广义康托洛维奇法解任意四边形板的弯曲问题

本文从变分原理和双线性坐标变换出发,采用基于三次B样条函数的广义康托洛维奇法得到了带有各种边界条件任意四边形板弯曲的近似解答。样条函数广义康托洛维奇法是一种数值型的康托洛维奇法,因而它既能化二维问题为一维同题,同时又具有样条函数法收敛快、精度高、处理边界条件方便等优点。推导出的计算格式适用于各种边界条件,使梯形板、平行四边形板和矩形板的弯曲问题为本文的特殊情况。本文方法与通常有限元法相比,具有计算量小、精度高等显著特点,且通用性强,是一种很有前途的计算方法。     

Three-dimensional static and dynamic analyses of the functionally graded cylinder bonded to the laminated plate under general loading

A graded finite element method code based on Rayleigh–Ritz energy formulation is developed and implemented to study the elastic behavior of a layered plate loaded by a solid isotropic cylinder and a functionally graded interlayer. The applied nonaxisymmetric loading to the inner cylinder induces a stress concentration in the flexible part of the joint. The effects of different thicknesses and power law exponents of functionally graded interlayer on the distribution of displacements and stresses are investigated, which verifies the ability of functionally graded material to control the stress and displacement waves. The time-dependent response of the structure is also obtained based on Newmark's time integration method.     

Application of third order shear deformation theory in buckling analysis of 2D-functionally graded cylindrical shell reinforced by axial stiffeners

This paper presents buckling analysis of a two-dimensional functionally graded cylindrical shell reinforced by axial stiffeners (stringer) under combined compressive axial and transverse uniform distributive load. The shell material properties are graded in the direction of thickness and length according to a simple power law distribution in terms of the volume fractions of the constituents. Primarily, the third order shear deformation theory (TSDT) is used to derive the equilibrium and stability equations. Since there is no closed form solution, the numerical differential quadrature method, (DQM), is applied for solving the stability equations. Initially, the obtained results for an isotropic shell using DQM were verified against those given in the literature for simply supported boundary conditions. The effects of load, geometrical and stringer parameters along with FG power index in the various boundary conditions on the critical buckling load have been studied. The study of results confirms that, stringers have significant effects on critical buckling load.     

Bending analysis of moderately thick functionally graded conical panels

Considering the application of functionally graded (FG) materials in various industries, the present study aims to investigate bending of moderately thick clamped FG conical panels subjected to uniform and non-uniform distributed loadings. Effective mechanical properties which are vary from one surface of the panel to the other assumed to be defined by a power law distribution. Three different ceramic–metal sets of materials are studied. First-order shear deformation theory (FSDT) is applied to drive the governing equations of the problem which consists of five highly coupled second order partial differential equations (PDEs). The governing equations are then solved by the Extended Kantorovich Method (EKM). It is also shown that the presented formulation and solution technique can be used to obtain accurate predictions for other types of structures such as circular cylinders and rectangular plates. Predictions for cylindrical panels and plates show very good agreement with published data in the literature. Due to lack of data for FG conical panels in the literature, finite element code ANSYS is used to validate results of the presented method for FG conical panels which show very good agreement.     

Bending analysis of thick laminated plates using extended Kantorovich method

This study is concerned with bending of moderately thick rectangular laminated plates with clamped edges. The governing equations, based on Reissner first-order shear deformation plate theory; in terms of deflection and rotations of the plate include a system of three second-order, partial differential equations (PDEs). Application of extended Kantorovich method (EKM) to the system of partial differential equations reduces the governing equations to a double set of three second-order ordinary differential equations in the variables x and y. These sets of equations were then solved in an iterative manner until convergence was achieved. Normally three to four iterations are enough to get the final results with desired accuracy. It is demonstrated that, unlike other weighted residual methods, in the extended Kantorovich method initial guesses to start iterations are arbitrary and not even necessary to satisfy the boundary conditions. Results of this study also reveal that the convergence of the EKM is rapid and the method is an efficient way to solve system of PDEs of the same type. To compare the results of this study, the problem was also analyzed using commercial finite element software, ANSYS. Results show reasonably good agreement with the finite element analysis.     

