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Finite Element Method on Shape Memory Alloy Structure and Its Applications

Chinese Journal of Mechanical Engineering 2019年第5期32卷 125-135页

作者： Bo Zhou zetian kang Zhiyong Wang Shifeng Xue College of Pipeline and Civil Engineering China University of Petroleum(East China)

It is significant to numerically investigate thermo-mechanical behaviors of shape memory alloy(SMA)structures undergoing large and uneven deformation for they are used in many engineering fields to meet special requirements To solve the problems of convergence in the numerical simulation on thermo-mechanical behaviors of SMA structures by universal finite element *** work suppose a finite element method to simulate the super-elasticity and shape memory effect in the SMA structure undergoing large and uneven *** scalars,named by phase-transition modulus and equivalent stiffness,are defined to make it easy to establish and implement the finite element method for a SMA *** incremental constitutive equation is developed to formulate the relationship of stress,strain and temperature in a SMA material based on phase-transition modulus and equivalent stiffness.A phase-transition modulus equation is derived to describe the relationship of phase-transition modulus,stress and temperature in a SMA material during the processes of martensitic phase transition and martensitic inverse phase transition.A finite element equation is established to express the incremental relationship of nodal displacement,external force and temperature change in a finite element discrete structure of *** incremental constitutive equation,phase-transition modulus equation and finite element equation compose the supposed finite element method which simulate the thermo-mechanical behaviors of a SMA *** SMA structures,which undergo large and uneven deformation,are numerically simulated by the supposed finite element *** of numerical simulation show that the supposed finite element method can effectively simulate the super-elasticity and shape memory effect of a SMA structure undergoing large and uneven deformation,and is suitable to act as an effective computational tool for the wide applications based on the SMA materials.

关键词： Shape memory alloy Incremental constitutive equation Finite element equation Phase-transition modulus Applications

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Modeling size-dependent thermo-mechanical behaviors of shape memory polymer Bernoulli-Euler microbeam

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Applied Mathematics and Mechanics(English Edition) 2019年第11期40卷 1531-1546页

作者： Bo ZHOU Xueyao ZHENG zetian kang Shifeng XUE College of Pipeline and Civil Engineering China University of Petroleum (East China)

The objective of this paper is to model the size-dependent thermo-mechanical behaviors of a shape memory polymer (SMP) ***-dependent constitutive equations,which can capture the size effect of the SMP,are proposed based on the modified couple stress theory (MCST).The deformation energy expression of the SMP microbeam is obtained by employing the proposed size-dependent constitutive equation and Bernoulli-Euler beam *** SMP microbeam model,which includes the formulations of deflection,strain,curvature,stress and couple stress,is developed by using the principle of minimum potential energy and the separation of variables *** sizedependent thermo-mechanical and shape memory behaviors of the SMP microbeam and the influence of the Poisson ratio are numerically investigated according to the developed SMP microbeam *** show that the size effects of the SMP microbeam are significant when the dimensionless height is small ***,they are too slight to be necessarily considered when the dimensionless height is large *** bending flexibility and stress level of the SMP microbeam rise with the increasing dimensionless height,while the couple stress level declines with the increasing dimensionless *** larger the dimensionless height is,the more obvious the viscous property and shape memory effect of the SMP microbeam *** Poisson ratio has obvious influence on the size-dependent behaviors of the SMP *** paper provides a theoretical basis and a quantitatively analyzing tool for the design and analysis of SMP micro-structures in the field of biological medicine,microelectronic devices and micro-electro-mechanical system (MEMS) self-assembling.

关键词： shape memory polymer (SMP) size-dependent constitutive equation microbeam model size effect modified couple stress theory (MCST)

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Nonlinear Finite Element Method Considering Martensite Plasticity for Shape Memory Alloy Structure

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Journal of Shanghai Jiaotong university(Science) 2021年第6期26卷 774-785页

作者： ZHOU Bo kang zetian WANG Zhiyong XUE Shifeng Department of Engineering Mechanics College of Pipeline and Civil EngineeringChina University of PetroleumQingdao 266580ShandongChina

