Nonlinear thermomechanical post-buckling of circular FGM plate with geometric imperfection

Nonlinear thermomechanical post-buckling of an imperfect functionally graded material (FGM) circular plate, subjected to both mechanical load and transversely non-uniform temperature rise, is presented. The material properties of FGM plates are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. Based on von Kármán's plate theory, equilibrium equations governing a large axi-symmetric deformation of the FGM circular plate under thermomechanical loads are derived. In the analysis, the geometric imperfections of the plate are taken into account. By using a shooting method the nonlinear ordinary differential equations with immovably clamped boundary conditions are solved numerically. Responses for the nonlinear thermomechanical post-buckling responses of the FGM plate are obtained. Numerical examples are presented that relate to the performances of perfect and imperfect, homogenous and graded plates. Characteristic curves of the post-buckling deformation of the imperfect FGM circular plate varying with thermal loads, imperfection parameters and volume fraction index are plotted. And then effects of the load parameters, materials constitution, and the geometric imperfection of the plate on the deformation are discussed in detail.     

对带几何缺陷的FGM圆板的非线性热力学后屈曲现象的分析

带有几何缺陷FGM圆板的非线性热力学后屈曲现象是由力学荷载及横向不均匀温度升高导致的。基于组成材料的体积分数导致的能量分布法则,FGM板的材料特性假定在板厚度方向呈梯度变化。根据VonK偄rm偄n平板理论,推导出FGM板在温度荷载作用下的轴对称大变形的计算公式。在此分析中同时考虑了板的几何缺陷。通过运用目标法,解决了那些带有固定边界条件的非线性方程。数值算例中考虑了是否带有几何缺陷、均质或非均质的钢板。带缺陷FGM圆板的后屈曲变形特征曲线根据温度荷载、缺陷参数和体积分数的变化绘制而成。文中同时讨论了荷载参数、材料构成及板的几何缺陷对变形的影响。     

Flexural stress analysis of uniform slender functionally graded material beams using non-linear finite element method

Functionally graded material (FGM) typically consists of two constituent materials combined together with a particular distribution. A non-linear flexural stress analysis of through-thickness functionally graded uniform slender beam, subjected to a uniformly distributed load, is studied using the versatile finite element method based on Euler–Bernoulli beam hypothesis. The von-Kármán strain–displacement relations are used to account for geometric non-linearity. Simply supported and clamped FGM beams with axially immovable ends are considered. Governing non-linear equations are obtained using the principle of virtual work. Numerical results are provided to show the effect of boundary conditions and volume fraction exponent on the non-linear structural behaviour, in terms of the strains and stresses, of the FGM beams, for the first time. A shift in the neutral axis, from the mid-thickness of the beam, is observed due to the large transverse deflections, for the homogenous as well as the FGM beams. The through thickness variation of the axial stress is observed to be non-linear for the FGM beams contrary to that of the homogenous beams, for which the axial stress variation is linear. The through thickness sudden change in the material properties, governed by higher values of volume fraction exponent, results in a steep gradient in the axial stress variation through the thickness of the FGM beam.     

带表面压电层的功能梯度梁的热弹性分析

进行了电场及热机械荷载作用下带压电致动器和传感器的功能梯度梁的分析研究。假定功能梯度材料的主属性沿厚度方向呈指数变化,而泊松比不变。组合梁受平面应力作用,压电层由正交异性材料组成。梁周围温度为0,底表面无应力。厚度方向采用状态空间法,纵向采用傅里叶级数法进行求解。将数值结果与已有结果对比,验证公式的准确度。最后,研究功能梯度材料指标、机电耦合、厚度比、热机械界面条件对梁抗弯性能的影响。     

多层与梯度非均匀材料弹性力学问题解析解的简明数学理论

扼要介绍笔者最近20a研究出的一种简明数学理论，此理论可广泛适用于推导功能梯度包括多层非均匀材料中三维弹性力学问题的解析解a此种梯度非均匀材料在工程和科学各领域有广泛应用。也介绍一些应用此理论的成果，这些应用包括弹性动力学、热弹性力学、煤层开挖引起的地表移动、道路结构设计和强度评价、静力触探、土-水耦合固结基础沉降以及断裂力学。     

大挠度功能梯度压杆的后屈曲分析

对一端固定一端自由功能梯度压杆的后屈曲问题进行了分析。依据组份材料的体积含量,假设材料的物性参数沿杆件的厚度按幂函数变化。基于Kirchhoff大变形理论,推导了大挠度功能梯度压杆后屈曲分析的控制微分方程和边界条件。采用微分求积法对所得控制微分方程和边界条件进行数值计算,得到压杆后屈曲时的自由端转角和自由端位移。分析了载荷、梯度指数和截面边长比对杆件后屈曲平衡路径的影响。     

