stacking sequences,various interesting features are observed which should be very helpful for the design of high-performance multiphase composites.

关键词： multiferroics sandwich composite magneto-electro-elastic(MEE)material multilayered plate nonlinear behavior

A Three-Dimensional Size-Dependent Layered Model for Simply-Supported and Functionally Graded Magnetoelectroelastic Plates

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Acta Mechanica Solida Sinica 2018年第5期31卷 652-671页

作者： Junhong Guo Jiangyi Chen Ernian pan Department of Mechanics Inner Mongolia University of Technology Hohhot 010051 China School of Mechanical Engineering Zhengzhou University Zhengzhou 450001 China Department of Civil Engineering and Department of Mathematics The University of Akron Akron OH 44325-3905 USA

A three-dimensional size-dependent layered model for simply-supported and func- tionally graded magnetoelectroelastic plates is presented based on the modified couple-stress theory. The functionally graded material is assumed to be exponential in the thickness direc- tion of the plate. The final governing equations are reduced to an eigensystem by expressing the extended displacements in terms of two-dimensional Fourier series. Using the propagator matrix method, the exact solutions of the magnetic, electric and mechanical fields of sandwich nanoplates with couple-stress effect and under the surface loads are derived. Numerical examples for two functionally graded sandwich plates made of piezoelectric BaTiO3 and magnetostrictive CoFe2O4 materials are presented to demonstrate the effect of the functional gradient factor and material length-scale parameter on the induced fields. The exact solutions presented in this work can also serve as benchmarks to various numerical methods for analyzing the size-dependent features in layered systems.

关键词： Functionally graded Magnetoelectroelastic Modified couple stress Layered plate Three-dimensional solution

General solutions of plane problem in one-dimensional quasicrystal piezoelectric materials and its application on fracture mechanics

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Applied Mathematics and Mechanics(English Edition) 2015年第6期36卷 793-814页

作者： Jing YU Junhong GUO Ernian pan Yongming XING School of Science Inner Mongolia University of Technology College of General Education Inner Mongolia Normal University Department of Civil Engineering University of Akron

Based on the fundamental equations of piezoelasticity of quasicrystals （QCs）, with the symmetry operations of point groups, the plane piezoelasticity theory of one- dimensional （1D） QCs with all point groups is investigated systematically. The gov- erning equations of the piezoelasticity problem for 1D QCs including monoclinic QCs, orthorhombic QCs, tetragonal QCs, and hexagonal QCs are deduced rigorously. The general solutions of the piezoelasticity problem for these QCs are derived by the opera- tor method and the complex variable function method. As an application, an antiplane crack problem is further considered by the semi-inverse method, and the closed-form so- lutions of the phonon, phason, and electric fields near the crack tip are obtained. The path-independent integral derived from the conservation integral equals the energy release rate.

关键词： quasicrystals （QCs） piezoelasticity fracture mechanics crack complexvariable method

TRANSIENT RESPONSE OF A BI-LAYERED MULTIFERROIC COMPOSITE PLATE

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Acta Mechanica Solida Sinica 2011年第1期24卷 83-91页

作者： Ruifeng Wang Qingkai Han Ernian pan Computer Modeling and Simulation Group College of Engineering University of Akron Akron Ohio 44325-3905 USA School of Mechanical Engineering and Automation Northeastern University Shenyang 110004 China

In this paper, a three-dimensional finite-element formulation for the multiferroic composite is developed and implemented into the commercial software ABAQUS for its transient analysis. First, a special three-dimensional eight-node solid element is designed to handle the multiferroic composite made of elastic, piezoelectric, and piezomagnetic materials. Second, a userdefined subroutine for this newly developed element is implemented into ABAQUS. Finally, the transient responses of a bi-layered multiferroic composite are calculated by using the direct time integration method. Two typical magnetic potential signals, Gauss and Ricker pulses, are applied to the composite with various time durations of excitation. The induced electric field shows that the transient response can be substantially influenced by the input signal, which could be tuned for the strongest electric output.

关键词： transient response multiferroic piezoelectric piezomagnetic composite finite element

Interaction energy of interface dislocation loops in piezoelectric bi-crystals

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Theoretical & Applied Mechanics Letters 2017年第2期7卷 76-80页

作者： Jianghong Yuan Yin Huang Weiqiu Chen Ernian pan State Key Laboratory of Traction Power SouthwestJiaotong University Chengdu Sichuan 610031 China School of Mechanics and Engineering Southwest Jiaotong University Chengdu Sichuan 610031 China Center for Mechanics and Materials and AML Department of Engineering Mechanics Tsinghua University Beijing 100084 China Department of Engineering Mechanics Zhejiang University Hangzhou 310027 China Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province Zhejiang University Hangzhou 310027 China Department of Civil Engineering and Department of Applied Mathematics University of Akron Akron OH 44325 USA

Interface dislocations may dramatically change the electric properties, such as polarization, of the piezoelectric crystals. In this paper, we study the linear interactions of two interface dislocation loops with arbitrary shape in generally anisotropic piezoelectric bi-crystals. A simple formula for calculating the interaction energy of the interface dislocation loops is derived and given by a double line integral along two closed dislocation curves. Particularly, interactions between two straight segments of the interface dislocations are solved analytically, which can be applied to approximate any curved loop so that an analytical solution can be also achieved. Numerical results show the influence of the bi-crystal interface as well as the material orientation on the interaction of interface dislocation loops.

