弹性浮板在周期集中载荷作用下的水弹性响应

基于线性水波理论和Mindlin厚板动力学理论,采用Wiener-Hopf方法,研究了水面上浮动弹性平板受周期集中载荷作用下的水弹性响应。流体被假设为不可压理想且等深,流动有势。首先分析求解了两种区域(自由水面下区域和浮板下区域)内等深流场的导波问题。而后将原来混合边值问题的求解归结为求解无穷线性代数方程组的问题。其次,采用该方法研究了三种周期集中载荷激励下浮板上挠度和动弯矩幅值的分布情况;最后,对浮板上挠度幅值分布与不同周期载荷的作用点的关系进行了研究。     

横向均布载荷下亚音速大挠度薄板的混沌运动

研究了亚音速气动力与横向均布周期载荷共同作用下,四边简支大挠度板的混沌运动.采用yon Karman板大变形理论与Hamilton变分原理,建立亚音速下大挠度板的运动方程,采用Lyapunov指数方法分析板从周期运动到混沌运动的来流速度阈值,应用四阶Runge-Kutta法对运动方程进行数值求解,计算系统的分岔图、位移时间历程曲线、相图和Poincaré映射,并与Lyapunov指数方法所得结果进行比较.研究结果表明,Lyapunov指数方法可以有效地判断出系统从周期运动到混沌运动的来流速度阈值,当来流速度达到速度阈值时,板由周期运动转化为混沌运动.     

轴向运动大挠度板的非线性动力学行为

该文研究了受周期激励轴向运动大挠度板横向振动的稳定性及分岔现象。在von Kàrmàn非线性大挠度板理论基础上,利用达朗贝尔原理建立系统的动力学模型。通过Galerkin截断,将时间变量和空间变量、位移函数和应力函数耦合在一起的偏微分方程离散,得到系统运动常微分方程。利用数值方法分析板随轴向运动速度、外激励力幅值、长宽比和轴向拉力变化时的运动分岔行为。利用最大Lyapunov指数和Poincaré映射图识别系统的动力学行为。结果发现,当板的某些参数变化时,系统出现分岔现象。不同参数时,系统呈现周期运动、倍周期运动、概周期运动,甚至混沌运动。     

集中载荷下四边固支正交各向异性矩形板的线性弯曲问题

采用载荷叠加法将集中载荷下四边固支正交各向异性矩形板线性弯曲的挠度分为3个部分:集中载荷下四边简支板的挠度、上下边简支左右边受弯矩的板的挠度、左右边简支上下边受弯矩的板的挠度,3个挠度之和在满足固支边界条件的情况下即为所要求的挠度的解。采用MATLAB软件编写程序进行计算,并将相同长宽的板在4种不同的厚度和载荷情况下的挠度计算结果与有限元分析结果进行比较,验证了解析解的正确性。最后讨论了经典的Kirchhoff薄板假设对于集中载荷的适用性问题。     

轴向变速运动大挠度薄板的非线性动力学行为

研究轴向变速运动大挠度薄板横向振动的稳定性及分岔现象。在von Kàrmàn非线性大挠度板理论基础上, 利用达朗贝尔原理建立系统的动力学模型。通过Galerkin截断, 将时间变量和空间变量、位移函数和应力函数耦合在一起的偏微分方程离散, 得到系统运动常微分方程。利用数值方法分析板随平均速度、速度脉动幅值和外激励力变化时的运动分岔行为。利用最大Lyapunov指数和Poincaré映射图识别系统的动力学行为。结果发现, 当板的某些参数变化时, 系统出现分岔现象。不同参数时, 系统呈现周期运动、倍周期运动、概周期运动, 甚至混沌运动。     

双模量矩形板的大挠度弯曲计算分析

双模量矩形板在外载荷作用下,会形成各向同性的拉伸区和压缩区,把双模量矩形板看成两种各向同性材料组成的层合板,采用弹性力学理论建立了双模量矩形板在外载荷作用下的静力平衡方程,利用静力平衡方程确定了双模量矩形板的中性面位置,推导出了双模量矩形板的大挠度弯曲变形微分方程。用加权残值法求得了双模量矩形板的大挠度弯曲变形时板中点挠度,把该方法计算结果与有限元计算结果进行了比较,说明了该计算方法是可靠的,并讨论分析了双模量对矩形板大挠度弯曲变形的影响。     

