弹性地基上矩形加肋板自由振动分析的无网格法

应用移动最小二乘无网格法研究弹性地基上矩形加肋板的自由振动问题。假设弹性地基与加肋板紧密接触,以弹簧模拟弹性地基,将弹性地基上的加肋板视为板与肋条组合的结构。基于一阶剪切理论,用无网格伽辽金法推出了板和肋条各自的动能与势能;再通过位移协调条件将两者的能量叠加,得到了弹性地基上整个加肋板的动能与势能。由Hamilton原理导出了弹性地基上加肋板自由振动的控制方程。采用完全转换法引入边界条件,求解自由振动方程,并编制了计算程序,给出了算例。将算例与ABAQUS有限元解及已有文献结果进行了比较分析,其相对误差均在5%以内,验证了该方法计算弹性地基上矩形加肋板结构自振频率的有效性。     

基于无网格法的弹性地基加肋斜板频率数值解

为了给实际地基工程中的经济效益提供技术指标参考,应用无网格法计算加肋斜板在地基上的自由振动行为,应用移动最小二乘近似MLS和一阶剪切变形原理描述加肋斜板的位移场,分别建立斜板与肋条的势能泛函,使用Winkler弹性地基模型处理加肋板与地基之间的接触势能。通过斜板与肋条的位移协调关系寻找斜板和肋条节点参数转换公式,确立加肋斜板的自由振动控制方程。本文运用了无网格法的优势,即使肋条位置改变也不需重置网格。与有限元解的对比验证了本文方法的有效性和精确性。     

黏弹性地基上功能梯度材料板的振动分析

为研究黏弹性地基上功能梯度材料板的自由和强迫振动特性,基于Reddy高阶剪切变形理论以及由Shen导得的广义Karman型方程,用双重Fourier级数法推导了三参数黏弹性地基上四边简支功能梯度材料板自由振动和动力响应的解析解,计算了各模态自振频率和半波冲击载荷作用下的动力响应,讨论了材料组分指数、黏弹性地基参数、边厚比等因素对自由振动和动力响应的影响.结果表明,黏弹性地基的剪切和压缩刚度显著提升了功能梯度材料板的振动频率,减小了动力响应;另外,地基的黏性对振动频率和动力响应也有一定的影响.     

黏弹性地基上石墨烯增强功能梯度矩形板的自由振动和动力响应

考虑黏弹性地基的影响,基于复合材料薄板理论建立了石墨烯增强功能梯度矩形薄板的运动方程,用Galerkin法和龙格库塔法求解其自振频率和动力响应,分析了地基参数、石墨烯含量和分布对自振频率和动力响应的影响.结果表明:黏弹性地基的剪切和压缩刚度提高了板的自振频率,减小了动力响应;地基黏性降低了板的自振频率和动力响应;在石墨...     

弹性地基上含孔隙功能梯度材料板的自由振动和动力响应

为研究弹性地基上含孔隙的材料特性沿厚度呈Sigmoid函数变化的功能梯度材料(S-FGM)板的振动特性,本文基于改进的Voigt模型,分别建立了孔隙为均匀分布和非均匀分布两种类型的功能梯度材料的物性参数模型.根据复合材料薄板理论导出了弹性地基上含孔隙的功能梯度材料板的运动方程,用伽辽金法寻求四边简支边界条件下板自由振动...     

Green函数法解非均匀弹性地基板的自由振动

把板在特定域中的Green函数当作影响函数,根据实际板的边界条件首先求出虚拟域中的Green函数“源”,继而确定板内任意点的挠度及内力。在板的振动问题中及板的分布惯性力的影响后就可得到其自振频率的本征方程,从而计算出其各阶自振频率的值。文中附有算例,并把其计算结果与已有解析解作了比较,表明它们之间具有良好的吻合。     

基于遗传算法的弹性地基加肋板肋梁无网格优化分析

基于遗传算法及一阶剪切理论, 提出一种弹性地基上加肋板肋条位置优化的无网格方法. 首先, 通过一系列点来离散平板及肋条, 并用弹簧模拟弹性地基, 从而得到加肋板的无网格模型; 其次, 基于一阶剪切理论及移动最小二乘近似原理导出位移场, 求出弹性地基加肋板总势能; 再次, 根据哈密顿原理导出结构的弯曲控制方程, 并通过完全转换法处理边界条件; 最后, 引入遗传算法和改进遗传算法, 以肋条的位置为设计变量、弹性地基板的中心点挠度最小值为目标函数, 对肋条位置进行优化达到地基板控制点挠度最小的目的. 以不同参数、载荷布置形式的弹性地基加肋板为例, 与ABAQUS有限元结果及文献解进行比较. 研究表明, 采用所提出的无网格模型可有效求解弹性地基上加肋板弯曲问题, 结果易收敛, 同时基于遗传算法与改进混合遗传算法所提出的无网格优化方法均可有效优化弹性地基加肋板肋条位置, 后者计算效率相对较高, 只进行了三次迭代便可获得稳定的最优解, 此外在优化过程中肋条位置改变时只需要重新计算位移转换矩阵, 又避免了网格重构.      