关键词： Interface dislocation Piezoelectric bi-crystals Anisotropic elasticity Interaction energy

Some fundamental issues and related solutions in anisotropic and layered solids

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Some fundamental issues and related solutions in anisotropic...

FREE VIBRATION OF FUNCTIONALLY GRADED, MAGNETO-ELECTRO-ELASTIC, AND MULTILAYERED PLATES

中国力学大会-2015

作者： pan ernian University of Akron

In this talk,I will review and present some of the fundamental issues with analytical solutions in both horizontally and spherically layered structures.My model structure consists of multilayered materials with fully coupled magnetoelectroelastic properties.Three typical but different areas are emphasized on the importance of multilayered structures.The first one is on the magnetoelectroelastic layered plates with applications mostly to

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Acta Mechanica Solida Sinica 2006年第2期19卷 160-166页

作者： Chen Jiangyi Chen Hualing pan ernian School of Mechanical Engineering Xi＇an Jiaotong University Xi＇an 710049 China Department of Civil Engineering University of Akron Ohio 44325-3905 USA

The state-space method is employed to evaluate the modal parameters of functionally graded, magneto-electro-elastic, and multilayered plates. Based on the assumption that the properties of the functionally graded material are exponential, the state equation of structural vibration which takes the displacement and stress of the structure as state variables is derived. The natural frequencies and modal shapes are calculated based on the general solutions of the state equation and boundary conditions given in this paper. The influence of the functionally graded exponential factor on the elastic displacement, electric, and magnetic fields of the structure are discussed by assuming a sandwich plate model with different stacking sequences.

关键词： functionally graded material magneto-electro-elastic plates modal shapes statespace method

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负荷勒夫数渐近值解析表达式

地球物理学报 2021年第10期64卷 3521-3531页

作者：周江存潘尔年中国科学院精密测量科学与技术创新研究院大地测量与地球动力学国家重点实验室武汉430077 College of Engineering Cleveland State UniversityClevelandOH 44115USA

地表质量负荷引起的地球变形问题是大地测量学和地球物理学中的一个重要的研究内容.负荷勒夫数的计算和收敛的负荷格林函数的构建是模拟地球负荷形变的基础,其中当球谐阶数趋于无穷大时负荷勒夫数的渐近值,在格林函数计算中发挥重要的作... 详细信息

地表质量负荷引起的地球变形问题是大地测量学和地球物理学中的一个重要的研究内容.负荷勒夫数的计算和收敛的负荷格林函数的构建是模拟地球负荷形变的基础,其中当球谐阶数趋于无穷大时负荷勒夫数的渐近值,在格林函数计算中发挥重要的作用.本文首先介绍了地表质量负荷的边值问题,然后简要回顾了目前已有的计算负荷勒夫数渐近值三种方法的推导过程,最后给出推导渐近值解析表达式的一种新方法.新方法运用求解地球变形边值问题的解析解方法,以及一种高效传播矩阵方法,建立地表边界条件与高阶负荷勒夫数之间的直接联系,解出了负荷勒夫数渐近值解析表达式.本文的解析表达式更准确地描述了负荷勒夫数的渐近特征.新方法仅涉及常系数常微分方程组的基解矩阵及基础的矩阵运算,原理简单易懂.

关键词：地表质量负荷负荷勒夫数渐近值解析解传播矩阵方法

The U-P solutions for Lamb's problem of a poroelastic medium

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The U-P solutions for Lamb's problem of a poroelastic medium

中国力学大会-2015

作者： Ding Boyang pan ernian Zheng Pei Zhejiang University City College The University of Akron's Department of Civil Engineering School of Mechanical Engineering University of Shanghai for Science and Technology

Based on the Homlolz’s solutions for Biot’s dynamics equation and Fourier transformation,with introducing dynamic parametersξ,ξ,authors performed the decoupling of fast and slow dilational wave of Biot’s dynamic equations.Further,through transformation of cylindrical coordinate and Sommerfeld’s identity,superposition of the influence field of a free sur-

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任意梯度分布圆柱壳的周向导波频散分析

应用基础与工程科学学报 2016年第6期24卷 1289-1295页

作者：陈江义潘尔年郑州大学机械工程学院河南郑州450001

利用半解析方法分析了周向导波在任意梯度分布圆柱壳的频散特性.在假设材料参数沿圆柱壳径向按任意梯度变化的基础上,应用带状单元法,将功能梯度壳分成若干子层.对于细分子层可认为其材料参数为常值,并以此构造带状单元,获得导波在圆柱... 详细信息

利用半解析方法分析了周向导波在任意梯度分布圆柱壳的频散特性.在假设材料参数沿圆柱壳径向按任意梯度变化的基础上,应用带状单元法,将功能梯度壳分成若干子层.对于细分子层可认为其材料参数为常值,并以此构造带状单元,获得导波在圆柱壳中周向传播时的特征值问题,通过求解该特征值问题,得到了导波的频散特性.最后通过算例讨论了材料参数沿径向按余弦函数分布时,不同梯度参数及内外径比对导波频散特性的影响.

关键词：功能梯度材料圆柱壳带状单元法频散特性导波