功能梯度混凝土管片的设计及材性研究

引入功能梯度材料设计原理,对盾构隧道衬砌管片进行分层设计,制备出功能梯度混凝土管片。并针对影响混凝土管片性能的关键性指标如抗渗性能、体积稳定性以及力学性能等进行了试验研究。结果表明,混凝土管片保护层材料抗渗性优良,氯离子扩散系数相比普通混凝土管片降低1个数量级;保护层材料与结构层材料体积稳定性良好,且具有较好的体积变形匹配性能;同时保护层及结构层混凝土力学性能均完全满足工程需要,有效保证了混凝土管片的高耐久、长寿命。     

功能梯度材料研究的进展综述

介绍了功能梯度材料的基本概念以及具有的优势，评述了FGM的应用现状与前景，提出了功能梯度材料在应用方面尚需解决的一些问题，表明了FGM有着广阔的应用前景。     

Analysis of functionally graded plates by an efficient finite element method with node-based strain smoothing

This paper presents an improved finite element approach in which a node-based strain smoothing is merged into shear-locking-free triangular plate elements. The formulation uses only linear approximations and its implementation into finite element programs is quite simple and efficient. The method is then applied for static, free vibration and mechanical/thermal buckling problems of functionally graded material (FGM) plates. In the FGM plates, the material properties are assumed to vary across the thickness direction by a simple power rule of the volume fractions of the constituents. The behavior of FGM plates under mechanical and thermal loads is numerically analyzed in detail through a list of benchmark problems. The numerical results show high reliability and accuracy of the present method compared with other published solutions in the literature.     

Thermal and mechanical instability of functionally graded truncated conical shells

Thermal and mechanical instability of truncated conical shells made of functionally graded material (FGM) is studied in this paper. It is assumed that the shell is a mixture of metal and ceramic that its properties changes as a function of the shell thickness. The governing equations are based on the first-order shell theory and the Sanders nonlinear kinematics equations. The results are obtained for a number of thermal and mechanical loads and are validated with the known data in the literature.     

功能梯度材料的进展

功能梯度材料是一种新型复合材料 .介绍了功能梯度材料的概念、制备工艺、应用领域、设计方法及其特征评价 ,并讨论了功能梯度材料研究的主要方面 .     

功能梯度压电板的精确解

对四边简支的功能梯度压电板进行精确分析,根据正交各向异性压电材料基本方程,导出了功能梯度压电材料的状态方程,假设材料性质沿板厚方向按统一的函数形式梯度分布,通过算例,分析了在电荷载作用下,材料性质的不同梯度变化对状态变量的影响。     

Manufacturing technique and performance of functionally graded concrete segment in shield tunnel

The quality of segment is very important to the service life of shield tunnel. Concerning the complex engineering environment of the Wuhan Yangtze River Shield Tunnel, the principle of functionally graded materials was introduced to design and produce the functionally graded concrete segment (FGCS). Its key manufacturing technique was proposed and its performance was tested. __________ Translated from Construction Technology, 2008, 37(1): 106–108 [译自:施工技术]     

径向荷载作用下功能梯度柱壳非线性后屈曲研究

基于柱壳非线性大变形理论,研究承受径向荷载的功能梯度柱壳的非线性后屈曲性能。依据功能梯度参数,功能梯度材料沿厚度方向的属性有差异。考虑依赖温度的材料属性,比较不同温度的影响。研究了功能梯度参数与空间参数的影响。最后,利用试验结果对理论结果进行修正。     

Exploring the synergy of building massing and façade design through evolutionary optimization

In performance-based architectural design optimization, the design of building massings and façades is commonly separated, which weakens the effectiveness in performance improvement. In response, this study proposes a hybrid massing-façade integrated design generation and optimization workflow to integrate the two elements in an evolutionary design process. Compared with the existing approaches, the proposed workflow emphasizes the diversity of building design generation, with which various combinations of building massing forms and façade patterns can be systematically explored. Two case studies and a corresponding comparison study are presented to demonstrate the efficacy of the proposed workflow. Results show that the optimization can produce designs coupling the potential of building massings and façades in performance improvement. In addition, the optimization can provide information that supports early-stage architectural design exploration. Such information also enables the architect to understand the performance implications associated with the synergy of building massing and façade design.     

Exploration and design of knitted composites for architectural application: The MeiTing project

Knitted composites are textile composite materials that consist of knitted textile reinforcement and polymer matrix. Knitted composites exhibit great design flexibility by allowing the customization of shapes, textures, and material properties. These features facilitate the optimization of buildings’ material systems and the creation of buildings with light weight and high material efficiency.To achieve such a lightweight, material-efficient building structure with knitted composites, this research investigates the material properties of knitted composites and proposes a design process for building-scale knitted composite systems. In the material study, this research examines certain mechanical properties of the material and the effects of additional design elements. In the design exploration, this research explores the design workflow of the structural form, element arrangement, and knit distribution of the material system at the macro-, meso-, and microscales. The project of MeiTing serves as proof of the concept and the design workflow.     