高阶剪切变形板理论下FG-GRC板的屈曲和弯曲分析

基于三阶剪切变形板理论(TSDPT)和正弦剪切变形板理论(SSDPT),研究了功能梯度石墨烯增强复合材料(FG-GRC)板的屈曲和弯曲行为,并通过与一阶剪切变形板理论(FSDPT)计算结果的比较,分析了TSDPT、SSDPT与FSDPT在FG-GRC板屈曲和弯曲力学行为研究过程中的差异。材料的有效杨氏模量通过修正的Halpin-Tsai微观力学模型估算,有效泊松比通过混合律确定。利用最小势能原理推导出了包含五个未知量的控制方程,并获得了简支FG-GRC矩形板弯曲挠度和临界屈曲载荷Navier形式的解析解。数值结果表明：与TSDPT和SSDPT相比,FSDPT明显高估了FG-X型FG-GRC板的临界屈曲载荷而明显低估了其弯曲挠度,且略微低估了FG-O型FG-GRC板的临界屈曲载荷而略微高估了其弯曲挠度,而UD型和FG-A型FG-GRC板在三种理论下的计算结果几乎完全一致;TSDPT和SSDPT在计算FG-GRC板的弯曲挠度和临界屈曲载荷时结果十分相近;当板的总层数NL小于10层～15层时,弯曲载荷比率和临界屈曲载荷比率的变化非常显著,当总层数NL超过10层～15层时,弯曲载荷比率和临界屈...     

双模量面板泡沫铝芯夹层圆板的非线性弯曲

采用弹性理论建立了双模量面板泡沫铝芯圆形夹层板在均布载荷作用下的静力平衡方程,利用静力平衡方程确定了夹层板的中性面位置。在考虑剪切变形影响的基础上,采用能量法研究了双模量面板泡沫铝芯圆形夹层板的轴对称非线性弯陆问题,求得了夹层板中心挠度与均布载荷的关系式,并把该方法计算结果与有限元计算结果进行了比较,验证了该方法是可靠...     

木托盘受力性能理论分析及有限元模拟

目的对木托盘静载堆码时的力学性能进行理论分析和有限元模拟。方法建立木托盘顶铺板和纵梁板的力学模型,通过理论计算获得选用松木和杨木LVL 2种不同材料时的最大应力和最大挠度;按国家标准建立木托盘有限元模型,进行网格划分、施加载荷和约束后,获得选用松木和杨木LVL 2种不同材料时的最大等效应力值和最大变形量,并与理论分析结果进行对比。结果理论分析和有限元分析结果规律一致,最大应力均出现在中间纵梁板上,最大变形均发生在顶铺板上,且数值差距较小,2种分析方法均合理可行。结论该研究为木托盘的性能分析提供了有效的方法。     

考虑裂纹效应的弹性板振动分析模型

针对含裂纹板的动力学问题,提出了一种耦合裂纹效应的弹性板动力学建模方法。该方法依据变形等效原则用虚拟外部载荷代替裂纹作用,并通过力学平衡原理建立了耦合裂纹项的弹性板运动方程,且基于Rice和Levy应力关系式推导出裂纹项表达式;在此基础上,结合Galerkin法和Berger经验,把含裂纹弹性板振动系统简化成一单自由度非线性振动模型进行动力学特性分析。通过算例探讨了裂纹尺度、阻尼以及激励力位置对弹性板振动特性的影响。结论表明,裂纹尺度和板尺寸对振动非线性作用明显,动应力幅值受阻尼与激励力位置的控制。     

Nonlinear behavior of functionally graded circular plates with various boundary supports under asymmetric thermo-mechanical loading

The equilibrium equations of the first-order nonlinear von Karman theory for FG circular plates under asymmetric transverse loading and heat conduction through the plate thickness are reformulated into those describing the interior and edge-zone problems of the plate. A two parameter perturbation technique, in conjunction with Fourier series method is used to obtain analytical solutions for nonlinear behavior of functionally graded circular plates with various clamped and simply-supported boundary conditions. The material properties are graded through the plate thickness according to a power-law distribution of the volume fraction of the constituents. The results are verified with known results in the literature. The load–deflection curves for different loadings, boundary conditions, and material constant in a solid circular plate are studied and discussed. It is shown that the behavior of FG plates with clamped or simply-supported boundary conditions are completely different. Under thermo-mechanical loading, snap-through buckling behavior is observed in simply-supported FG plates which are immovable in radial direction. Moreover, it is found that linear theory is inadequate for analyzing FG and also homogenous plates with immovable boundary supports in radial direction and subjected to thermal loading, even for deflections that are normally considered small.     

