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基于刚性板的小挠度理论,考虑混凝土的材料非线性,推导了双参数弹性地基上混凝土矩形薄板热弹性问题的动力方程。采用级数法,导出了热环境下双参数弹性地基上四边简支混凝土矩形薄板的固有频率计算公式和强迫振动下的挠度函数。为便于工程应用,给出了双参数弹性地基上四边简支混凝土矩形薄板在恒向变温和温度均匀变化时的固有频率和均布荷载作用下的挠度函数。针对Winlder弹性地基的情况,讨论了板的材料弹性常数、几何尺寸(长宽比)、相对厚度、刚度系数k和温度对薄板固有频率和挠度函数的影响,从而为工程结构中热环境下弹性地基上混凝土矩形薄板的振动计算提供了理论依据。 相似文献
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弹性基支自由边矩形板的非线性振动问题 总被引:2,自引:0,他引:2
弹性地基上四边自由矩形板的非线性振动分析是板理论中一个相当困难的问题,到目前为止这个问题还没有得到解决。本文首先给出一个包含三角函数和多项式组成的挠度函数和应力函数,这些函数满足在四个自由边上的全部边界条件。然后利用伽辽金法得到Dufing方程。 相似文献
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针对含集中质量的离散固支弹性板基波频率的求解问题,采用小挠度弹性板变形理论与Rayleigh-Ritz能量法,建立含多集中质量弹性板的振动能量方程及其模态方程。结合弹性板的离散点固支边界条件,完成离散固支弹性板的基波振型函数的解析描述,并利用能量极值法,完成随着集中质量大小与位置变化的离散固支弹性板基波振型函数插值系数及其基波频率的解析。以不含集中质量离散固支弹性板为特例求解,与有限元分析计算结果相比对,验证求解离散固支弹性板基波频率方法的可行性。此外,以含两个集中质量的矩形弹性板为计算实例,完成了集中质量大小以及位置变化的基波振型函数插值系数k及其振型函数、基波频率f的曲面描述与分析。上述解析分析方法可为工程电路板PCB的动态设计提供了可行的理论分析方法。 相似文献
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形状记忆合金纤维正交各向异性层合矩形板的非线性弯曲振动 总被引:3,自引:0,他引:3
研究了形状记忆合金(SMA)纤维混杂复合材料大挠度层合板的非线性自由与受迫振动特性。基于描述SMA力学行为的Brinson理论以及层合板材料性能预测的混合率, 建立了SMA纤维混杂复合材料大挠度层合板的本构方程, 基于对称层合各向异性弹性板的非线性理论, 建立了以横向挠度和应力函数表示的板的横向振动方程和相容方程。采用Galerkin近似解法将振动方程化为时间变量的含有三次非线性项的Duffing型常微分方程, 采用谐波平衡法(HBM)获得系统的固有频率方程和强迫振动稳态频率响应方程。数值计算表明: 非线性板自由振动频率比与激励温度的关系具有与线性板相同的特征, 马氏体相向奥氏体相转变阶段温度对板的振动频响特性曲线的影响最显著, 同时也讨论了SMA纤维含量、 板的纵横比以及自由振动幅值对板的非线性频率比的影响。 相似文献
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弹性地基上自由矩形板的非线性动静态分析 总被引:20,自引:2,他引:18
弹性地基上四边自由矩形板动力和静力问题的非线性分析是板理论中的一个特别困难的问题。至今为止,这个问题还没有解决。 本文首先选择由三角函数和多项式组成的挠度函数和应力函数。这些函数满足四个自由边界上的边界条件,然后利用伽辽金方法得到Duffing方程。文中最后给出了算例。 相似文献
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Soumen Shaw 《International Journal for Computational Methods in Engineering Science and Mechanics》2019,20(1):64-71
In this note, deflection of a thin rectangular isotropic micropolar plate is observed under the influence of transverse loading. From the properties of asymptotic solution, a set of hypotheses is considered and the corresponding governing equations of bending are derived. The solutions are validated by comparing the numerical results and with their counterparts reported in literature for classical Timoshenko plate theory and the Kirchhoff’s theory of plate deformation. 相似文献
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基于解析试函数的各向异性材料厚薄通用板单元 总被引:1,自引:1,他引:0
该文采用满足Kirchhoff假设的薄板理论,推导了各向异性材料系列解析试函数,并利用该系列解析试函数构造了一个四边形应力杂交板单元。首先,该文从薄板理论的基本方程出发,推导了各向异性材料薄板中面挠度w应满足的特征微分方程。然后,从该方程出发求得w的系列特征通解,由w特征通解可进一步求得广义位移、广义应变和广义应力的解析试函数。同时,根据广义应力利用平衡条件构造了相应的横向剪力解析试函数。最后,根据已有的广义应力和横向剪力解析试函数构造了一个四边形应力杂交板单元ATF-PH4。数值算例表明:上述方法构造出的单元模型有很好的精度、收敛性,且对网格畸变不敏感,同时能较好地解决板单元的厚薄通用性问题。 相似文献
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While the expansion formula for displacements and the hypothesis that the material parameters can vary along the thickness direction in an arbitrary fashion are retained, the plate theory of functionally graded materials suggested by Mian and Spencer is extended in this paper in two aspects. First, the material is assumed to be transversely isotropic, rather than isotropic. Second, the tractions-free conditions on the top and bottom surfaces are replaced by the conditions of uniform loads applied on the surfaces. The governing equations are derived rigorously, which are expressed in terms of three components of the mid-plane displacement. The mid-plane deflection satisfies a fourth-order partial differential equation, which is similar to that in the classical plate theory (CPT). The two in-plane displacements satisfy two second-order partial differential equations and are coupled with the mid-plane deflection. Boundary conditions are expressed in the form of those adopted in the CPT. Three-dimensional elasticity solutions are presented for a uniformly loaded rectangular plate with two opposite edges simply supported and six different types of supports at the other two edges. Numerical results are given for a simply supported functionally graded plate, and good agreement with exact solutions is obtained. 相似文献
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By assuming a kinematically admissible, time-dependent velocity field and considering the global equilibrium of all the forces acting on each rigid segment during large deflection of a plate, a complete theoretical investigation is undertaken herein to trace the large deflection dynamic plastic response (including the transient phase) of simply-supported or fully-clamped rectangular plates. This procedure deduces two modifying factors ƒ1 and ƒ2 which reflect the effect of the membrane forces and are employed to formulate the governing equations in the case of large deflections. The present prediction of the final plate deflection coincides excellently with the corresponding experimental results for deflections up to 5–10 times the plate thickness. This theory greatly improves the estimates based on the bending-only theory and provides a new way to trace the transient phase of dynamically loaded plates when the effect of membrane forces is significant. 相似文献
