Finite Element Multi-mode Approach to Thermal Postbuckling of Functionally Graded Plates

Postbuckling analysis of functionally graded ceramic-metal plates under temperature field is presented using finite element multi-mode method. The three-node triangular element based on the Mindlin plate theory is employed to account for the transverse shear strains, and the von-Karman nonlinear strain-displacement relation is utilized considering the geometric nonlinearity. The effective material properties are assumed to vary through the thickness direction according to the power law distribution of the volume fraction of constituents. The temperature distribution along the thickness is determined by one dimensional Fourier equations of heat conduction. The buckling mode shape solved from eigen-buckling analysis is adopted as the assumed mode function to reduce the degrees of freedom of nonlinear postbuckling equilibrium equations. The postbuckling response is obtained by solving the nonlinear equilibrium equations, and compared with the Newton- Raphson numerical results. The effects of boundary conditions, material gradient index and temperature distribution on postbuckling behavior are examined.     

Bending,Free Vibration and Buckling Analysis of Functionally Graded Plates via Wavelet Finite Element Method

Following previous work, a wavelet finite element method is developed for bending, free vibration and buckling analysis of functionally graded (FG) plates based on Mindlin plate theory. The functionally graded material (FGM) properties are assumed to vary smoothly and continuously throughout the thickness of plate according to power law distribution of volume fraction of constituents. This article adopts scaling functions of two-dimensional tensor product BSWI to form shape functions. Then two-dimensional FGM BSWI element is constructed based on Mindlin plate theory by means of two-dimensional tensor product BSWI. The proposed two-dimensional FGM BSWI element possesses the advantages of high convergence, high accuracy and reliability with fewer degrees of freedoms on account of the excellent approximation property of BSWI. Numerical examples concerning various length-to-thickness ratios, volume fraction indexes, aspect ratios and boundary conditions are carried out for bending, free vibration and buckling problems of FG plates. These comparison examples demonstrate the accuracy and reliability of the proposed WFEM method comparing with the exact and referential solutions available in literatures.     

边界元法分析功能梯度涂层材料

在常规边界元法中引入几乎奇异积分的解析算法,使边界元法可以分析涂层结构的强度.计算了在赫兹压力作用下,各向同性涂层和功能梯度涂层两种涂层结构中的Tresca应力分布,绘制了应力等值线图.计算发现使用各向同性涂层时,Tresca应力的最大值出现在涂层和基体交界面上,且在交界面上应力存在明显的不连续性.通过边界元法分析,发现采用功能梯度涂层,可以降低最大的Tresca应力值,削减交界面上的应力不连续性.     

A Finite Element Analysis for Evaluation of J-Integral in Plates Made of Functionally Graded Materials with a Semicircular Notch

Journal of Failure Analysis and Prevention - This work introduces a numerical investigation using finite element method to evaluate the J-integral at crack tip in titanium boride...     

复合材料层压板单面贴补修理建模分析研究

胶接修理技术是一种优质、高效、低成本的结构修理技术.针对复合材料层板的胶接贴补修理进行计算模拟分析,并与实验结果相对比.采用ABAQUS有限元软件对层压板的损伤板和单面贴补修理板进行有限元建模,分析修补前后的应力分布情况,计算出失效强度与完好板进行对比,得出修补后的强度恢复率.     

正交各向异性功能梯度材料平板振动分析

基于一阶剪切理论,研究四边简支正交各向异性功能梯度材料(FGM)板的自由振动和受迫振动。假设剪应力沿厚度方向呈抛物线分布,利用剪切应变能与剪切余能相等原理,得到正交各向异性功能梯度平板的剪切修正系数。利用虚位移原理得到功能梯度平板运动方程,并采用Navier方法对运动方程进行求解。通过与有关文献及有限元计算结果对比,验证该方法的正确性。在此基础上,分析厚度方向上由纤维和基体按照不同体积梯度分布的三种(P-,S-,C-FGM)平板的固有振动和受激振动特性,结果表明纤维体积分数变化区间越大,梯度型式及梯度指数对其振动特性影响越显著;纤维体积分数关于平板中面反对称分布(S-FGM)时,平板振动特性受梯度指数影响较小。     

Analysis of Functionally Graded Magneto-Electro-Elastic Composites Using Hybrid/Mixed Finite Elements and Node-Wise Material Properties

A new class of hybrid/mixed finite elements, denoted "HMFEM-C", has been developed for modeling magneto-electro-elastic (MEE) materials. These elements are based on assuming independent strain-fields, electric and magnetic fields, and collocating them with the strain-fields, electric and magnetic fields derived from the primal variables (mechanical displacements, electric and magnetic potentials) at some cleverly chosen points inside each element. The newly developed elements show significantly higher accuracy than the primal elements for the electric, magnetic as well as the mechanical variables. HMFEM-C is invariant through the use of the element-fixed local orthogonal base vectors, and is stable since it is not derived from a multi-field variational principle; hence it completely avoids LBB conditions that govern the stability of hybrid/mixed elements. In this paper, node-wise material properties are used in order to better simulate the spatial material grading of the functionally graded materials (FGM). A computer code was developed, validated and used to calculate the three magnetoelectric (ME) voltage coefficients for piezoelectric-piezomagnetic (PE-PM) composites, namely, the out-of-plane, transverse and in-plane ME voltage coefficients. The effects of the piezoelectric phase volume fraction as well as the mechanical boundary conditions and loadings on the ME voltage coefficients are investigated. Also, the effects of grading functions in PE-PM composites with functionally graded layers, as well as single-layered functionally graded magneto-electro-elastic materials, on the three ME voltage coefficients are presented.     