基于遗传算法的弹性地基加肋板肋梁无网格优化分析

基于遗传算法及一阶剪切理论,提出一种弹性地基上加肋板肋条位置优化的无网格方法.首先,通过一系列点来离散平板及肋条,并用弹簧模拟弹性地基,从而得到加肋板的无网格模型;其次,基于一阶剪切理论及移动最小二乘近似原理导出位移场,求出弹性地基加肋板总势能;再次,根据哈密顿原理导出结构的弯曲控制方程,并通过完全转换法处理边界条件;最后,引入遗传算法和改进遗传算法,以肋条的位置为设计变量、弹性地基板的中心点挠度最小值为目标函数,对肋条位置进行优化达到地基板控制点挠度最小的目的.以不同参数、载荷布置形式的弹性地基加肋板为例,与ABAQUS有限元结果及文献解进行比较.研究表明,采用所提出的无网格模型可有效求解弹性地基上加肋板弯曲问题,结果易收敛,同时基于遗传算法与改进混合遗传算法所提出的无网格优化方法均可有效优化弹性地基加肋板肋条位置,后者计算效率相对较高,只进行了三次迭代便可获得稳定的最优解,此外在优化过程中肋条位置改变时只需要重新计算位移转换矩阵,又避免了网格重构.     

轴对称自由振动功能梯度材料微圆板中的热弹性阻尼

基于经典弹性薄板理论和单向耦合热传导理论,研究了材料性质沿厚度连续变化的功能梯度微圆板的热弹性阻尼特性．首先,考虑热力耦合效应,建立了功能梯度微圆板轴对称横向自由振动微分方程．然后,忽略温度梯度在面内的变化,建立了单向耦合变系数一维热传导方程．采用分层均匀化近似方法,将变系数热传导方程转化为一系列常系数的微分方程,利用上下表面的热边界条件和层间连续性条件获得了微圆板温度场解析解．将所得温度场代入微圆板的自由振动微分方程,得到了包含热弹性阻尼的复频率,从而获得了反映热弹性阻尼水平的逆品质因子．最后,针对材料性质沿板厚按幂函数变化的陶瓷-金属功能梯度微圆板,定量地分析材料梯度指数、几何尺寸、边界条件、温度环境等对微圆板热弹性阻尼的影响．     

功能梯度矩形板的三维弹性分析

将功能梯度三维矩形板的位移变量按双三角级数展开，以弹性力学的平衡方程为基础．导出位移形式的平衡方程。引入状态空间方法，以三个位移分量及位移分量的一阶导数为状态变量，建立状态方程。考虑四边简支的边界条件，由状态方程得到了功能梯度三维矩形板的静力弯曲问题和自由振动问题的精确解。由给出的均匀矩形板自由振动问题的计算结果表明．与已有的理论解以及有限元方法的计算结果相吻合。假设功能梯度三维矩形板的材料常数沿板的厚度方向按照指数函数的规律变化．进一步给出了功能梯度三维矩形板的自由振动问题和静力弯曲问题的算例分析，并讨论了材料性质的梯度变化对板的动力响应和静力响应的影响。     

Three-dimensional free vibration analysis of multi-directional functionally graded piezoelectric annular plates on elastic foundations via state space based differential quadrature method

The three-dimensional free vibration analysis of a multi-directional functionally graded piezoelectric(FGP) annular plate resting on two parameter(Pasternak)elastic foundations is investigated under different boundary conditions. The material properties are assumed to vary continuously along the radial and thickness directions and have exponent-law distribution. A semi-analytical approach named the state space based differential quadrature method(SSDQM) is used to provide an analytical solution along the thickness using the state space method(SSM) and an approximate solution along the radial direction using the one-dimensional differential quadrature method(DQM).The influence of the Winkler and shear stiffness of the foundation, the material property graded variations, and the circumferential wave number on the non-dimensional natural frequency of multi-directional FGP annular plates is studied.     

基于无网格法的非均匀弹性地基上变厚度加筋板弯曲与固有频率分析

采用基于移动最小二乘近似的无网格方法并结合一阶剪切变形理论,分析了非均匀弹性地基上变厚度加筋板的弯曲和固有频率问题.首先,用节点对变厚度板和筋条分别进行离散,导出变厚度板和筋条的势能;其次,利用筋条与变厚度板之间的位移协调条件将筋条的节点参数转换为板的节点参数,再将两者的势能进行叠加得到变厚度加筋板的总势能,并根据能量...     

