有限厚度圆柱壳热冲击问题的广义热弹性解

针对包含有界边界的轴对称结构受热冲击作用的广义热弹性问题进行了研究分析.基于Lord-Shulman广义热弹性理论(L-S理论),构建了热冲击下有限厚度圆柱壳热弹性响应的广义热弹性模型.借助Laplace(拉普拉斯)变换技术以及Bessel函数的渐进特性,推导了温变载荷作用下,圆柱壳内部位移、温度以及应力场的解析表达式.该表达式不仅可以清楚地揭示热冲击下热波、热弹性波在壳体内部的传播、反射以及叠加的作用过程,更可准确地捕捉到热波、热弹性波波前位置处的阶跃现象,并对热冲击诱发的动态热应力峰值进行有效预测.     

悬臂矩形板在对称边界荷载下的屈曲

本文用变分法对悬臂矩形板在对称边界荷载下的稳定性进行研究.我们将对在悬臂矩形板的一对相对的自由边作用有不同的对称边界荷载时,求出薄板的最小临界力.文中分别讨论了有一对集中力,均布荷载,局部均布荷载,三角形分布荷载及一对集中力偶作用之下悬臂矩形板发生屈曲时的最小临界荷载.     

不用克希霍夫—拉夫假设的弹性圆板理论再探

本文在不用克希霍夫一拉夫假设的弹性板一般理论的基础上,建立了不用克希霍夫一拉夫假设的弹性圆板的一级近似理论,对圆板在四周固定和均布载荷的条件下,得到了具体的轴对称分析解,并和经典的圆薄板解进行了比较,证明本文新解更加接近实验结果,本文也具体地讨论了理论结果中厚度增大时的影响。     

功能梯度板的柱面弯曲弹性力学解

在推广后的England-Spencer功能梯度板理论基础上,研究了功能梯度板在不同荷载作用下的柱面弯曲问题.采用该理论中的位移展开公式,并且材料参数沿板厚方向可以任意连续变化,并将材料由各向同性推广到正交各向异性.假设板在y方向无限长,最终建立了一个从弹性力学理论出发的正交各向异性功能梯度板在横向分布荷载作用下柱面弯曲问题的板理论.通过算例分析,讨论了边界条件、材料梯度及板厚跨比等因素对功能梯度板静力响应的影响.     

Elasticity Solutions for Cylindrical Bending of Functionally Graded Piezoelectric Material Plates北大核心CSCD

功能梯度压电材料（FGPM）同时兼具功能梯度材料和压电材料特性,可为多功能或智能化轻质结构设计提供支撑,在诸多领域有着广泛的应用前景.将Mian和Spencer功能梯度板理论由功能梯度弹性材料推广到功能梯度压电材料,解析研究了FGPM板的柱面弯曲问题,其中,材料弹性常数、压电和介电参数沿板厚方向可以任意连续变化.最终,给出了FGPM板受横向均布荷载作用下柱面弯曲问题的弹性力学解.通过算例分析,重点讨论了压电效应对FGPM板静力响应的影响.     

中厚板热后屈曲分析

依据Reissner-Mindlin板理论考虑转动惯量和横向剪切变形影响,本文给出中厚板在(1)均布和非均布(线性)热荷载作用下;(2)单向压缩和均布热荷载共同作用下的后屈曲分析。采用摄动法导出完善和非完善中厚板的热屈曲载荷和热后屈曲平衡路径,并与经典薄板理论结果进行了比较。     

不用克希霍克—拉夫假设的弹性圆板理论再探

本文在不用克希霍夫－拉夫假设的弹性板一般理论的基础上，建立了不用克希霍夫－拉夫假设的弹性圆板的一级近似理论，对圆板的四周固定和均布载荷的条件下，得到了具体的轴对称分析解，并和红典的圆薄板解进行了比较，证明本文新解更加接近实验结果，本文也具体地讨论了理论结果中厚度增大时的影响。     

二维周期性单胞网格结构的等效热弹性分析

分析了含周期性杆件胞元的二维网格结构的热弹性性质.根据拟膜法推导了网格结构的等效热膨胀系数.将结构的拟膜的等效热膨胀系数表示成为胞元内各杆几何与物理参数的显式函数形式.基于胞元在热荷载作用变形后的新尺寸给出了拟膜的等效弹性参数表达式.通过数值算例分析了结构在降温、增温和温度不变条件下的变形差异.然后,用网格结构、拟连续体的数值解与理论解进行了对比分析.结果表明上述热弹性参数表达式正确.由此将拟膜法推广到二维网格结构的热弹性分析中.     

厚板在集中荷载作用下的弯曲

本文根据[1]中提出的简化理论,利用两变元的δ-函数的性质[2]和级数解法,处理了在集中荷载作用下两对边简支,另两对边为任意的矩形厚板的弯曲问题.考虑了横向剪力对于弯曲变形的影响.当板的厚度h很小时,忽略公式中所有h2以上的项,则所得的结果与薄板弯曲问题的相应解一致[3].在本文的最后,我们还得到了在任意线分布荷载作用下相应问题的解.     