梯度功能材料板瞬态温度场有限元分析

采用有限元法与有限差分法相结合的方法,对梯度功能材料板的瞬态温度场进行了分析,并且通过ＺｒＯ２和Ｔｉ－６Ａｌ－４Ｖ组成的梯度功能材料对本方法的正确性进行了检验,最后给出了加热、冷却过程的瞬态温度场分布。     

压电介质夹杂功能梯度压电带界面双裂纹反平面问题

利用积分方程方法,本文研究了夹在两个均匀压电半空间的功能梯度压电带界面共线双裂纹的反平面问题。在电渗透型边界条件下,通过Fourier余弦变换将所考虑的问题化为一对偶积分方程,再用Copson方法将该对偶积分方程转化为Fredholm方程进行数值求解,从而给出了裂纹尖端的应力强度因子,电位移强度因子的表达式。分析了裂纹长度,功能梯度非均匀参数以及材料的几何尺寸等对应力强度因子的影响。     

功能梯度材料Timoshenko型剪切梁的自由振动分析

基于Timoshenko梁理论,研究各向异性功能梯度材料梁的自由振动。假设材料参数沿梁厚度方向按同一函数规律变化,建立了功能梯度材料梁的振动方程,求得简支条件下其自振频率表达式。通过算例,给出指数函数梯度变化Timoshenko梁的自振频率和模态图,结果表明不同梯度变化对材料结构动力响应有较大影响。该方法为发展功能梯度材料梁的设计与数值计算提供了理论依据。     

Heat Conduction Analysis of Nonhomogeneous Functionally Graded Three-Layer Media

Functionally graded material (FGM) is a particulate composite with continuously changing its thermal and mechanical properties in order to raise the bonding strength in the discrete composite made from different phases of material constituents. Furthermore, FGM is a potent tool to create an intermediate layer in metal–ceramic composites to avoid the properties discontinuities and reduce, thereby, the residual stresses. For the nonhomogeneous problem, the mathematical derivation is much complicated than the homogeneous case since the material properties vary with coordinate. To analyze the problem, the Fourier transform is applied and the general solution in transform domain is obtained. The inverse Fourier transform is performed to get the results in physical domain for temperature and heat fluxes. Numerical results for the full-field distributions of temperature and heat fluxes with different functionally graded parameters are presented. The continuous characteristics of the temperature and heat flux along the interface are emphasized and some interesting phenomena are presented in this study. The results show that all the fields (temperature and heat fluxes) are continuous at the interface if the conductivities are continuous at the interface. Moreover, the first derivatives of temperature and heat flux qy are continuous at the interface.     

Material and Geometric Nonlinear Analysis of Functionally Graded Plate-Shell Type Structures

A nonlinear formulation for general Functionally Graded Material plate-shell type structures is presented. The formulation accounts for geometric and material nonlinear behaviour of these structures. Using the Newton–Raphson incremental-iterative method, the incremental equilibrium path is obtained, and in case of snap-through occurrence the automatic arc-length method is used. This simple and fast element model is a non-conforming triangular flat plate/shell element with 24 degrees of freedom for the generalized displacements. It is benchmarked in the solution of some illustrative plate- shell examples and the results are presented and discussed with numerical alternative models. Benchmark tests with material and geometrically nonlinear behaviour are also proposed.     

新型陶瓷刀具材料的热应力分析

运用有限元方法计算了梯度功能陶瓷刀具ＦＧ－２内的热应力,计算结果表明,在高速切削条件下,梯度功能陶瓷刀具内的热应力明显小于普通陶瓷刀具;同时进行的切削实验也表明在高速切削的条件下,ＦＧ－２的破损寿命明显好于ＳＧ－４．说明梯度功能陶瓷刀具适应于高速切削．     

Levy Solution for Buckling Analysis of Functionally Graded Rectangular Plates

In this article, an analytical method for buckling analysis of thin functionally graded (FG) rectangular plates is presented. It is assumed that the material properties of the plate vary through the thickness of the plate as a power function. Based on the classical plate theory (Kirchhoff theory), the governing equations are obtained for functionally graded rectangular plates using the principle of minimum total potential energy. The resulting equations are decoupled and solved for rectangular plate with different loading conditions. It is assumed that the plate is simply supported along two opposite edges and has arbitrary boundary conditions along the other edges. The critical buckling loads are presented for a rectangular plate with different boundary conditions, various powers of FGM and some aspect ratios.     