磁弹性板的精化理论

将Cheng精化理论推广到磁弹性板的研究中,对磁弹性板进行了精确的分析。从Huang和Wang给出的线性软磁材料的位移通解出发,利用中面上位移及其沿板厚方向的梯度,将板内的位移表示出来,并获得板内应力张量。利用Pao和Yeh给出的线性边界条件和Lur’e算子方法,给出磁弹性板的精化理论。其中挠度方程略去高阶项后,与磁弹性薄板的挠度方程一致。     

Large deflection behavior of functionally graded plates under pressure loads

Large deflection analysis of rectangular functionally graded plates is studied in this paper. It is assumed that the mechanical properties of the plate, graded through the thickness, are described by a simple power law distribution in terms of the volume fractions of constituents. The plate is assumed to be under pressure load. The fundamental equations for rectangular plates of FGM are obtained using the Von-Karman theory for large deflection and the solution is obtained by minimization of the total potential energy. Numerical results for rectangular functionally graded plates are given in dimensionless graphical forms. The effects of material properties on the stress field through the thickness are determined and discussed.     

含周期性裂纹正交各向异性板平面问题的应力场分析

通过引入适当的Westergaard应力函数,采用复变函数方法和待定系数法对含周期性裂纹正交各向异性纤维增强复合材料板的Ⅰ 型、Ⅱ型问题中裂纹尖端附近的应力场进行了力学分析。在远处对称载荷与斜对称载荷作用下,先给出Ⅰ型、Ⅱ型问题在裂纹尖端处的应力强度因子,然后导出用应力强度因子表示的Ⅰ型、Ⅱ型裂纹问题应力场的解析表达式。此外,应力场大小与材料常数有关,这是正交各向异性材料不同于各向同性材料的特征。由于裂纹的周期分布,应力强度因子的大小取决于形状因子。结果表明,形状因子随着裂纹长度的增加而增大,随着裂纹间距的增大而逐渐下降,当裂纹间距趋于无穷大时,退化为含单个中心裂纹正交各向异性纤维增强复合材料板的结果。      

Static and free vibrational analysis of beams and plates by differential quadrature method

Summary The new approach for application of boundary conditions in the differential quadrature (DQ) method, proposed earlier by the present authors, is extended to generalized force boundary conditions in two dimensions. A variety of problems is then analyzed by theDQ method with the new approach for application of boundary conditions, such as deflections of beams and circular and rectangular plates under nonuniformly distributed loadings, deflection of a rectangular plate on a Winkler foundation, and buckling and free vibrational analyses of circular plates. It is found that the present method gives good accuracy and is computationally efficient. Exact solutions can be obtained by theDQ method if analytical solutions are polynomials and the method is insensitive to the spacing of grid points for the cases considered.     

Mathematical analysis of flexural vibrations of inhomogeneous rectangular plates and beams subjected to cyclic loadings of temperature change and external force

Flexural vibrations of rectangular plates and beams which consist of functionally inhomogeneous materials due to cyclic loadings of external force and temperature change are analyzed mathematically. Effects of aspect ratio of rectangular plates and loading frequency on the interference between the flexural vibration due to cyclic loading and that due to cyclic heating are discussed. The amplification factor in the dynamic behavior to the quasi-static one is also studied. Especially, comparing transient responses in flexural vibration of rectangular plates with those of beams, the difference in the amplifications of out-of-plane deflection and stresses between plates and beams is discussed.     

余弦分布压力下矩形薄板的屈曲

针对不同支承条件,两对边受半余弦非线性分布压力下弹性矩形薄板的屈曲问题,进行了分析研究。对于只产生对称变形的矩形薄板,基于辛弹性力学的平面矩形域理论,给出了精确的面内应力分布。运用Galerkin法分析计算了半余弦分布压力下矩形薄板的屈曲载荷。根据各种不同支承矩形薄板弯曲的位移边界条件,借助于符号运算软件Maple,编写了相应的用户计算程序。对九种不同支承组合下的弹性矩形薄板进行了计算,得到了不同长宽比矩形薄板的屈曲载荷系数。通过与已有文献结果的比较表明,该文求解方法是有效和精确的。基于所给出的结果,可望为解决矩形薄板在非线性分布载荷下的屈曲分析提供一种新的研究方法。     

A meshfree radial point interpolation method for analysis of functionally graded material (FGM) plates

A meshfree model is presented for the static and dynamic analyses of functionally graded material (FGM) plates based on the radial point interpolation method (PIM). In the present method, the mid-plane of an FGM plate is represented by a set of distributed nodes while the material properties in its thickness direction are computed analytically to take into account their continuous variations from one surface to another. Several examples are successfully analyzed for static deflections, natural frequencies and dynamic responses of FGM plates with different volume fraction exponents and boundary conditions. The convergence rate and accuracy are studied and compared with the finite element method (FEM). The effects of the constituent fraction exponent on static deflection as well as natural frequency are also investigated in detail using different FGM models. Based on the current material gradient, it is found that as the volume fraction exponent increases, the mechanical characteristics of the FGM plate approach those of the pure metal plate blended in the FGM.