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压电材料修正后的H-R混合变分原理及其层合板的精确法 总被引:4,自引:1,他引:3
将三维弹性体的Hellinger-Reissner(H-R)混合变分原理引入到具有机-电耦合效应的压电材料静力学问题中,建立了压电材料修正后的H-R混合变分原理,通过变分运算和分部积分得到了压电材料的状态向量方程。给出了四边简支的压电材料层合板静力学状态向量方程的精确求解方法,数值实例的结果证明了方法是正确性的。这里的理论和求解方法同样适应于纯弹性材料板和压电材料板混合的层合板静力学问题的分析。变分原理将有利于压电材料问题相应的半解析法或有限元法的推导。 相似文献
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研究了压电结构中压电片厚度和嵌入深度的优化问题。首先给出了压电层合板的高阶耦合分析模型;然后以不受约束的含压电铺层复合材料板为代表,在压电层厚度方向施加电场时板自由变形,假设板任意微元横截面上内力为零,以其弯(扭)曲曲率最大为优化目标,建立了求解压电片最优厚度和嵌入深度问题的约束优化模型。最后分别以各向同性板中嵌入各项同性压电片和复合材料板中嵌入各向异性压电片为例进行了分析,绘出了目标函数的三维曲面图及等高线图,结果表明压电片的作动效能与其厚度和嵌入位置密切相关,而最优厚度和嵌入位置是由压电片和基体的材料特性决定的。 相似文献
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用压电元件实现复合材料层合板振动控制的数值分析 总被引:9,自引:0,他引:9
采用板的一阶剪切变形理论,对含有压电材料层的复合材料层合板,从机电耦合的变分方程及Hamilton原理出发,建立起求解其动态响应 的有限元方程。同时也给出了压电材料层作为传感元件时的传感方程及作为作动元件时的作动方程。并采用速度反馈控制实现了层合板的主动振动。最后给出了计算实例。 相似文献
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机电耦合载荷下的压电层合板瞬态响应分析 总被引:1,自引:0,他引:1
针对压电层合板在机电耦合激振下的瞬态响应问题, 提出一种高效混合数值计算方法。经过位移场、 电势场在厚度方向的离散, 利用机电耦合理论和哈密顿原理, 推导出结构的运动方程。引入傅里叶变换, 得到波数域内运动控制方程。应用模态分析方法求解波数域内的位移场和电势场, 对结果进行傅里叶逆变换, 得到空间域内的瞬态响应。以PZT-5A/0° PVDF铺层两相材料复合压电层合板为算例, 分析了力、 电耦合线载荷激励下, 位移场和电势场的瞬态响应历程与分布规律, 计算结果给出了该结构的动力学基本特征。该方法结合了有限元法、 傅里叶变换和模态分析法, 计算高频载荷激振下的压电层合板瞬态响应较一般有限元法大幅减少了单元的划分。该方法可推广至分析任意机电载荷下的各类铺层材料压电层合板瞬态响应问题。 相似文献
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基于一阶剪切效应Mindlin板理论,建立了在热载下含分布式压电作动器的复合材料层合板有限元分析模型和控制方程,分别研究了该板在内外表面存在温差的情况下的热变形,以及使用压电作动器对热变形区域进行形状修复的问题;在分析中考虑了压电作动器与复合材料层合板间含有胶接层的影响。由典型算例结果讨论,得到如下结论:1)使用压电作动器可以有效地对复合材料层合板的表面热变形形状进行修复;2)压电作动器的分布位置对修复效果影响很大;3)在电压达到一定数值后,继续增加电压值对修复效果贡献很小。 相似文献
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研究了间隙波在功能梯度压电板和压电半空间结构中的传播性质.功能梯度压电板的材料性能沿x2方向呈指数变化,首先推导了间隙波传播时的解析解,利用界面条件得到了间隙波的频散方程,基于推导的频散方程,结合数值算例分析了功能梯度压电材料的梯度、压电层厚度以及材料性能对间隙波相速度的影响,研究结果对功能梯度压电材料的覆层结构在声波器件中的应用具有重要的参考价值. 相似文献
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For the stiffened composite laminated plates with interfacial imperfections, the problem of static response and sensitivity analysis was investigated in Hamilton system. Firstly, the meshfree formulation of Hamilton canonical equation for the composite laminated plate with interfacial imperfections was deduced by the linear spring-layer and the state-vector equation theory. And then, based on the equation of plates and stiffeners, governing equation of the composite stiffened laminated plate was assembled by using the spring-layer model again to ensure the compatibility of stresses and the discontinuity of displacements at the interface between plate and stiffeners. At last, a three-dimensional hybrid governing equation was developed for the static response analysis and sensitivity analysis. 相似文献
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Based on the higher-order global–local theories, a finite element model is proposed to study the bending behavior of stiffened laminated plates. The proposed model treats the embedded stiffeners as the part of laminated plate, so that the compatibility of displacements and stresses between the plate and the stiffeners can be automatically satisfied. Distributions of the displacements and stresses through the thickness of laminates were also given for the first time, which can serve as references for future investigations as such information is lacking in the published literature. In addition, the impact of the stiffeners on the bending response of the stiffened laminated plates is also studied in terms of the quantity, the collocation and the geometry of stiffeners. Numerical results showed that the higher-order global–local theories are more suitable for predicting the bending response of thick and moderately thick stiffened laminated plates compared to the first order theory commonly used in engineering. By varying the quantity, the collocation and the geometry of stiffeners, the stiffness and the strength of stiffened laminated plates can be remarkably improved. 相似文献