Bending Analysis of Curved Sandwich Beams with Functionally Graded Core

In this article, bending analysis of curved sandwich beams with transversely and functionally graded (FG) core is studied. The Euler–Bernoulli beam theory is used to model the thin face-sheets and high-order shear theory is used to analyze the core. Equilibrium/field equations, compatibility and boundary conditions are used to derive the set of governing equations. The numerical solution of the governing nonlinear differential equations is based on the series Fourier–Galerkin method. Finally, the effect of geometric properties on radial deflection of core and the effect of core radius and Young's modulus on radial deflection, circumferential displacement, and stresses are investigated.     

Magnetothermoelastic Bending Analysis of a Functionally Graded Material Cylindrical Shell

An analytic method for bending analysis of a cylindrical shell composed by a functionally graded material (FGM), placed in a uniform magnetic field, subjected to mechanical and thermal loads is presented. Based on the classical linear shell theory, the equations with the radial deflection and horizontal displacement are derived, and exact solution of the magnetothermoelastic bending problem is obtained. For the FGM cylindrical shell with fixed and simply supported boundary conditions, the effects of mechanical load, thermal load, magnetic intensity, volume exponent, and geometric parameters on the bending deformation of the FGM cylindrical shell are discussed.     

Investigation of Functionally Graded and Viscoelastic Layers Effects on the Dynamic Behavior of Functionally Graded Electro-Rheological Sandwich Beams

Vibration characteristics of functionally graded electro-rheological (FGER) sandwich beams are investigated. While a vast majority of studies have been reported about functionally graded material (FGM) or electrorheological fluids (ERF) composite beams, few, if any, works are conducted about FGER models. In order to validate the present finite element formulation of the FGER beam model, the results of the developed finite element (FE) model are compared with the results of an experimental test on a fabricated ERF composite beam. The effects of FGM volume fraction index, electric field, and thickness of the viscoelastic core are studied on the natural frequencies and modal loss factors of the FGER beam.     

Steady‐State Creep Analysis of Functionally Graded Rotating Cylinder

Axi‐symmetric component like cylinder etc. has to operate under severe thermo‐mechanical loads, which cause significant creep. It, thus, reduces its service life. The present study investigates the steady‐state creep in a functionally graded rotating cylinder at constant angular speed. The cylinder is made up of aluminium matrix and reinforced with silicon carbide particles. The thermal gradient in the functionally graded rotating cylinder is estimated by performing finite element analysis on ANSYS software (ANSYS Inc., Canonsburg, USA). The creep behaviour of the cylinder has been described by threshold stress‐based creep law. The creep parameters are obtained by conducting regression analysis. The mathematical models have been developed to describe steady‐state creep in the cylinder. The study reveals that the radial, tangential, axial and effective stresses in the cylinder are significantly affected by the presence of particle gradient alone as well as with the presence of particle & thermal gradient both. It has been found that the creep rates have been reduced significantly by imposition of particle and thermal gradients together and thus increases the service life of cylinder.     

Thermal Buckling Analysis of Piezoelectric Functionally Graded Plates with Temperature-Dependent Properties

In this study, the thermal buckling analysis of hybrid laminated plates made of two-layered functionally graded materials (FGMs) that are integrated with surface-bonded piezoelectric actuators referred to as (P/FGM)_s are investigated. Material properties for both substrate FGM layers and piezoelectric layers are temperature-dependent. Uniform temperature rise as a thermal load and constant applied actuator voltage are considered for this analysis. By definition of four new analytic functions, the five coupled governing stability equations, which are derived based on the first-order shear deformation plate theory, are converted into fourth-order and second-order decoupled partial differential equations (PDEs). Considering a Levy-type solution, these two PDEs are reduced to two ordinary differential equations. One of these equations is solved using an accurate analytical solution, which is named as power series Frobenius method. The effects of parameters, such as the plate aspect ratio, ratio of piezoelectric layer thickness to thickness of FGM layer, gradient index, actuator voltage, and the temperature dependency on the critical buckling temperature difference, are illustrated and explained. The critical buckling temperatures of (P/FGM)_s with six various boundary conditions are reported for the first time and can be served as benchmark results for researchers to validate their numerical and analytical methods in the future.     

The Parametric Analysis of a Bonded Overlap Joint Resulting in Design Guidelines and a Representation for Finite Element Analysis

Abstract: The sensitivity of the joint's stiffness to changes in certain parameters (geometric and material properties) has been investigated and an understanding of the joint's behaviour gained from this parametric study. This insight into simple overlap joint behaviour has been used to fashion some design guidelines aimed at increasing joint stiffness. A representation that can be successfully substituted for certain adhesively bonded overlap joints in finite element (FE) analyses is also suggested.