Buckling of symmetrically laminated rectangular plates with general boundary conditions – A semi analytical approach

A semi-analytical extended Kantorovich approach for the buckling analysis of symmetrically laminated rectangular plates with general boundary conditions is presented. The solution is derived as a multi-function expansion that allows the analysis of laminated plates characterized by a non-separable solution. Among these, the cases of buckling of angle-ply laminates under inplane compression and shear buckling of any type of plate are the most common ones. The formulation is based on the variational principal of total energy minimization and the iterative extended Kantorovich method. The exact element method is adopted for the solution of the resulting differential eigenvalue problem. The capabilities of the proposed approach and its applicability to buckling analysis of composite laminated plates that cannot be analyzed using the classical single-term extended Kantorovich method are demonstrated numerically. The results are compared with exact solutions (where available), and with approximate results from other numerical methods. The accuracy and convergence of the proposed approach are also discussed.     

梯度热电材料的研究进展

热电材料梯度化是在保证各组分单一材料的热电性能的基础上,拓宽其应用温度范围,使各组分材料都能工作在最佳温区,以确保热电材料在一定的工作温度范围内具有较高的ZT值,保证其高的热电转换效率.介绍了热电材料的研究基础及其梯度化设计,对梯度热电材料在国内外的研究进展进行了综述并对未来的研究趋势进行了展望.     

非保守功能梯度材料杆的后屈曲分析

对受切向均布随从力作用的右端可移简支功能梯度材料(FGM)杆,基于轴线可伸长杆的大变形理论建立了非线性控制微分方程组,用打靶法对由金属和陶瓷所构成的FGM杆的后屈曲特性进行了数值分析,给出了不同梯度指标下FGM杆的后屈曲特征曲线,并与金属和陶瓷两种单相材料杆的相应特性进行了比较,讨论了FGM杆长高比对其后屈曲特性的影响。     

Simulation of crack paths in functionally graded materials

One of the main interests of fracture mechanics in functionally graded materials is the influence of such an inhomogeneity on crack propagation processes. Using the Griffith’ energy principle, the change of energy has to be calculated, if the crack starts to propagate. In homogeneous linear-elastic structures (asymptotically precise) formulas for the energy release rate are known, but a direct transfer of these methods to functionally graded materials can lead to very inaccurate results. Moreover, the influence of the inhomogeneity on the crack path cannot be seen. Here, a simple model for functionally graded materials is introduced. For this model, a formula for the change of potential energy is derived, giving detailed information on the effect of the gradation on crack propagation.     

分布载荷作用下简支功能梯度夹层板的弯曲分析

研究了四边简支具有功能梯度芯材的夹层板在分布载荷作用下的弯曲问题。基于Reissner假设,根据功能梯度材料的本构方程得出了应力、位移及内力的表达式,得到功能梯度夹层板的平衡方程;针对四边简支的边界条件,通过将挠度w与横向剪力Qx、Qy用双三角级数展开的方法,求解平衡方程。采用本文方法分别求解了均布载荷作用下、芯材弹性模量线性变化的功能梯度夹层板与芯材为均质各向同性材料的夹层板的弯曲挠度,并通过与经典解及有限元解进行比较,证明了本文方法的正确性。     

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．     

Evaluation of nonlocal higher order shear deformation models for the vibrational analysis of functionally graded nanostructures

Small scale effects in the functionally graded beam are investigated by using various nonlocal higher-order shear deformation beam theories. The material properties of a beam are supposed to vary according to power law distribution of the volume fraction of the constituents. The nonlocal equilibrium equations are obtained and an exact solution is presented for vibration analysis of functionally graded (FG) nanobeams. The accuracy of the present model is discussed by comparing the results with previous studies and a parametric investigation is presented to study the effects of power law index, small-scale parameter, and aspect ratio on the vibrational behavior of FG nanostructures.     

复杂边界条件功能梯度板三维分析的半解析方法

推导出适应功能梯度材料构件分析的半解析方法基本算式,并针对功能梯度构件的材料参数随空间坐标变化的特点,将材料参数纳入到力学方程中进行整体积分计算,从而编制统一程序计算不同边界条件下的板件问题.该法适应性强而又简洁高效,且不同于一般的半解析法,可采用一维离散,给出三维分析结果,是一种解决功能梯度构件力学性能分析的有效数值方法.文中用半解析法分析几种具有不同复杂边界条件的功能梯度板,给出了板件的力学量三维分布形态.