Winkler地基模型上功能梯度材料涂层的摩擦接触问题

研究Winker地基模型上功能梯度材料涂层在一刚性圆柱形冲头作用下的摩擦接触问题。功能梯度材料涂层表面作用有法线向和切线向集中作用力。假设材料非均匀参数呈指数形式变化,泊松比为常量,利用Fourier积分变换技术将求解模型的接触问题转化为奇异积分方程组,再利用切比雪夫多项式对所得奇异积分方程组进行数值求解。最后,给出了功能梯度材料非均匀参数、摩擦系数、Winker地基模型刚度系数及冲头曲率半径对接触应力分布和接触区宽度的影响情况。     

Closed-form solutions for free vibration of rectangular FGM thin plates resting on elastic foundation

This article presents closed-form solutions for the frequency analysis of rectangular functionally graded material(FGM) thin plates subjected to initially in-plane loads and with an elastic foundation. Based on classical thin plate theory, the governing differential equations are derived using Hamilton's principle. A neutral surface is used to eliminate stretching–bending coupling in FGM plates on the basis of the assumption of constant Poisson's ratio. The resulting governing equation of FGM thin plates has the same form as homogeneous thin plates. The separation-ofvariables method is adopted to obtain solutions for the free vibration problems of rectangular FGM thin plates with separable boundary conditions, including, for example, clamped plates. The obtained normal modes and frequencies are in elegant closed forms, and present formulations and solutions are validated by comparing present results with those in the literature and finite element method results obtained by the authors. A parameter study reveals the effects of the power law index n and aspect ratio a/b on frequencies.     

功能梯度石墨烯增强复合材料板的自由振动

基于高阶函数剪切变形板理论,研究了可移动简支边界条件下功能梯度石墨烯增强复合材料板的自由振动。利用修正的Halpin-Tsai模型估计了复合材料的等效杨氏模量。基于Hamilton原理构建其偏微分方程。通过Navier方法计算得到了板的量纲为一的频率,并与已有成果进行了比较,验证了本文计算模型的优越性。数值计算结果表明:功能梯度石墨烯增强复合材料板的量纲为一的基频受石墨烯小块的分布模式影响很大,随着石墨烯含量的增加而单调增加;固定石墨烯小块的厚度和长宽比,量纲为一的基频随着长厚比的增加而单调增加。     

Three-dimensional elastostatic solutions for transversely isotropic functionally graded material plates containing elastic inclusion

Based on the generalized England-Spencer plate theory, the equilibrium of a transversely isotropic functionally graded plate containing an elastic inclusion is studied. The general solutions of the governing equations are expressed by four analytic functions α(ζ), β(ζ), φ(ζ), and ψ(ζ) when no transverse forces are acting on the surfaces of the plate. Axisymmetric problems of a functionally graded circular plate and an infinite func-tionally graded plate containing a circular hole subject to loads applied on the cylindrical boundaries of the plate are firstly investigated. On this basis, the three-dimensional (3D) elasticity solutions are then obtained for a functionally graded infinite plate containing an elastic circular inclusion. When the material is degenerated into the homogeneous one, the present elasticity solutions are exactly the same as the ones obtained based on the plane stress elasticity, thus validating the present analysis in a certain sense.     

Free vibration of functionally graded sandwich plates using four-variable refined plate theory

This paper uses the four-variable refined plate theory (RPT) for the free vibration analysis of functionally graded material (FGM) sandwich rectangular plates.Unlike other theories, there are only four unknown functions involved, as compared to five in other shear deformation theories. The theory presented is variationally consistent and strongly similar to the classical plate theory in many aspects. It does not require the shear correction factor, and gives rise to the transverse shear stress variation so that the transverse shear stresses vary parabolically across the thickness to satisfy free surface conditions for the shear stress. Two common types of FGM sandwich plates are considered, namely, the sandwich with the FGM facesheet and the homogeneous core and the sandwich with the homogeneous facesheet and the FGM core. The equation of motion for the FGM sandwich plates is obtained based on Hamilton's principle. The closed form solutions are obtained by using the Navier technique. The fundamental frequencies are found by solving the eigenvalue problems. The validity of the theory is shown by comparing the present results with those of the classical, the first-order, and the other higher-ordex theories. The proposed theory is accurate and simple in solving the free vibration behavior of the FGM sandwich plates.     

Unified two-phase nonlocal formulation for vibration of functionally graded beams resting on nonlocal viscoelastic Winkler-Pasternak foundation

A nonlocal study of the vibration responses of functionally graded (FG) beams supported by a viscoelastic Winkler-Pasternak foundation is presented. The damping responses of both the Winkler and Pasternak layers of the foundation are considered in the formulation, which were not considered in most literature on this subject, and the bending deformation of the beams and the elastic and damping responses of the foundation as nonlocal by uniting the equivalently differential formulation of well-posed strain-driven (ε-D) and stress-driven (σ-D) two-phase local/nonlocal integral models with constitutive constraints are comprehensively considered, which can address both the stiffness softening and toughing effects due to scale reduction. The generalized differential quadrature method (GDQM) is used to solve the complex eigenvalue problem. After verifying the solution procedure, a series of benchmark results for the vibration frequency of different bounded FG beams supported by the foundation are obtained. Subsequently, the effects of the nonlocality of the foundation on the undamped/damping vibration frequency of the beams are examined.