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| 1 | 基于物理中面FGM梁的非线性力学行为显示文摘当坐标面置于功能梯度材料(FGM)梁的物理中面上时,其本构方程中,面内力与弯矩并不耦合,这使得问题的控制方程以及边界条件得以简化。该文利用物理中面概念,基于一阶非线性梁理论,导出了FGM梁的基本方程,分析研究了热载荷作用下FGM梁的过屈曲、弯曲以及在这些构形上的振动等问题。假设功能梯度材料性质只沿梁厚度方向,并按成分含量的幂指数函数形式变化。利用打靶法数值地求解了所得方程。数值结果表明:热载荷作用下,FGM夹紧梁发生过屈曲变形,而简支梁则发生较为复杂的热弯曲变形;热载荷作用下,FGM夹紧梁和简支梁的动态行为也有明显区别;另外,剪切变形对FGM梁的力学行为也有显著的影响。 | 牛牧华 马连生 | 2011 | 工程力学2011，28，6： | 11 |
| 2 | 考虑热对材料参数影响的FGM梁热后屈曲特性研究显示文摘功能梯度梁热后屈曲特性研究对于推进功能梯度材料在航天器热防护设计中的应用有着重要意义。基于经典梁的几何非线性理论和物理中面的概念,建立了热载荷作用下功能梯度梁的运动微分方程,通过化简得到一个仅关于挠度的四阶微分-积分方程,并与固支边界条件构成特征值问题,分析研究了功能梯度梁的热后屈曲及在此基础上的振动问题。首先证明了通过哈密顿原理推导的运动方程是轴线可伸长理论的近似形式。接着考虑热对材料物性参数的影响,并对梁的长细比、功能梯度指数和温度比作了详细分析,研究了这些参数对热后屈曲路径和后屈曲振动的影响规律。结果表明:只有在长细比较大时才可以不考虑温度对材料物性参数的影响,否则误差较大;长细比、功能梯度指数和温度比的增大会增大无量纲热屈曲载荷,同时使屈曲路径和频率-载荷曲线向热载荷增大的方向移动。 | 何昊南 于开平 | 2019 | 工程力学2019，36，4： | 9 |
| 3 | 基于物理中面FGM简支梁的弯曲行为显示文摘基于一阶非线性梁理论,利用物理中面概念导出了FGM梁的基本方程,分析了热载荷作用下简支FGM梁的弯曲行为。当坐标面置于功能梯度材料(FGM)梁的物理中面上时,其本构方程中,面内力与弯矩并不耦合,使得问题的控制方程以及边界条件得以简化。分析中假设功能梯度材料性质只沿梁厚度方向、并按成分含量的幂指数形式变化;利用打靶法数值地求解了所得方程。数值结果表明:热载荷作用下,夹紧FGM梁发生过屈曲变形,而简支梁则发生较为复杂的热弯曲变形;在同一热载荷作用下,简支FGM梁将会产生三种构形问题;剪切变形对夹紧FGM梁的热变形影响比简支梁更明显。 | 马连生 牛牧华 | 2010 | 应用力学学报2010，27，3： | 6 |
| 4 | 热荷载作用下Timoshenko功能梯度夹层梁的静态响应显示文摘在精确考虑轴线伸长和一阶横向剪切变形的基础上建立了Timoshenko功能梯度夹层梁在热载荷作用下的几何非线性控制方程.采用打靶法数值求解所得强非线性边值问题,获得了两端固支功能梯度夹层梁在横向非均匀升温作用下的静态热过屈曲和热弯曲变形数值解.分析了功能梯度材料参数变化、不同表层厚度和升温参数对夹层梁弯曲变形、拉-弯耦合变形的影响,并给出温度函数在夹层梁厚度方向的具体分布形式. | 钮鹏 李世荣 金春福 杨刚 | 2011 | 固体力学学报2011，32，5： | 6 |
| 5 | 非均匀热载荷作用下功能梯度梁的非线性静态响应显示文摘由于功能梯度材料结构沿厚度方向的非均匀材料特性,使得夹紧和简支条件的功能梯度梁有着相当不同的行为特征。该文给出了热载荷作用下,功能梯度梁非线性静态响应的精确解。基于非线性经典梁理论和物理中面的概念导出了功能梯度梁的非线性控制方程。将两个方程化简为一个四阶积分-微分方程。对于两端夹紧的功能梯度梁,其方程和相应的边界条件构成微分特征值问题;但对于两端简支的功能梯度梁,由于非齐次边界条件,将不会得到一个特征值问题。导致了夹紧与简支的功能梯度梁有着完全不同的行为特征。直接求解该积分-微分方程,得到了梁过屈曲和弯曲变形的闭合形式解。利用这个解可以分析梁的屈曲、过屈曲和非线性弯曲等非线性变形现象。最后,利用数值结果研究了材料梯度性质和热载荷对功能梯度梁非线性静态响应的影响。 | 毛丽娟 马连生 | 2017 | 工程力学2017，34，6： | 5 |
| 6 | 热过屈曲梁振动的解析解显示文摘该文导出了面内热载荷作用下,梁在其过屈曲构形附近微幅振动的解析解。首先基于经典梁理论,推导了控制轴向和横向变形的基本方程。然后,将2个非线性方程化为一个关于横向挠度的四阶非线性积分-微分方程。假设梁的振幅以及由此引起的附加应变为无限小,另设其响应为谐振,则该非线性积分-微分方程将化为两组耦合的微分方程:一组控制非线性静态响应;另一组就是叠加于梁屈曲构形之上的线性振动方程。直接求解这些问题,可以得到梁热过屈曲构形以及固有频率的解析解,这些解是外加热载荷的函数。该文得到的精确解可以用于验证或改进各类近似理论和数值方法。 | 马连生 | 2012 | 工程力学2012，29，10： | 4 |
| 7 | Bending Solutions of FGM Reddy-Bickford Beams in Terms of Those of the Homogenous Euler-Bernoulli Beams显示文摘In this paper, correspondence relations between the solutions of the static bending of functionally graded material (FGM) Reddy-Bickford beams (RBBs) and those of the corresponding homogenous Euler-Bernoulli beams are presented. The effective material properties of the FGM beams are assumed to vary continuously in the thickness direction. Governing