This work presents a nonlinear finite element method to simulate the macroscopic mechanical responses and the effects of martensite plasticity in a shape memory alloy(SMA)structure.A linear relationship formulation is adopted to express the influence of martensite plasticity on the inverse martensitic phase transition of SMA *** with a trigonometric-type phase transition evolution law and an exponential-type plastic flow evolution law,an incremental mechanical model with two internal variables is supposed based on the macroscopic experimental phenomena.A nonlinear finite element equation is formulated and solved by the principle of virtual displacement and Newton-Raphson method *** employing the proposed nonlinear finite element method,the uniform tensile bar and three-point bending beam are simulated and *** illustrate that the presented nonlinear finite element method is suitable to act as an effective computational tool for the wide applications based on the SMA material considering the effects of martensite plasticity because all material constants related to the method can be obtained from macroscopic experiments.

关键词： shape memory alloy(SMA)structure martensite plasticity incremental mechanical model nonlinear finite element method

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Study on size-dependent bending behavior of axially functionally graded microbeams via nonlocal strain gradient theory

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Journal of Southeast University(English Edition) 2019年第4期35卷 453-463页

作者： kang zetian Wang Zhiyong Zhou Bo Xue Shifeng College of Pipeline and Civil Engineering China University of Petroleum(East China)Qingdao 266580China

Based on the nonlocal strain gradient theory(NSGT),the static bending behaviors of an axially functionally graded(AFG)Bernoulli-Euler microbeam subjected to concentrated and distributed loads are *** material property of the AFG microbeam changes continuously along the longitudinal *** the basis of the minimum potential energy principle,the equations of motion and associated classical and non-classical boundary conditions are ***,Galerkin’s weighted residual method in conjunction with the normalization technique are utilized to solve the governing differential *** transverse deformations of the AFG microbeam suffering the sinusoidal distributed load within the framework of NSGT,nonlocal elasticity theory(NET),strain gradient theory(SGT)and classical elasticity theory(CET)are *** is observed that the bending flexibility of the microbeam decreases with the increase in the ratio of the material length scale parameter to the beam ***,the bending flexibility increases with the increase in the material nonlocal *** functionally graded parameter plays an important role in controlling the transverse *** study provides a theoretical basis and a technical reference for the design and analysis of AFG micro-beams in the related regions.

关键词： axially functionally graded microbeam nonlocal strain gradient theory bending Galerkin method normalization method

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功能梯度形状记忆合金复合梁的力学行为

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复合材料学报 2019年第8期36卷 1901-1910页

作者：康泽天周博薛世峰中国石油大学(华东)储运与建筑工程学院

功能梯度形状记忆合金(Functionally graded shape memory alloy,FGSMA)兼具功能梯度材料和形状记忆合金材料的双重特性,广泛应用于微机电、航空航天等工程领域。为研究FGSMA复合梁的弯曲行为,本文对形状记忆合金(SMA)力学本构方程进行... 详细信息

功能梯度形状记忆合金(Functionally graded shape memory alloy,FGSMA)兼具功能梯度材料和形状记忆合金材料的双重特性,广泛应用于微机电、航空航天等工程领域。为研究FGSMA复合梁的弯曲行为,本文对形状记忆合金(SMA)力学本构方程进行简化处理,并根据复合材料层合板理论建立了FGSMA复合梁的力学模型,据此研究了SMA体积分数沿厚度方向呈线性变化的FGSMA悬臂梁内SMA纤维铺设角度对悬臂梁横截面应变、中面轴向位移、中性面高度和相变层高度的影响以及悬臂梁中面应变、曲率、SMA马氏体相变临界层高度和中性面高度随弯矩载荷的变化规律。研究结果表明:在弯矩载荷作用下,悬臂梁中性面位置与中面位置不重合,且悬臂梁上下层SMA马氏体相变临界层位置不对称;截面轴向应变绝对值随铺设角度增大而增大,截面纵向应变绝对值随铺设角度增大先增大后减小,中面轴向位移随铺设角度增大先增大后减小;随着铺设角度增大,悬臂梁中性面高度逐渐增大,拉伸状态下相变结束临界层高度先减小后增大,压缩状态的趋势相反;随着弯矩载荷绝对值逐渐增大,中性面位置高度表现出先稳定后减小然后逐渐增大的趋势,相变临界层逐渐向中性面位置靠拢;中面正应变和挠曲率随着弯矩载荷绝对值逐渐增大而发生变化,且变化率先增大后减缓。