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Chung-Li Liao Chu-Ren Cheng 《International journal for numerical methods in engineering》1994,37(24):4167-4183
The dynamic stability of laminated composite stiffened or non-stiffened plates and shells due to periodic in-plane forces at boundaries is investigated in this paper. A three-dimensional (3-D) degenerated shell element and a 3-D degenerated curved beam element are used to model plates/shells and stiffeners, respectively. The characteristic equations to find the natural frequencies, buckling loads and their corresponding mode shapes are obtained from the finite element equation of motion. Then, the method of Hill's infinite determinants or the method of multiple scales is applied to analyse the dynamic instability regions. Numerical results are presented to demonstrate the effects of various parameters, such as skew angle, lamination scheme, stiffened scheme, in-plane force type and curvature of cylindrical shell, on the dynamic stability of stiffened and non-stiffened plates and shells subjected to in-plane pulsating forces at boundaries. 相似文献
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A very simple displacement-based hexahedral 32-node element (denoted as DPH32), with over-integration in the thickness direction, is developed in this paper for static and dynamic analyses of laminated composite plates and shells. In contrast to higher-order or layer-wise higher-order plate and shell theories which are widely popularized in the current literature, the proposed method does not develop specific theories of plates and shells with postulated kinematic assumptions, but simply uses the theory of 3-D solid mechanics and the widely-available solid elements. Over-integration is used to evaluate the element stiffness matrices of laminated structures with an arbitrary number of laminae, while only one element is used in the thickness direction without increasing the number of degrees of freedom. A stress-recovery approach is used to compute the distribution of transverse stresses by considering the equations of 3D elasticity. Comprehensive numerical results are presented for static, free vibration, and transient analyses of different laminated plates and shells, which agree well with existing solutions in the published literature, or solutions of very-expensive 3D models by commercial FEM codes. It is clearly shown that the proposed methodology can accurately and efficiently predict the structural and dynamical behavior of laminated composite plates and shells in a very simple and cost-effective manner. 相似文献
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A new stiffened plate element for stability analysis of laminated stiffened plates has been presented. The basic plate element is a combination of Allman's plane stress triangular element and a Discrete Kirchhoff–Mindlin plate bending element. The element includes transverse shear effects. The model accommodates any number of arbitrarily oriented stiffeners within the plate element and eliminates constraints on the mesh division of the plate. The element has no problem associated with shear locking – a phenomenon usually encountered in isoparametric elements. The stability analysis of laminated stiffened plates has been carried out under different loading conditions with the present element. 相似文献
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复合材料大变形任意加筋板单元 总被引:7,自引:2,他引:5
本文构造了用于复合材料偏心加筋板状结构大变形分析的任意加筋板单元。在此模型中,肋骨可放置在板单元内任意位置和任意方向,因而在网格划分时,可不必顾及肋骨的具体位置。在板和肋骨的基本方程中,引用Von-Karman大变形理论计及大变形的影响,按照 Mindlin-Reissoner一阶剪切变形理论考虑横向剪切变形。任意加筋板单元具有和常规板单元相同的自由度。数值计算表明本文的有限元模型具有很高的精度。 相似文献
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以Hamilton正则方程的半解析法为基础,为一类双壳结构的振动特性提出了一种新的数学模型。基本步骤:(1)独立地建立内外壳和连接筋的线性方程组;(2)考虑到内外壳和连接筋的界面上的应力和位移的连续性,联立内外壳和连接筋的方程,从而得到全结构的方程组。主要优点是:采用了同一种Hamiltonian等参元离散壳和连接筋,结构的转动惯性、剪切变形等因素都得到了考虑,而且不限制壳的厚度和筋的高度;该方法象一般的有限元法一样适应复杂的边界条件和由多种材料构成的结构。本文的方法可推广用来研究加筋复合材料或加筋压电材料层合壳及相应的双壳结构的动力学问题。 相似文献