equations for the titled problem are formulated via the principle of virtual displacements based on the third-order shear deformation beam theory, in which the higher-order shear force and bending moment are included. General solutions of the displacements and the stress resultants of the FGM RBBs are derived analytically in terms of the deflection of the reference homogenous Euler- Bernoulli beam with the same geometry, loadings and end conditions, which realize a classical and homogenized expression of the bending response of the shear deformable non-homogeneous FGM beams. Particular solutions for the FGM RBBs under specified end constraints and load conditions are given to validate the theory and methodology. The key merit of this work is to be capable of obtaining the high-accuracy solutions of thick FGM beams in terms of the classical beam theory solutions without dealing with the solution of the complicated coupling differential equations with boundary conditions of the problem. | You-Ming Xia Shi-Rong Li Ze-Qing Wan | 2019 | Acta Mechanica Solida Sinica2019，32，4： | 2 |
| 8 | 基于物理中面FGM经典梁的非线性力学行为显示文摘利用物理中面概念,基于经典非线性梁理论,导出FGM梁的基本方程,分析研究热载荷作用下FGM梁的过屈曲、弯曲以及在这些构形上的振动等问题.假设功能梯度材料性质只沿梁厚度方向,并按成分含量的幂指数函数形式变化.利用打靶法数值地求解所得方程.数值结果表明:热载荷作用下,FGM夹紧梁发生过屈曲变形,而简支梁则发生较为复杂的热弯曲变形;热载荷作用下,FGM夹紧梁和简支梁的动态行为也有明显区别. | 马连生 牛牧华 | 2010 | 兰州理工大学学报2010，36，5： | 2 |
| 9 | 基于改进萤火虫算法的结构损伤识别显示文摘提出一种基于改进萤火虫算法的结构损伤识别方法。将结构损伤模拟成杨氏模量的减少。对于没有邻居的萤火虫,让它们在自身位置附近随机搜索,同时引入新的移动方式来提高算法的精度和收敛速度,避免算法过早的陷入局部最优,克服萤火虫算法在高维目标函数中寻优能力不足的问题。采取功能梯度梁(Axial functionally graded,AFG)作为研究对象,利用欧拉-伯努利梁单元建立力学模型。采用了简支梁作为算例,将结果和基本萤火虫算法、领导者萤火虫和自适应步长萤火虫算法作对比,说明改进的有效性。 | 胡磊 吕中荣 刘济科 | 2017 | 中山大学学报(自然科学版)2017，56，2： | 1 |
| 10 | ANALYSIS OF SHAKEDOWN OF FG BREE PLATE SUBJECTED TO COUPLED THERMAL-MECHANICAL LOADINGS显示文摘The static and kinematic shakedown of a functionally graded (FG) Bree plate is analyzed. The plate is subjected to coupled constant mechanical load and cyclically varying temperature. The material is assumed linearly elastic and nonlinear isotropic hardening with elastic modulus,yield strength and the thermal expansion coeffcient varying exponentially through the thickness of the plate. The boundaries between the shakedown area and the areas of elasticity,incremental collapse and reversed plasticity are determined,respectively. The shakedown of the counterpart made of homogeneous material with average material properties is also analyzed. The comparison between the results obtained in the two cases exhibits distinct qualitative and quantitative difference,indicating the importance of shakedown analysis for FG structures. Since FG structures are usually used in the cases where severe coupled cyclic thermal and mechanical loadings are applied,the approach developed and the results obtained are significant for the analysis and design of such kind of structures. | Xianghe Peng Ning Hu Hengwei Zheng Cuirong Fang | 2009 | Acta Mechanica Solida Sinica2009，22，2： | 0 |