Crashworthiness design of functionally graded foam-filled multi-cell thin-walled structures

Foam-filled thin-walled structure has recently gained attention due to its excellent crashworthiness. Based on the previous study, a new kind of foam-filled thin-walled structure called as functionally graded foam-filled thin-walled structure has more excellent crashworthiness than the traditional uniform foam-filled thin-walled structure. Moreover, as far as we know multi-cell thin-walled structure has more excellent crashworthiness than the traditional single-cell thin-walled structure. As an integrator of the above two kinds of excellent thin-walled structures, functionally graded foam-filled multi-cell thin-walled structure (FGFMTS) may has extremely excellent crashworthiness. Based on our study, the crashworthiness of the FGFMTSs is significantly affected by the design parameter of the graded functional parameter m. Thus, in order to obtain the optimal design parameters, the FGFMTSs with different cross sections and different wall materials are optimized using the multiobjective particle swarm optimization (MOPSO) algorithm to achieve maximum specific energy absorption (SEA) capacity and minimum peak crushing force (PCF). At the same time, the corresponding uniform foam-filled multi-cell thin-walled structures (UFMTS) which have the same weight as these FGFMTSs are also optimized in our study. In the multiobjective design optimization (MDO) process, polynomial functional metamodels of SEA and PCF of FGFMTSs are used to reduce the computational cost of crash simulations by finite element method. The MDO results show that the FGFMTS with PCF in the initial period of its crash not only has better crashworthiness than the traditional UFMTS with the same weight but also performs superior balance of crashing stability. Thus, the optimal design of the FGFMTS with PCF occurring in the initial crash is an extremely excellent energy absorber and can be used in the practical engineering.     

Coupled thermoelasticity of functionally graded plates based on the third-order shear deformation theory

In this paper, the analytical solution is presented for a plate made of functionally graded materials based on the third-order shear deformation theory and subjected to lateral thermal shock. The material properties of the plate, except Poisson's ratio, are assumed to be graded in the thickness direction according to a power-law distribution in terms of the volume fractions of the constituents. The solution is obtained under the coupled thermoelasticity assumptions. The temperature profile across the plate thickness is approximated by a third-order polynomial in terms of the variable z with four unknown multiplier functions of (x,y,t) to be calculated. The equations of motion and the conventional coupled energy equation are simultaneously solved to obtain the displacement components and the temperature distribution in the plate. The governing partial differential equations are solved using the double Fourier series expansion. Using the Laplace transform, the unknown variables are obtained in the Laplace domain. Applying the analytical Laplace inverse method, the solution in the time domain is derived. Results are presented for different power law indices and the coupling coefficients for a plate with simply supported boundary conditions. The results are validated based on the known data for thermomechanical responses of a functionally graded plate reported in the literature.     

三维轴对称功能梯度材料瞬态热传导问题的自然单元法

为了更有效地求解三维轴对称功能梯度材料瞬态热传导问题,对无网格自然单元法应用于此类问题进行了研究,并发展了相应的计算方法。基于几何形状和边界条件的轴对称性,三维的轴对称问题可降为二维平面问题。为了简化本质边界条件的施加,轴对称面上的温度场采用自然邻近插值进行离散。功能梯度材料特性的变化由高斯点的材料参数进行模拟。时间域上,采用传统的两点差分法进行离散求解,进而得到瞬态温度场的响应。数值算例结果表明,提出的方法是行之有效的,理论及方法不仅拓展了自然单元法的应用范围,而且对三维轴对称瞬态热传导分析具有普遍意义。     

Gradientenbetontechnologie

The technology of graded concrete – From the development of concrete mixtures and the conceptual design to the automatized manufacturing In accordance with the principle form follows force, the DFG Priority Programme (SPP) 1542 – Leicht Bauen mit Beton – focuses on energy efficient building elements which are designed specifically for desired operational demands. This concept is a specific adaption of the component's inner structure and works in parallel to the optimization of its outer shape which is often limited due to the outer geometry of slabs, walls and supporting pillars. The technology of graded concrete provides an innovative possibility to adapt the inner structure of a concrete component in order to meet defined static and structural‐physical requirements. The challenging demands imposed by the technology of graded concrete require a holistic approach including the development of the concrete mixtures, the design of the building components and finally the automatized manufacturing. In collaboration between the departments ILEK, IWB and ISYS of the University of Stuttgart a complete process chain for the manufacturing of functionally graded concrete components was realized. This approach for concrete results in fully recyclable building elements with significant savings in mass and energy.