矩形薄板弯曲的近似解法——康托洛维奇-伽辽金法

本文从广义梁微分方程出发,推导出三次样条梁函数。由于采用了广义函数,在集中荷载,集中弯矩等得到截断多项式的解。弹性薄板偏微分方程荷载项采用了广义函数(δ函数及σ函数),无论是集中荷载、集中弯矩、均布荷载,小方块荷载都可表示成为x、y两个方向的截断多项式变形曲线。利用康托洛维奇法将偏微分方程转换成为常微分方程,再用伽辽金法可得良好的近似解。文内算例较为丰富,包括各种边界弹性薄板,各种荷载、变截面薄板以及悬臂板等。     

Free vibration analysis of FGM cylindrical shells surrounded by Pasternak elastic foundation in thermal environment considering fluid-structure interaction

This paper presents an investigation on partially fluid-filled cylindrical shells made of functionally graded materials (FGM) surrounded by elastic foundations (Pasternak elastic foundation) in thermal environment. Material properties are assumed to be temperature dependent and radially variable in terms of volume fraction of ceramic and metal according to a simple power law distribution. The shells are reinforced by stiffeners attached to their inside and outside in which the material properties of shell and the stiffeners are assumed to be continuously graded in the thickness direction. The formulations are derived based on smeared stiffeners technique and classical shell theory using higher-order shear deformation theory which accounts for shear flexibility through shell's thickness. Displacements and rotations of the shell middle surface are approximated by combining polynomial functions in the meridian direction and truncated Fourier series with an appropriate number of harmonic terms in the circumferential direction. The governing equations of liquid motion are derived using a finite strip element formulation of incompressible inviscid potential flow. The dynamic pressure of the fluid is expanded as a power series in the radial direction. Moreover, the quiescent liquid free surface is modeled by concentric annular rings. A detailed numerical study is carried out to investigate the effects of power-law index of functional graded material, fluid depth, stiffeners, boundary conditions, temperature and geometry of the shell on the natural frequency of eccentrically stiffened functionally graded shell surrounded by Pasternak foundations.     

Wave propagation and transient response of a functionally graded material plate under a point impact load in thermal environments

In this paper, the wave propagation and transient response of an infinite functionally graded plate under a point impact load in thermal environments are studied. The thermal effects and temperature-dependent material properties are taken into account. The temperature field considered is assumed to be a uniform distribution over the plate surface and varies in the thickness direction only. Material properties are assumed to be temperature-dependent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. Considering the effects of transverse shear deformation and rotary inertia, the governing equations of the wave propagation in the functionally graded plate are derived from Hamilton’s principle. The analytic dispersion relation of the functionally graded plate is obtained by means of integral transforms and a complete discussion of dispersion for the functionally graded plate is given. Using the dispersion relation and integral transforms, exact integral solutions of the functionally graded plate under a point impact load in thermal environments are obtained. The influences of the volume fraction distributions and temperature field on the wave propagation and transient response of functionally graded plates are discussed in detail. The results carried out can be used in the ultrasonic inspection techniques and provide a theoretical basis for engineering applications.     

An evolutionary method for optimization of plate buckling resistance

Optimization of plate buckling resistance is very complicated, because the in-plane stress resultants in the prebuckled state of a plate are functions of thickness distribution. This paper discusses the problem of finding the optimum thickness distribution of isotropic plate structures, with a given volume and layout, that would maximise the buckling load. A simple numerical method using the finite-element analysis is presented to obtain the optimum thickness distribution. Optimum designs of compression-loaded rectangular plates with different boundary conditions and plate aspect ratios are obtained by using the proposed method. Optimum designs from earlier studies and the methods of buckling analysis used to attain these results are discussed and compared with the designs from the proposed method. This paper also examines the reliability of the optimality criterion generally used for plate buckling optimization, which is based on the uniform strain energy density.     

Bending of thick functionally graded plates resting on Winkler–Pasternak elastic foundations

The static response of simply supported functionally graded plates (FGP) subjected to a transverse uniform load (UL) or a sinusoidally distributed load (SL) and resting on an elastic foundation is examined by using a new hyperbolic displacement model. The present theory exactly satisfies the stress boundary conditions on the top and bottom surfaces of the plate. No transverse shear correction factors are needed, because a correct representation of the transverse shear strain is given. The material properties of the plate are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of volume fractions of material constituents. The foundation is modeled as a two-parameter Pasternak-type foundation, or as a Winkler-type one if the second parameter is zero. The equilibrium equations of a functionally graded plate are given based on the hyperbolic shear deformation theory of plates presented. The effects of stiffness and gradient index of the foundation on the mechanical responses of the plates are discussed. It is established that the elastic foundations significantly affect the mechanical behavior of thick functionally graded plates. The numerical results presented in the paper can serve as benchmarks for future analyses of thick functionally graded plates on elastic foundations.     