| 11 | A numerical method based on boundary integral equations and radial basis functions for plane anisotropic thermoelastostatic equations with general variable coefficients显示文摘A boundary integral method with radial basis function approximation is proposed for numerically solving an important class of boundary value problems governed by a system of thermoelastostatic equations with variable coe?cients. The equations describe the thermoelastic behaviors of nonhomogeneous anisotropic materials with properties that vary smoothly from point to point in space. No restriction is imposed on the spatial variations of the thermoelastic coe?cients as long as all the requirements of the laws of physics are satis?ed. To check the validity and accuracy of the proposed numerical method, some speci?c test problems with known solutions are solved. | W.T.ANG X.WANG | 2020 | Applied Mathematics and Mechanics(English Edition)2020，41，4： | 0 |
| 12 | Free vibration characteristics of sectioned unidirectional/bidirectional functionally graded material cantilever beams based on finite element analysis显示文摘Advancements in manufacturing technology,including the rapid development of additive manufacturing(AM),allow the fabrication of complex functionally graded material(FGM)sectioned beams.Portions of these beams may be made from different materials with possibly different gradients of material properties.The present work proposes models to investigate the free vibration of FGM sectioned beams based on onedimensional(1D)finite element analysis.For this purpose,a sample beam is divided into discrete elements,and the total energy stored in each element during vibration is computed by considering either the Timoshenko or Euler-Bernoulli beam theory.Then,Hamilton’s principle is used to derive the equations of motion for the beam.The effects of material properties and dimensions of FGM sections on the beam’s natural frequencies and their corresponding mode shapes are then investigated based on a dynamic Timoshenko model(TM).The presented model is validated by comparison with three-dimensional(3D)finite element simulations of the first three mode shapes of the beam. | N.V.VIET W.ZAKI Quan WANG | 2020 | Applied Mathematics and Mechanics(English Edition)2020，41，12： | 0 |
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