关键词：功能梯度材料形状记忆合金悬臂梁复合材料力学力学模型

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形状记忆合金管接头热机耦合行为的有限元数值模拟

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机械工程学报 2018年第18期54卷 68-75页

作者：康泽天周博薛世峰中国石油大学(华东)储运与建筑工程学院

为了克服形状记忆合金(Shape memory alloy, SMA)管接系统在装配过程中的数值模拟不够精细,SMA管接头紧固力影响因素研究不够详尽的缺点,基于热力学Gibbs自由能,推导SMA在相变过程中应力张量增量与马氏体体积分数增量之间的关系,基于非... 详细信息

为了克服形状记忆合金(Shape memory alloy, SMA)管接系统在装配过程中的数值模拟不够精细,SMA管接头紧固力影响因素研究不够详尽的缺点,基于热力学Gibbs自由能,推导SMA在相变过程中应力张量增量与马氏体体积分数增量之间的关系,基于非线性有限元分析软件ABAQUS二次开发功能,同时考虑材料弹性模量的变化以及马氏体相变的温度效应,编写ABAQUS用户材料子程序,对连接系统的装配过程进行数值模拟,有效描述整个管接系统在热力耦合作用下的相变和力学行为。数值结果表明,被连接管壁的应力最大值出现在内壁靠近管接头端口位置;管接头端口附近接触应力梯度很大,沿轴向从零迅速增加到最大值,然后逐渐回落到一个较高的稳定接触应力值;管接头管壁内的应力和马氏体相变沿管壁由内向外呈梯度分布;整体接触压应力水平表现出与管接头壁厚成正相关,与管接头内径成负相关,与扩径内压无关特性。更准确模拟了SMA管接系统在装配过程中的相变和力学行为,详尽分析了管接头产生紧固力的影响因素,为SMA管接头的设计提供理论基础和指导。

关键词：形状记忆合金管接头本构方程有限元分析

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Thermo-mechanical Behaviors of Functionally Graded Shape Memory Alloy Timoshenko Composite Beams

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Transactions of Nanjing University of Aeronautics and Astronautics 2021年第1期38卷 29-43页

作者： ZHOU Bo kang zetian MA Xiao XUE Shifeng YANG Jie College of Pipeline and Civil Engineering China University of Petroleum(East China)Qingdao 266580P.R.China School of Engineering RMIT UniversityMelbourne 3083Australia

This paper focuses on the thermo-mechanical behaviors of functionally graded(FG)shape memory alloy(SMA)composite beams based on Timoshenko beam *** volume fraction of SMA fiber is graded in the thickness of beam according to a power-law function and the equivalent parameters are *** governing differential equations,which can be solved by direct integration,are established by employing the composite laminated plate *** influences of FG parameter,ambient temperature and SMA fiber laying angle on the thermo-mechanical behaviors are numerically simulated and discussed under different boundary *** indicate that the neutral plane does not coincide with the middle plane of the composite beam and the distribution of martensite is asymmetric along the *** the increments of the functionally graded parameter and ambient temperature make the composite beam become ***,the influence of the SMA fiber laying angle can be *** work can provide the theoretical basis for the design and application of FG SMA structures.

关键词： shape memory alloy(SMA) shear deformation thermal effect laminated plate theory functionally graded(FG)beam

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Size-dependent behaviors of viscoelastic axially functionally graded Timoshenko micro-beam considering Poisson effects

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Journal of Southeast University(English Edition) 2020年第2期36卷 170-180页

作者： Zhou Bo Zheng Xueyao kang zetian Xue Shifeng College of Pipeline and Civil Engineering China University of Petroleum (East China) Qingdao 266580 China

