共查询到17条相似文献,搜索用时 109 毫秒
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提出了一种求解矩形加肋板线性弯曲问题的移动最小二乘无网格法。将矩形加肋板模拟成平板与肋条组成的复合结构。先基于一阶剪切变形理论,由移动最小二乘近似建立板和肋条的位移场,再利用板与肋条叠合处的位移协调条件,推导肋条与板的节点参数转换方程,最后利用此方程将板与肋条的应变能叠加,推导出整个加肋板的刚度方程。由于本文提出的加肋板无网格模型中不涉及到网格,肋条不必像有限元那样必须沿网格线布置,肋条位置的改变也不会导致板网格的重新划分。文末算例表明由本文方法得到的解与采用实体单元得到的ANSYS有限元解吻合良好,证明了本文方法的准确性。 相似文献
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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. 相似文献
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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. 相似文献
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在加肋板无网格模型中, 肋条的位置对各种工况下加肋板受力性能的影响至关重要. 文章基于一阶剪切变形和移动最小二乘法理论提出一种考虑非线性影响的加肋板无网格模型, 并利用遗传算法优化肋条位置. 首先, 采用离散节点分别对平板和肋条进行离散, 得到加肋板的无网格离散模型; 其次, 通过冯·卡门大挠度理论得到非矩形板几何非线性问题的弯曲控制方程; 再次, 通过哈密顿原理得到加肋非矩形板自由振动问题的控制方程; 最后引入遗传算法, 以肋条的位置为设计变量、非矩形加肋板中心点挠度最小或自振频率最大为目标函数, 对肋条位置进行优化. 在考虑了几何非线性影响的肋条位置优化过程中, 肋条位置改变时只需重新计算位移转换矩阵, 避免了网格重构. 本文以全局荷载下单肋条菱形板为例与理论解进行对比, 进行有效性验证. 再以板的中点挠度最小和自振频率最大为优化目标, 对局部荷载作用下不同形状、不同肋条布置方式的加肋板进行优化, 分析方法的收敛性及稳定性. 相似文献
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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。 相似文献
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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,并根据能量法得到其动能;最后,利用最小势能原理及Hamilton原理分别得到弯曲控制方程与振动控制方程.由于采用的方法不能直接施加位移边界,故采用完全转换法处理位移边界.本文先计算变厚度板的弯曲及非均匀弹性地基板的固有频率,与文献对比验证方法的有效性;然后对非均匀弹性地基上变厚度加筋板弯曲与 自由振动进行了计算,并将计算结果与有限元结果进行了对比.结果表明,本文方法计算所得结果与文献解及有限元结果之间的误差均小于5%,验证了该方法在计算非均匀弹性地基上变厚度加筋板弯曲与固有频率问题的有效性. 相似文献
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Thermoelastic buckling behavior of thick rectangular plate made of functionally graded materials is investigated in this article.
The material properties of the plate are assumed to vary continuously through the thickness of the plate according to a power-law
distribution. Three types of thermal loading as uniform temperature raise, nonlinear and linear temperature distribution through
the thickness of plate are considered. The coupled governing stability equations are derived based on the Reddy’s higher-order
shear deformation plate theory using the energy method. The resulted stability equations are decoupled and solved analytically
for the functionally graded rectangular plates with two opposite edges simply supported subjected to different types of thermal
loading. A comparison of the present results with those available in the literature is carried out to establish the accuracy
of the presented analytical method. The influences of power of functionally graded material, plate thickness, aspect ratio,
thermal loading conditions and boundary conditions on the critical buckling temperature of aluminum/alumina functionally graded
rectangular plates are investigated and discussed in detail. The critical buckling temperatures of thick functionally graded
rectangular plates with various boundary conditions are reported for the first time and can be served as benchmark results
for researchers to validate their numerical and analytical methods in the future. 相似文献
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研究在平面声波斜入射情况下,无穷大双周期加筋的微穿孔薄板结构的振动响应及吸声性能.首先在马大猷和Takahashi微穿孔板声学理论基础上,建立了微穿孔加筋薄板结构振动的半解析模型;然后应用傅里叶变换及空间波数分析方法,将周期加筋微穿孔薄板的振动位移及辐射声压表示为频域内波数的分量迭加形式;最后通过对波数分量进行求解,并利用傅里叶逆变换得到双周期加筋的微穿孔薄板的振动响应及吸声系数表达式.计算结果表明,薄板的弯曲振动在水中对吸声的影响较大,空气中仅对轻质穿孔板的低频吸声效果有一定影响;同时微穿孔率对周期加筋薄板吸声系数的影响明显,通过改变穿孔率和加筋周期等可有效地提高水中微穿孔薄板结构的吸声性能. 相似文献
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An approach is presented to study the nonlinear forced vibration of a stiffened plate. The stiffened plate is divided into one plate and some stiffeners, with the plate considered to be geometrically nonlinear, and the stiffeners taken as geometrically nonlinear Euler beams. Assuming the displacement of the stiffened plate, Lagrange equation and modal superposition method are used to derive the dynamic equilibrium equations of the stiffened plate according to energy of the system. A stiffened plate with four clamped edges subjected to harmonic excitation is studied by means of the method of multiple scales; the first approximation solutions of the double-modal motion of the system are obtained. Numerical examples for different stiffened plates are presented to discuss the steady response of the primary resonance and the amplitude?Cfrequency relationship; and some nonlinear forced vibration characteristics of the stiffened plate are obtained, which are useful for engineering design. 相似文献
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K. Asemi H. Ashrafi M. Shariyat 《Journal of Applied Mechanics and Technical Physics》2016,57(4):690-700
Static and free vibration analyses of plates with circular holes are performed based on the three-dimensional theory of elasticity. The plates are made of a functionally graded material (FGM), and the volume fractions of the constituent materials vary continuously across the plate. The effective properties of the FGM plate are estimated by using the Mori–Tanaka homogenization method. A graded finite element method based on the Rayleigh–Ritz energy formulation is used to solve the problem. Effects of different volume fractions of the materials and hole sizes on the behavior of FGM plates under uniaxial tension are investigated. Natural frequencies of a fully clamped FGM plate with a circular cutout are derived. The results obtained are compared with available experimental data. 相似文献
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Bending of functionally graded piezoelectric rectangular plates 总被引:25,自引:0,他引:25
By introducing two displacement functions as well as two stress functions, two independent state equations with variable coefficients
are derived from the three-dimensional theory equations of piezoelasticity for transverse isotropy. A laminated approximation
is used to transform the state equations to those with constant coefficients in each sub-layer. The bending problem of a functionally
graded rectangular plate is then analyzed based on the state equations. Numerical results are presented and the effect of
material gradient index is discussed.
Supported by the National Natural Sciences Foundation of China (No. 10002016). 相似文献