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In this study, the nonlinear thermo-elastic bending analysis of a functionally graded carbon nanotube-reinforced composite plate resting on two parameter elastic foundations is investigated. The material properties of the carbon nanotube-reinforced composite plates are assumed to be temperature dependent and graded in the thickness direction. The nonlinear formulations are based on a first-order shear deformation plate theory and large deflection von Karman equations. A dynamic relaxation method is employed to solve the plate nonlinear partial differential equations. The effects of volume fraction of carbon nanotubes, thermal gradient, temperature dependency, elastic foundation, boundary conditions, plate width-to-thickness ratio, aspect ratio, and carbon nanotubes distribution are studied in detail. 相似文献
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This article investigates the bending response of an orthotropic rectangular plate resting on two-parameter elastic foundations. Analytical solutions for deflection and stresses are developed by means of the simple and mixed first-order shear deformation plate theories. The present mixed plate theory accounts for variable transverse shear stress distributions through the thickness and does not require a shear correction factor. The governing equations that include the interaction between the plate and the foundations are obtained. Numerical results are presented to demonstrate the behavior of the system. The results are compared with those obtained in the literature using three-dimensional elasticity theory or higher-order shear deformation plate theory to check the accuracy of the simple and mixed first-order shear deformation theories. 相似文献
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The effects of three-parameter elastic foundations and thermo-mechanical loading on axisymmetric large deflection response of a simply supported annular FGM plate are investigated. An annular FGM plate, resting on a three-parameter elastic foundation under a transverse uniform loading and a transverse non-uniform temperature, is considered. The mechanical and thermal properties of the FGM plate are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The mathematical modeling of the plate and the resulting nonlinear governing equations of equilibrium are derived based on the first-order shear deformation theory (FSDT) in conjunction with nonlinear von Karman assumptions. A polynomial-based differential quadrature method is used as a simple but powerful numerical technique to discretize the nonlinear governing equations and to implement the boundary conditions. Finally, the effects of certain parameters, such as nonlinear foundations stiffness, volume fraction index, and temperature, on the axisymmetric large deflection response of the FGM plate are obtained and discussed in detail. 相似文献
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Thermal post-buckling and flutter characteristics of composite plates embedded with shape memory alloy fibers 总被引:4,自引:0,他引:4
It is investigated that the composite plate embedded with shape memory alloy (SMA) fibers is subject to the aerodynamic and thermal loading in the supersonic region. The nonlinear finite element equations based on the first-order shear deformation plate theory (FSDT) are formulated for the laminated composite plate embedded with SMA fibers (SMA composite plate). The von Karman strain–displacement relation is used to account for the large deflection. The incremental method considering the influence of the initial deflections and initial stresses is adopted for the temperature-dependent material properties of SMA fibers and composite matrix. The first-order piston theory is used for modeling aerodynamic loads. This study shows the effect of the SMA on the critical temperature, thermal post-buckling deflection, natural frequency and critical dynamic pressure of the SMA composite plate. 相似文献
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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. 相似文献