A size-dependent continuum-based model is developed for the functionally graded(FG)Timoshenko micro-beams with viscoelastic properties,in which material parameters vary according to the power law along its axial *** size effect is incorporated by employing the modified couple stress theory and Kelvin-Voigt viscoelastic model,so that viscous components are included in the stress and the deviatoric segments of the symmetric couple stress *** components of strain,curvature,stress and couple stress are formulated by combining them with the Timoshenko beam *** on the Hamilton principle,the governing differential equations and boundary conditions for the micro-beam are expressed with arbitrary beam section shape and arbitrary type of *** size effect,FG effect,Poisson effect,and the influence of the beam section shape on the mechanical behaviors of viscoelastic FG micro-beams are investigated by taking the simply supported micro-beam subjected to point load as an *** show that the size effect on deflection,normal stress and couple stress are obvious when the size of the micro-beam is small enough,and the FG effects are obvious when the size of the micro-beam is large ***,the Poisson ratio influences the size effect significantly and the beam section shape is also an important factor influencing the mechanical behavior of the micro-beam.

关键词： viscoelastic functionally graded micro-beam size-dependent behaviors size effect functionally graded effect Poisson effect space

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Modeling size-dependent behaviors of axially functionally graded Bernoulli-Euler micro-beam

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Mechanical Engineering Science 2020年第1期2卷 17-29页

作者： Shuai WANG zetian kang Shichen ZHOU Bo ZHOU Shifeng XUE College of Pipeline and Civil Engineering China University of Petroleum(East China)Qingdao 266580P.R.China

This work focus on the mechanical behaviors,which are related to the size effect,functionally graded(FG)effect and Poisson effect,of an axially functionally graded(AFG)micro-beam whose elastic modulus varies according to sinusoidal law along its axial *** displacement field of the AFG micro-beam is set according to the Bernoulli-Euler beam *** the modified couple stress theory(MCST),the components of strain,curvature,stress and couple stress are expressed by the second derivative of the deflection of the AFG micro-beam.A size-dependent model related to FG effect and Poisson effect,which includes the formulations of bending stiffness,deflection,normal stress and couple stress,is developed to predict the mechanical behaviors of the AFG microbeam by employing the principle of minimum potential *** mechanical behaviors of a simply supported AFG micro-beam are numerically investigated using the developed model for demonstrating the size effects,FG effects and Poisson effects of the AFG *** show that the mechanical behaviors of AFG micro-beams are distinctly size-dependent only when the ratio of micro-beam height to material length-scale parameter is small *** FG parameter is an important factor that determines and regulates the size-dependent behaviors of AFG *** influences of Poisson’s ratio on the mechanical behaviors of AFG micro-beams are not negligible,and should be also considered in the design and analysis of an AFG *** work supplies a theoretical basis and a technical reference for the design and analysis of AFG micro-beams in the related regions.

关键词： axially functionally graded micro-beam size-dependent behaviors size effect functionally graded effect Poisson effect

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正交各向异性功能梯度微板的自由振动行为

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中南大学学报（自然科学版） 2020年第5期51卷 1200-1210页

作者：康泽天张岩周博薛世峰中国石油大学(华东)储运与建筑工程学院山东青岛266580

基于新修正偶应力理论,利用哈密顿原理推导正交各向异性功能梯度Kirchhoff微板的控制微分方程和边界条件,建立微板动力学模型,并利用纳维解法对其进行求解。利用建立的模型,对正交各向异性功能梯度四边简支微板的自由振动和受双向正弦... 详细信息

基于新修正偶应力理论,利用哈密顿原理推导正交各向异性功能梯度Kirchhoff微板的控制微分方程和边界条件,建立微板动力学模型,并利用纳维解法对其进行求解。利用建立的模型,对正交各向异性功能梯度四边简支微板的自由振动和受双向正弦分布横向载荷作用下的弯曲行为进行研究,分析材料各向异性,尺度参数与板厚比以及功能梯度参数对微板挠度、偶应力和前三阶固有频率尺度效应的影响。研究结果表明:应用本文模型求解的微板挠度比经典弹性板理论解的小,而其固有频率比经典弹性板理论解的大;板厚与材料尺度参数比越小,微板挠度、偶应力和固有频率的尺度效应越明显;功能梯度参数对微板挠度、偶应力和固有频率的尺度效应有一定影响;沿2个正交方向的材料尺度参数对微板挠度、偶应力和固有频率的尺度效应影响程度不同。

关键词：正交各向异性功能梯度尺度效应能量法偶应力理论

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