Bifurcation and chaos of thin circular functionally graded plate in thermal environment

A ceramic/metal functionally graded circular plate under one-term and two-term transversal excitations in the thermal environment is investigated, respectively. The effects of geometric nonlinearity and temperature-dependent material properties are both taken into account. The material properties of the functionally graded plate are assumed to vary continuously through the thickness, according to a power law distribution of the volume fraction of the constituents. Using the principle of virtual work, the nonlinear partial differential equations of FGM plate subjected to transverse harmonic forcing excitation and thermal load are derived. For the circular plate with clamped immovable edge, the Duffing nonlinear forced vibration equation is deduced using Galerkin method. The criteria for existence of chaos under one-term and two-term periodic perturbations are given with Melnikov method. Numerical simulations are carried out to plot the bifurcation curves for the homolinic orbits. Effects of the material volume fraction index and temperature on the criterions are discussed and the existences of chaos are validated by plotting phase portraits, Poincare maps. Also, the bifurcation diagrams and corresponding maximum Lyapunov exponents are plotted. It was found that periodic, multiple periodic solutions and chaotic motions exist for the FGM plate under certain conditions.     

Post buckling response of functionally graded materials plate subjected to mechanical and thermal loadings with random material properties

In this paper, the second order statistics of post buckling response of functionally graded materials plate (FGM) subjected to mechanical and thermal loading with nonuniform temperature changes subjected to temperature independent (TID) and dependent (TD) material properties is examined. Material properties such as material properties of each constituent’s materials, volume fraction index are taken as independent random input variables. The basic formulation is based on higher order shear deformation theory (HSDT) with von-Karman nonlinear kinematic using modified C⁰ continuity. A direct iterative based C⁰ nonlinear finite element method (FEM) combined with mean centered first order perturbation technique (FOPT) proposed by last two authors for the composite plate is extended for Functionally Graded Materials (FGMs) plate with reasonable accuracy to compute the second order statistics (mean and coefficient of variation) of the post buckling load response of the FGM plates. The effect of random material properties with amplitude ratios, volume fraction index, plate thickness ratios, aspect ratios, boundary conditions and types of loadings subjected to TID and TD material properties are presented through numerical examples. The performance of outlined present approach is validated with the results available in literatures and independent Monte Carlo simulation (MCS).     

Geometrically nonlinear shell finite element based on the geometry of a planar curve

An engineering approach for constructing a curved triangular finite element of a thin shell is considered. The approach is based on the assumption that the triangle sides are planar nearly circular curves before and after deformation. A geometrically nonlinear formulation of a triangular finite element of a thin Kirchhoff–Love shell is given. The predictive capabilities of the element are tested using benchmark problems of nonlinear deformation of elastic plates and shells.     

Effect of random system properties on bending response of thermo-mechanically loaded laminated composite plates

In this paper, effect of random variation in system properties on bending response of geometrically linear laminated composite plates subjected to transverse uniform lateral pressure and thermal loading is examined. System parameters such as the lamina material properties, expansion of thermal coefficients, lamina plate thickness and lateral load are modeled as basic random variables. The basic formulation is based on higher order shear deformation theory to model the system behavior of the composite plate. A C⁰ finite element method in conjunction with the first order perturbation technique procedure developed earlier by authors for the plate subjected to lateral loading is employed to obtain the second order response statistics (mean and variance) of the transverse deflection of the plate. Typical numerical results for the second order statistics of the transverse central deflection of geometrically linear composite plates with temperature independent and dependent material properties subjected to uniform temperature and combination of uniform and linearly varying temperature distribution are obtained for various combinations of geometric parameters, uniform lateral pressures, staking sequences and boundary conditions. The performance of the stochastic laminated composite model is demonstrated through comparison of mean transverse central deflection with those results available in literature and standard deviation of the deflection with an independent Monte Carlo simulation.     

Nonlinear response of shear deformable FGM curved panels resting on elastic foundations and subjected to mechanical and thermal loading conditions

This paper presents an analytical investigation on the nonlinear response of thick functionally graded doubly curved shallow panels resting on elastic foundations and subjected to some conditions of mechanical, thermal, and thermomechanical loads. Material properties are assumed to be temperature independent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of constituents. The formulations are based on higher order shear deformation shell theory taking into account geometrical nonlinearity, initial geometrical imperfection and Pasternak type elastic foundation. By applying Galerkin method, explicit relations of load-deflection curves for simply supported curved panels are determined. Effects of material and geometrical properties, in-plane boundary restraint, foundation stiffness and imperfection on the buckling and postbuckling loading capacity of the panels are analyzed and discussed. The novelty of this study results from accounting for higher order transverse shear deformation and panel-foundation interaction in analyzing nonlinear stability of thick functionally graded cylindrical and spherical panels.     

与线弹性结构连接的弹性基础圆板大挠度问题

本文处理边界与线弹性结构连接的弹性基础圆板的轴对称大挠度问题.用混合边界条件方法[1]建立了问题的确定积分方程组,并进行了简化.用摄动法给出了解答.计算了圆板与圆柱壳组合问题的例子.